ngram black hole scalar field conformal field theory conformal field quantum field theory effective action boundary condition quantum field cosmological constant general relativity modulus space low energy central charge gauge theory magnetic field finite temperature anti-de sitter gauge field angular momentum first order open string heterotic string exact solution quantum gravity second order n = supersymmetric gauge theory dimensional reduction special case strong coupling effective field theory super yang-mills critical point black hole solution effective theory free energy fixed point standard model differential equation effective field effective potential supersymmetric gauge scalar field theory supersymmetric yang-mills other hand supersymmetric yang-mills theory extra dimension higher spin electromagnetic field higher order superconformal field theory anomalous dimension closed string previous work massive gravity \cal n flat space super yang-mills theory gravitational field large class ads/cft correspondence higher dimension dark energy global symmetry free field superconformal field critical exponent bosonic string entanglement entropy high energy supersymmetric theory classical solution explicit expression space-time dimension hilbert space abelian gauge black hole entropy gravitational wave non-abelian gauge electric field conformal symmetry scalar potential new class recent work initial condition cosmological model kinetic term two-point function spacetime dimension explicit example n limit minimal model electric charge high temperature chiral symmetry infinite number critical value conformal invariance energy-momentum tensor late time anti-de sitter space arbitrary dimension n=4 sym einstein gravity nonlinear sigma model dark matter cosmic string arbitrary number recent result minkowski space green function spatial dimension weak coupling hole solution black hole horizon heterotic string theory tree level previous result upper bound auxiliary field integrable system particular case boundary state complex structure early universe irreducible representation calabi-yau manifold critical temperature large number first law quantum fluctuation antisymmetric tensor topological string low temperature topological field theory gauge symmetry numerical result harmonic oscillator quantum correction such theory important role dirac equation explicit form matrix model general solution nonlinear sigma magnetic flux yang-mills theory einstein equation noncommutative geometry chemical potential spontaneous symmetry new type magnetic charge previous paper cosmological solution non-linear sigma model topological charge general form fundamental representation feynman diagram analytic continuation gauge group large n new solution integrable model black hole background topological field perturbative expansion such model supersymmetric extension present paper internal space exact result general class non-abelian gauge theory lower bound physical state finite number supersymmetric quantum gravitational theory cosmological perturbation general case new result quasinormal mode physical interpretation black string external field first time gauge invariance short distance spontaneous breaking conformal anomaly dual description near horizon holographic model dual field spontaneous symmetry breaking dynamical system superconformal algebra sine-gordon model lorentz invariance dual field theory riemann surface explicit formula wide class local operator closed form flat spacetime large distance noncommutative space free fermion black hole thermodynamics gauge transformation stress-energy tensor integral representation non-linear sigma light-cone gauge cosmic microwave background current algebra cosmological constant problem recent development complete set holographic entanglement entropy explicit construction three-point function supersymmetric quantum mechanic several example simple model lowest order asymptotic symmetry classical level derivative expansion free parameter light cone symmetric solution scalar curvature condensed matter fundamental string black brane scale factor big bang discrete symmetry canonical quantization inflationary model dual theory classical field boundary term asymptotic behavior naked singularity dimensional regularization n =2 radiative correction higgs field s * scalar perturbation classical limit latter case first step new method supersymmetric field theory chiral fermion symmetric space linear combination four-point function conformal transformation new approach supersymmetric solution such solution finite size explicit solution numerical simulation excited state noncommutative gauge theory abelian gauge theory curved space imaginary part boundary theory topological defect holographic entanglement different type conformal dimension general formula quantum mechanic antisymmetric tensor field derivative term conformal block initial state cosmic microwave gauged supergravity bekenstein-hawking entropy effective lagrangian fermionic field explicit calculation crucial role eleven-dimensional supergravity superconformal symmetry static solution main result lorentz symmetry asymptotic expansion sufficient condition large scale simple example one-loop correction detailed analysis constant curvature infinite set n =1 earlier work saddle point chiral model primary field noncommutative gauge cosmological evolution higher spin field relativistic quantum calabi-yau threefolds recent progress supersymmetric field chiral anomaly perfect fluid good agreement chiral symmetry breaking linear sigma model abelian higgs model canonical transformation hamiltonian formulation statistical mechanic abelian higgs possible application certain class present work physical quantity first class superconformal theory supersymmetric model modified gravity double field theory euclidean space noncommutative field theory general result same time hamiltonian formalism massive particle second class generalized uncertainty principle black ring n=2 supergravity wide range central extension analytic solution critical behavior second part noncommutative field null energy condition analytic expression magnetic monopoles free theory curved spacetime numerical solution gravitational collapse general method strong coupling limit abelian gauge field algebraic structure exact expression new feature bosonic field spinor field quantum effect unitary representation matrix element local gauge gravitational coupling black branes finite volume quantum level supersymmetric su near-horizon geometry harmonic superspace low energy limit general property dual cft one-parameter family higher derivative one-to-one correspondence gravitational interaction low energy effective action conserved quantity classical equation second law conformal theory integral equation one-loop level dual gauge thermodynamic property modular invariance special attention gauge field theory ads_5 x flow equation thermodynamic bethe ansatz exact renormalization group gauge invariant invariant action recent paper necessary condition holographic dual ads_5 x s^5 general expression total energy classical action physical property gross-neveu model holographic description dimensional theory generalized uncertainty topological quantum anomaly cancellation specific example spectral curve large volume mechanical system n > initial data shear viscosity linear sigma yang-baxter equation klein-gordon equation einstein-hilbert action spectral index n =4 special relativity null energy relativistic particle topological phase various dimension scalar particle dual gauge theory perfect agreement positive energy fractional quantum hall classical theory massive field recent proposal double field ten dimension topological invariant holographic renormalization conserved charge accelerated expansion marginal deformation specific heat analytical solution consistent truncation scalar-tensor theory internal symmetry unified theory negative energy concrete example third order new model s * * topological quantum field particular attention elliptic genus arbitrary spin general theory numerical method hidden symmetry higher spin theory bosonic string theory near horizon geometry small value giant graviton de sitter loop quantum physical system variational principle previous study symplectic structure tachyon condensation conical singularity non-minimal coupling thermodynamic bethe classical string local supersymmetry n=4 sym theory projective space scalar theory critical dimension functional renormalization group differential geometry gauss-bonnet term scale invariance composite operator special class functional integral magnetic moment low-energy limit massive vector minimal surface higher curvature infrared divergence numerical study physical degree type iib first order phase elementary particle free particle large value quantum theory interesting feature mean field hubble parameter gravitational anomaly certain condition two-dimensional quantum numerical calculation first part thermodynamic quantity similar result curved background thermal equilibrium extrinsic curvature anti-de sitter spacetime n=2 supersymmetry yukawa coupling free field theory gravitational action chiral superfields magnetic monopole differential form second order phase strong evidence derivative correction various aspect boundary field same result chiral primary quantum information cft correspondence friedmann equation semiclassical approximation kaluza-klein theory flat background schwinger-dyson equation arbitrary function canonical ensemble minimal length natural way superconformal index linear perturbation local field metric perturbation chiral field different way inflationary universe exact renormalization type ii chiral ring non-perturbative effect n=1 supergravity one-loop order inflationary scenario perturbative calculation dynamical symmetry local symmetry supersymmetric vacuum infinite family early time fermi surface first principle apparent horizon topological string theory soliton solution nonabelian gauge finite density first example fractional quantum no-go theorem different value infinite tower chiral gauge thermodynamic limit holographic principle geometric interpretation final state observational data lattice gauge theory general framework gravitational background wess-zumino term covariant derivative holographic superconductors dynamical variable large-n limit same way seiberg-witten map low energy effective theory two-point correlation function sigma model odd dimension iib supergravity flat direction massive scalar one-point function tensor product local lorentz first class constraint classical field theory second class constraint lie algebra phase transition numerical analysis slow-roll inflation flat connection warp factor flat space-time quantum number gauss-bonnet gravity free massless loop quantum gravity hypergeometric function lagrangian formulation cosmic censorship logarithmic correction dimensional supergravity such system reduced density matrix higher genus lagrangian density brst symmetry supersymmetric qcd massive mode modular transformation long distance d = explicit result massive graviton square root finite energy functional renormalization conformal group large mass next-to-leading order simple form dirac fermion black hole evaporation effective string false vacuum four-dimensional theory same form quantum state proper time invariant theory cosmological term new family brief review topological term inner product black hole physic complex structure modulus fourth order local quantum earlier result modular form conformal gauge black hole geometry metric tensor linear dilaton calabi-yau threefold cosmological horizon electric-magnetic duality planck scale general structure flux compactifications holographic duality gravitational perturbation explicit computation mutual information natural generalization broken phase black hole information holographic duals special geometry cosmic acceleration numerical evidence lattice gauge wheeler-dewitt equation fundamental matter black brane solution infinite series twisted sector arbitrary value planck mass kinetic energy black hole formation long time liouville field complex plane different approach solvable model scalar hair maximal supergravity asymptotic freedom wess-zumino-witten model fine tuning extended phase space toda field theory thermal state spectral function chiral multiplets highest weight extremal limit scalar field model quantum phase transition riemannian manifold n=8 supergravity small perturbation spatial infinity simple lie pure yang-mills simplest case non-abelian gauge field higgs branch d dimension compact dimension penrose limit conserved current conformal bootstrap detailed study black hole spacetimes open string field relativistic quantum field general formalism general gauge mechanical model further evidence derivative gravity physical meaning holographic superconductor collective coordinate systematic study extended object quantum phase higher order correction particular class asymptotic behaviour pp-wave background dimensional quantum geometrical interpretation chiral algebra non-relativistic limit weak field chiral matter wzw model small scale flat spacetimes two-point correlation long range free boson born-infeld action black hole mass general coordinate particular choice universality class holographic theory conformal supergravity simple way cosmological singularity bosonic sector n=1 supersymmetry one-loop amplitude dynamical triangulation broken symmetry modulus stabilization higher spin gauge invariant partition function modular invariant new example particular example dimensional space integrable structure special value topological insulator dynamical exponent full set possible implication spherical symmetry ward identity potential term scalar mode chiral gauge theory general feature lorentz violation toda field spectral parameter dimensional gauge theory effective coupling analytical result reduced density nonlinear realization positive definite cosmological background gravitational field equation new way arbitrary gauge quantum system dimensional gravity single field initial value open string theory two-dimensional quantum gravity chiral primary operator dirac field n=4 super-yang-mills brst charge hamiltonian system loop correction landau gauge f-theory compactifications recent study angular velocity effective description real part simple expression coherent state euclidean action null infinity brst cohomology dimensional gauge hamiltonian approach direct product seiberg-witten curve asymptotic safety low frequency other word conformal algebra nonlinear electrodynamics systematic way simple case noncommutative spacetime lax pair critical phenomenon n=2 gauge theory supersymmetric sigma model n=2 theory unruh effect non-commutative geometry analytical expression asymptotic region exponential potential central role hooft coupling special emphasis conformal weight eternal inflation hamiltonian reduction known result integral approach conformal gravity black hole spacetime double scaling limit particular emphasis gravitational effect conformal factor finite value theory side broad class minimal coupling effective mass curved space-time infrared limit massive fermion different method charged particle hamiltonian constraint complete agreement rotational symmetry spatial curvature topological soliton kaluza-klein reduction wess-zumino model ads_5 \times mass term covariant gauge bps solution inflationary cosmology grand unification simplest example ads/cft duality complex scalar cosmological scenario pure gauge extended phase theoretical physic orbifold singularity wilson line additional term slow roll young diagram topological order functional equation scalar manifold hermitian matrix scalar mass non-critical string new set landau level minkowski spacetime hagedorn temperature hamiltonian analysis nonabelian gauge theory minimal supergravity spectral density effective equation chern-simons term radial coordinate massless field higher spin gravity integrable spin chain dark energy model spectral flow functional form covariant formulation supersymmetric case previous analysis long wavelength massive type iia gauge group su compact space novel feature massive gauge randall-sundrum model excellent agreement stochastic quantization d > physical consequence tensor-to-scalar ratio potential energy space-time supersymmetry quasi-normal mode holomorphic function witten index cubic interaction integrable field theory massive gravity theory parallel plate appropriate choice cosmological implication ultraviolet divergence differential operator semiclassical limit unbroken supersymmetry tachyon field dimensional spacetime observational constraint derivative coupling back reaction experimental data integral formulation near-horizon limit dynamical equation homogeneous space constrained system basic property physical implication seiberg-witten theory calabi-yau compactifications spontaneous breakdown monopole solution random matrix quantum cosmology chiral superfield horava-lifshitz gravity two-loop order classical dynamic noncommutative parameter classical mechanic first-order phase transition invariant partition scalar product higher rank spinor equation complete classification fifth dimension many case seiberg duality other field gravitational constant nonminimal coupling possible extension new kind strong interaction ansatz equation path integral global structure bps state s-matrix element geometric structure leading term external source certain case n=4 super-yang-mills theory condensed matter physic strong constraint thermal fluctuation fermionic string dual string invariant field general procedure noncommutative quantum tree amplitude landau-ginzburg model type iia gravitational radiation string field theory boundary field theory new formulation calabi-yau space wilson loop green-schwarz superstring dual pair specific value n=2 gauge non-perturbative correction various type higher loop internal manifold scalar quantum field analytic result odinger equation same order global supersymmetry dynamical mass sym theory heterotic superstring mathematical structure generic value primary operator direct sum abelian vector unified description pure yang-mills theory scalar field potential first case eleven dimension small mass supersymmetric version such state open problem finite time non-fermi liquid double scaling \cal o spatial direction certain limit loop order induced gravity scalar quantum even dimension exact formula n expansion dimensional field physical application uv completion key ingredient scalar matter new insight collective field boundary cft complete intersection dimensional field theory fayet-iliopoulos term key role supersymmetric generalization toy model unitary gauge full quantum topological gravity schwarzschild solution various property one-loop contribution general covariance einstein-maxwell theory specific case total number relativistic field topological sector specific model integrable spin condensed matter system anti-de sitter black hole heavy quark affine toda abjm theory physical observables main feature regular solution topological property kaluza-klein mode perturbative string two-dimensional model inflationary phase original theory new term covariant quantization mixed state geodesic motion free field realization strong coupling regime loop equation fermionic degree topological mass real time quark-gluon plasma null geodesic functional determinant previous calculation commutative limit relevant operator chiral condensate partial wave second derivative wall solution second case pure gravity tree-level amplitude form factor noncommutative plane n c broken supersymmetry infinite volume string field lagrangian description topological theory large spin massive vector field supersymmetric sigma new form such background stationary solution general dimension symmetric tensor integrable field dual model boundary value logarithmic term holographic dark energy relativistic field theory canonical commutation relation compact manifold translational invariance axial gauge sine-gordon theory quantum geometry fundamental theory thermodynamical property orthogonal polynomial general condition liouville field theory n gauge theory local quantum field anti-de sitter space-time small number general argument scalar operator 4-point function supersymmetric u solar system analytic property possible way different phase large radius gauged supergravities chiral operator modular group canonical formalism brst quantization susy gauge theory generic feature discrete spectrum on-shell action affine lie lorentzian signature certain value other case harmonic function supersymmetric action orientifold plane spatial coordinate natural interpretation d=11 supergravity bosonic part two-dimensional gravity gravitational chern-simons dimensional case axial anomaly spectral problem wave function warped product small fluctuation elliptic curve fine structure hep-th ] general background dimensional space-time uv divergence spatial section four-point correlation function second-order phase transition simple lie algebra long string dual formulation feynman graph new perspective new theory nonperturbative effect hamiltonian structure self-dual yang-mills gravitational instantons little string theory quartic interaction theoretical model first-order phase weak gravity vortex solution closed bosonic bound state anomaly equation general construction constant background four-dimensional gauge three-point correlation function four-dimensional gauge theory toric variety one-loop approximation lorentz transformation euclidean time electric flux universal form brans-dicke theory massive type one-loop quantum world-volume theory gravitational potential n gauge hyperbolic space bose-einstein condensate gravitational chern-simons term scalar model different gauge recent year present result physical theory spectral action perturbative correction certain range particular value lower dimension minkowski space-time perturbative quantum dyson-schwinger equation systematic method differential calculus complex geometry new mechanism natural extension discrete torsion yang-mills field supersymmetric localization \mathcal n spin-2 field new phase dimensional model asymptotic symmetry algebra large scale structure 3-point function loop expansion 2-point function wick rotation wormhole solution finite n arbitrary background former case present evidence superconformal chern-simons spectral triple analytic structure gauge boson singular point supersymmetric standard model free field representation bosonic string field such field hamilton-jacobi equation powerful tool higgs mass abelian chern-simons exact agreement dual geometry little string brst invariance quasinormal frequency external momentum self-adjoint extension other model 3-form flux possible generalization special choice holographic rg uv/ir mixing dynamical supersymmetry massive state massive thirring model reduced phase space strong coupling expansion single trace other approach numerical computation massless particle integrable deformation supersymmetric background dual gravity more detail orbifold model extended supersymmetry recent conjecture new physic general analysis classical gravity elliptic function better understanding non-renormalization theorem closed string field different choice high frequency low-energy theory metastable vacuum massless fermion functional relation perturbative approach realistic model exact form effective superpotential such operator inverse power space-time symmetry euclidean quantum four-point correlation riemannian geometry quantum deformation classical background average action spontaneous supersymmetry classical gauge chaotic inflation infinite class hawking temperature open question covariant form conformal perturbation theory vacuum expectation value normal mode threshold correction born-infeld theory canonical commutation quantum entanglement equal footing suitable choice gravitational sector upper limit spacetime geometry vacuum fluctuation finite radius 11-dimensional supergravity monte carlo two-dimensional field theory circular wilson loop high energy physic closed bosonic string einstein field equation exceptional field theory local gauge symmetry finite size effect scalar degree two-dimensional theory noncommutative torus remarkable property fractional branes aharonov-bohm effect brst transformation chiral boson appropriate limit canonical structure low energy dynamic light cone gauge closed string theory invariant formulation noncommutative u big crunch off-shell formulation asymptotic form compact object full theory chern-simons-matter theory arbitrary order negative value extra term yangian symmetry modified version supersymmetric string symmetric phase euclidean path massive theory heterotic string compactifications weak gravity conjecture higher order term affine lie algebra integral quantization continuous symmetry circular orbit adm mass simple proof integrable hierarchy possible solution arbitrary mass spacetime supersymmetry effective gauge critical coupling derivative theory cardy formula alternative approach massive iia integral formalism massive dirac soft supersymmetry fundamental field translational symmetry d-brane configuration newtonian potential simple formula internal structure free scalar conformal perturbation perturbative analysis positive integer quantum version liouville theory special point phase space simple method chern class arbitrary gauge group random matrix theory anti-de sitter spacetimes topological string amplitude low energy theory linear equation quadratic order big rip dynamical field several aspect local minimum nonrelativistic limit static potential modular property symplectic form interesting property topological vertex kalb-ramond field effective lagrangians holographic qcd gauge coupling local observables pedagogical introduction holographic renormalization group black hole microstates invariant field theory weak energy condition one-loop quantum correction simple derivation final result open superstring heavy ion logarithmic divergence three-point correlation susy gauge effective supergravity open bosonic various example physical field light front massive thirring poisson bracket relative entropy nonzero temperature possible relation detailed discussion holographic dark diverse dimension topological structure gromov-witten invariant null vector standard model gauge effective model sasaki-einstein manifold n-point function current density super-yang-mills theory large charge new formula conformal matter quadratic action metric fluctuation asymptotic value integral formula arbitrary genus mathematical physic recent observation continuous spectrum essential role dynamical degree toroidal compactification geodesic equation particular interest finite temperature and density first order formalism general coordinate transformation topological gauge non-trivial topology closed expression negative curvature exceptional group perturbative solution finite part minimal area careful analysis higgs phase ads_4 x non-zero temperature geometric transition conformal boundary one-matrix model symmetric representation second-order phase explicit realization certain type dual supergravity algebraic approach dynkin diagram marginal stability new technique non-geometric flux gravitational correction ava-lifshitz gravity basic idea massive case thermal field noncommutative theory single particle constant term fundamental group two-dimensional field internal energy physical spectrum possible connection time-dependent solution negative tension marginal operator noncritical string linear response heterotic m-theory topological string partition non-abelian gauge group euclidean quantum gravity non-commutative gauge theory global symmetry group superconformal chern-simons theory low energy effective field qualitative feature new light higher-spin gauge horizon area global u einstein-maxwell-dilaton theory scalar qed spin connection supersymmetric configuration black-hole solution soft theorem massive spin unitary matrix geometrical structure integral method singular vector algebraic curve brief discussion holographic correspondence cosmic censorship conjecture thermo field dynamic nekrasov partition function thermal field theory high temperature limit finite size correction classical field equation thermodynamical quantity einstein-gauss-bonnet gravity ward-takahashi identity electromagnetic interaction sinh-gordon model symmetric product transverse space supersymmetric ad effective interaction chiral multiplet precise agreement noncommutative yang-mills instanton solution boundary action space-time geometry imaginary time quadratic term gauss-bonnet coupling other theory antisymmetric representation big bang singularity holographic rg flow quantum gravity effect heavy ion collision massive gauge theory near horizon limit higher-spin field noncommutative space-time other method supersymmetric chern-simons flat solution critical behaviour universal property spectral dimension large family correlation function brownian motion tadpole cancellation general model stationary point unstable mode conformal quantum large gauge sachdev-ye-kitaev model standard quantum free quantum majorana fermion geometric approach heterotic compactifications arbitrary representation bosonic case fermionic sector abelian case effective hamiltonian standard result scale invariant supersymmetric standard earlier paper internal degree finite distance scalar sector reduced phase massive string one-loop calculation low-energy dynamic -dimensional spacetime interesting case systematic approach weak interaction three-dimensional gravity important feature five-dimensional supergravity limiting case langevin equation weak coupling limit topological gauge theory one-loop partition function central charge c topological sigma model weak coupling regime nonlinear equation phenomenological implication physical parameter extremal surface toric geometry particular model linear order uv cutoff holographic complexity near-horizon region solitonic solution steady state higher-derivative term circular wilson analytic function boundary stress tensor noncommutative quantum mechanic compact lie group effective string theory black hole interior fermionic zero mode short note linear potential new representation large time specific form global charge canonical variable new version four-point amplitude high spin tachyonic instability extended version finite set generalized geometry conformal space corresponding field massive spin-2 schwarzschild-de sitter key feature eigenvalue distribution lagrangian formalism phenomenological model systematic analysis non-commutative gauge different kind algebraic geometry four-dimensional space-time cubic vertex approximate solution graceful exit n f new symmetry wave equation holomorphic vector bundle quantum information theory entangled state different number second quantization integral measure boundary operator cosmological scale first one symplectic manifold true vacuum classical vacuum time-dependent background hooft limit vacuum expectation thermal bath ale space ads_3 x dynamical evolution critical theory general gauge theory relativistic wave equation flat space limit chiral schwinger model affine toda field two-dimensional dilaton gravity initial value problem asymptotic symmetry group