118975283
Chiral 2D “strange metals” from N=4$$ \mathcal{N}=4 $$ SYM
A bstractFamiliar field theories may contain closed subsectors made out of only fermions, which can be used to explore new and unusual phases of matter in lower dimensions. We focus on the fermionic su(1, 1) sector in N=4$$ \mathcal{N}=4 $$ SYM and on its ground states, which are Fermi surface states/operators. By computing their spectrum to order (gYM2N)2, we argue that fluctuations around this Fermi surface, within the sector and in the limit kF → ∞, are governed by a chiral 1+1 dimensional sector of the “strange metal” coset SU(N )N ⊗ SU(N )N /SU(N )2N . On the gravity side, the conjectured dual configuration is an S = 0 degeneration of a rotating black hole. On general grounds we expect that the near horizon excitations of (S = 0, Ω = 1, J → ∞) degenerations of black holes will be governed by a chiral sector of a 1+1 CFT.
126363487
The Large N limit of superconformal field theories and supergravity
We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds. This is shown bytaking some branes in the full M/string theory and thentaking a low-energy limit where the field theory on thebrane decouples from the bulk. We observe that, in this limit, we can still trust thenear-horizon geometry for large N. The enhancedsupersymmetries of the near-horizon geometry correspondto the extra supersymmetry generators present in thesuperconformal group (as opposed to just the super-Poincaregroup). The 't Hooft limit of 3 + 1 N = 4 super-Yang–Mills at the conformal pointis shown to contain strings: they are IIB strings. Weconjecture that compactifications of M/string theory on various anti-de Sitterspacetimes is dual to various conformal field theories.This leads to a new proposal for a definition ofM-theory which could be extended to include fivenoncompact dimensions.
10882387
Anti-de Sitter space and holography
Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of ${\cal N}=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the ${\cal N}=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.
3265656
Strange Metals in One Spatial Dimension
We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of massive Dirac fermions transforming in the adjoint representation of the gauge group. The only global symmetry of this theory is a U(1) associated with the conserved Dirac fermion number, and we study the theory at variable, nonzero densities. The high density limit is characterized by a deconfined Fermi surface state with Fermi wave vector equal to that of free gauge-charged fermions. Its low energy fluctuations are described by a coset conformal field theory with central charge c=(N2-1)/3 and an emergent N=(2,2) supersymmetry: the U(1) fermion number symmetry becomes an R-symmetry. We determine the exact scaling dimensions of the operators associated with Friedel oscillations and pairing correlations. For N>2, we find that the symmetries allow relevant perturbations to this state. We discuss aspects of the N→∞ limit, and its possible dual description in AdS3 involving string theory or higher-spin gauge theory. We also discuss the low density limit of the theory by computing the low lying bound state spectrum of the large N gauge theory numerically at zero density, using discretized light cone quantization.
15583645
Weakly Renormalized Near 1/16 SUSY Fermi Liquid Operators in N = 4 SYM
We discuss a class of Fermi Liquid Operators in N = 4 SYM. We show that these operators are eigenstates of the full quantum dilatation operator. We compute their 1 and 2 loop anomalous dimensions, and show that, similar to Fermi liquids in condensed matter systems, these corrections are suppressed by an arbitrarily small parameter, which is the equivalent of one over the Fermi energy. These operators are, at the classical level, descendants of 1/16 BPS operators, with some scaling properties similar to those of the 1/16 Black Holes in AdS_5.
118641685
Degenerate rotating black holes, chiral CFTs and Fermi surfaces I — Analytic results for quasinormal modes
A bstractIn this work we discuss charged rotating black holes in AdS5 × S5 that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface operators in a subsector of $ \mathcal{N} = 4 $ SYM. We add a massless uncharged scalar to the five dimensional supergravity theory, such that it still forms a consistent truncation of the type IIB ten dimensional supergravity and analyze its quasinormal modes. Separating the equation of motion to a radial and angular part, we proceed to solve the radial equation using a matched asymptotic expansion method applied to Heun’s equation with two nearby singularities. We use the continued fraction method for the angular Heun equation and obtain numerical results for the quasinormal modes. In the case of the near-supersymmetric black hole we present some analytic results for the decay rates of the scalar perturbations. The spectrum of quasinormal modes obtained is similar to that of a chiral 1 + 1 CFT, which is consistent with the conjectured field-theoretic dual. In addition, some of the modes can be found analytically.
11624487
New rotating non-extremal black holes in D=5 maximal gauged supergravity
Abstract We obtain new non-extremal rotating black hole solutions in maximal five-dimensional gauged supergravity. They are characterised by five parameters, associated with the mass, the two angular momenta, and two independently-specifiable charge parameters. Two of the three charges associated with the U ( 1 ) 3 Cartan subgroup of the SO ( 6 ) gauge group are equal, whilst the third can be independently specified. These new solutions generalise all the previously-known non-extremal rotating solutions in five-dimensional gauged supergravity with independent angular momenta. They describe regular black holes, provided the parameters lie in appropriate ranges so that naked singularities and closed-timelike curves (CTCs) are avoided. We also construct the BPS limit, and show that regular supersymmetric black holes or topological solitons arise if the parameters are further restricted in an appropriate manner.
125210680
Five-Dimensional Gauged Supergravity Black Holes with Independent Rotation Parameters
We construct new non-extremal rotating black hole solutions in SO(6) gauged fivedimensional supergravity. Our solutions are the first such examples in which the two rotation parameters are independently specifiable, rather than being set equal. The black holes carry charges for all three of the gauge fields in the U(1) 3 subgroup of SO(6), albeit with only one independent charge parameter. We discuss the BPS limits, showing in particular that these include the first examples of regular supersymmetric black holes with independent angular momenta in gauged supergravity. We also find non-singular BPS solitons. Finally, we obtain another independent class of new rotating non-extremal black hole solutions with just one non-vanishing rotation parameter, and one non-vanishing charge.
14628213
AdS dual of the critical O(N) vector model
Abstract We suggest a general relation between theories of infinite number of higher-spin massless gauge fields in AdS d +1 and large N conformal theories in d dimensions containing N -component vector fields. In particular, we propose that the singlet sector of the well-known critical 3-d O ( N ) model with the ( φ a φ a ) 2 interaction is dual, in the large N limit, to the minimal bosonic theory in AdS 4 containing massless gauge fields of even spin.
118959569
W symmetry in conformal field theory
Abstract We review various aspects of W algebra symmetry in two-dimensional conformal field theory and string theory. We pay particular attention to the construction of W algebras through the quantum Drinfeld-Sokolov reduction and through the coset construction.
15125974
An AdS_3 Dual for Minimal Model CFTs
We propose a duality between the 2d W{sub N} minimal models in the large N't Hooft limit, and a family of higher spin theories on AdS{sub 3}. The 2d conformal field theories (CFTs) can be described as Wess-Zumino-Witten coset models, and include, for N=2, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the renormalization group flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an AdS{sub 4} dual for the singlet sector of large N vector models.
118634257
Minimal model holography
We review the duality relating 2D WN minimal model conformal field theories, in a large-N ’t Hooft like limit, to higher spin gravitational theories on AdS3. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.
13949235
= 4 SYM to two loops: compact expressions for the non-compact symmetry algebra of the (1,1|2) sector
We begin a study of higher-loop corrections to the dilatation generator of = 4 SYM in non-compact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higher-loop corrections. Remarkably, we find a short and simple expression for the two-loop dilatation generator. Our solution for the non-compact (1,1|2) sector consists of nested commutators of four (g1) generators and one simple auxiliary generator. Moreover, the solution does not require the planar limit; we conjecture that it is valid for any gauge group. To obtain the two-loop dilatation generator, we find the complete (g3) symmetry algebra for this sector, which is also given by concise expressions. We check our solution using published results of direct field theory calculations. By applying the expression for the two-loop dilatation generator to compute selected anomalous dimensions and the bosonic (2) sector internal S-matrix, we confirm recent conjectures of the higher-loop Bethe ansatz of hep-th/0412188.
15838211
On symmetry enhancement in the (1, 1|2) sector of = 4 SYM
Strong evidence indicates that the spectrum of planar anomalous dimensions of = 4 super Yang-Mills theory is given asymptotically by Bethe equations. A curious observation is that the Bethe equations for the (1, 1|2) subsector lead to very large degeneracies of 2M multiplets, which apparently do not follow from conventional integrable structures. In this article, we explain such degeneracies by constructing suitable conserved nonlocal generators acting on the spin chain. We propose that they generate a subalgebra of the loop algebra for the (2) automorphism of (1, 1|2). Then the degenerate multiplets of size 2M transform in irreducible tensor products of M two-dimensional evaluation representations of the loop algebra.
118488341
Horizons, holography and condensed matter
The holographic correspondence creates an interface between classical gravitational physics and the dynamics of strongly interacting quantum field theories. This chapter will relate the physics of charged, asymptotically Anti-de Sitter spacetimes to the phenomenology of low temperature critical phases of condensed matter. Common essential features will characterise both the gravitational and field theoretic systems. Firstly, an emergent scaling symmetry at the lowest energy scales appears as an emergent isometry in the interior, `near horizon' regime of the spacetime. Secondly, the field theoretic distinction between fractionalized and mesonic phases appears as the presence or absence of a charge-carrying horizon in the spacetime. A perspective grounded in these two characteristics allows a unified presentation of `holographic superconductors', `electron stars' and `charged dilatonic spacetimes'.
233207
Holographic non-Fermi-liquid fixed points
Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this ‘holographic duality’, various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS2) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.
55231045
Infinite Chiral Symmetry in Four Dimensions
We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four-dimensional theory. Infinite chiral symmetry has far-reaching consequences for the spectral data, correlation functions, and central charges of any four-dimensional theory with $${\mathcal{N}=2}$$N=2 superconformal symmetry.
118480845
EVH black holes, AdS3 throats and EVH/CFT proposal
Within class of generic black holes there are extremal black holes (with vanishing Hawking temperature T) and vanishing horizon area Ah, but with finite Ah/T ratio, the Extremal Vanishing Horizon (EVH) black holes. We study the near horizon limit of a four dimensional EVH black hole solution to a generic (gauged) Einstein-Maxwell dilaton theory and show that in the near horizon limit they develop a throat which is a pinching orbifold limit of AdS3. This is an extension of the well known result for extremal black holes the near horizon limit of which contains an AdS2 throat. We show that in the near EVH near horizon limit the pinching AdS3 factor turns to a pinching BTZ black hole and that this near horizon limit is indeed a decoupling limit. We argue that the pinching AdS3 or BTZ orbifold is resolved if the near horizon limit is accompanied by taking the 4d Newton constant G4 to zero such that the Bekenstein-Hawking entropy S = Ah/(4G4) remains finite. We propose that in this limit the near horizon EVH black hole is dual to a 2d CFT. We provide pieces of evidence in support of the EVH/CFT correspondence and comment on its connection to the Kerr/CFT proposal and speculation show the EVH/CFT maybe used to study generic e.g. Schwarzchild-type black holes.
15010088
Kerr/CFT Correspondence
Quantum gravity in the region very near the horizon of an extreme Kerr black hole (whose angular momentum and mass are related by J=GM{sup 2}) is considered. It is shown that consistent boundary conditions exist, for which the asymptotic symmetry generators form one copy of the Virasoro algebra with central charge c{sub L}=(12J/({Dirac_h}/2{pi})). This implies that the near-horizon quantum states can be identified with those of (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state reduces to a thermal density matrix with dimensionless temperature T{sub L}=(1/2{pi}) and conjugate energy given by the zero mode generator, L{sub 0}, of the Virasoro algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy S{sub micro}=(2{pi}J/({Dirac_h}/2{pi})) for the CFT, which reproduces the macroscopic Bekenstein-Hawking entropy S{sub macro}=(Area/4({Dirac_h}/2{pi})G). The results apply to any consistent unitary quantum theory of gravity with a Kerr solution. We accordingly conjecture that extreme Kerr black holes are holographically dual to a chiral two-dimensional conformal field theory with central charge c{sub L}=(12J/({Dirac_h}/2{pi})), and, in particular, that the near-extreme black hole GRS 1915+105 is approximately dual to a CFT with c{sub L}{approx}2x10{sup 79}.
118600898
Hidden Conformal Symmetry of the Kerr Black Hole
Extreme and very-near-extreme spin $J$ Kerr black holes have been conjectured to be holographically dual to two-dimensional (2D) conformal field theories (CFTs) with left and right central charges ${c}_{L}={c}_{R}=12J$. In this paper it is observed that the 2D conformal symmetry of the scalar wave equation at low frequencies persists for generic nonextreme values of the mass $M\ensuremath{\ne}\sqrt{J}$. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The $2\ensuremath{\pi}$ periodic identification of the azimuthal angle $\ensuremath{\phi}$ is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures ${T}_{L}={M}^{2}/2\ensuremath{\pi}J$ and ${T}_{R}=\sqrt{{M}^{4}\ensuremath{-}{J}^{2}}/2\ensuremath{\pi}J$. The well-known low-frequency scalar-Kerr scattering amplitudes coincide with correlators of a 2D CFT at these temperatures. Moreover, the CFT microstate degeneracy inferred from the Cardy formula agrees exactly with the Bekenstein-Hawking area law for all $M$ and $J$. These observations provide evidence for the conjecture that the Kerr black hole is dual to a ${c}_{L}={c}_{R}=12J$ 2D CFT at temperatures (${T}_{L},{T}_{R}$) for every value of $M$ and $J$.
55669946
Emergent IR dual 2d CFTs in charged AdS5 black holes
We study the possible dynamical emergence of IR conformal invariance describing the low energy excitations of near-extremal R-charged global AdS5 black holes. We find interesting behavior especially when we tune parameters in such a way that the relevant extremal black holes have classically vanishing horizon area, i.e. no classical ground-state entropy, and when we combine the low energy limit with a large N limit of the dual gauge theory. We consider both near-BPS and non-BPS regimes and their near horizon limits, emphasize the differences between the local AdS3 throats emerging in either case, and discuss potential dual IR 2d CFTs for each case. We compare our results with the predictions obtained from the Kerr/CFT correspondence, and obtain a natural quantization for the central charge of the near-BPS emergent IR CFT which we interpret in terms of the open strings stretched between giant gravitons.
119279543
Near-extremal vanishing horizon AdS5 black holes and their CFT duals
A bstractWe consider families of charged rotating asymptotically AdS5 Extremal black holes with Vanishing Horizon (EVH black holes) whose near horizon geometries develop locally AdS3 throats. Using the AdS3/CFT2 duality, we propose an EVH/CFT2 correspondence to describe the near-horizon low energy IR dynamics of near-EVH black holes involving a specific large N limit of the 4d $ \mathcal{N}=4 $ SYM. We give a map between the UV and IR near-EVH excitations, showing that the ‘UV first law’ of thermodynamics reduces to the ‘IR first law’ satisfied by the near horizon BTZ black holes in this near-EVH limit. We also discuss the connection between our EVH/CFT proposal and the Kerr/CFT correspondence in the cases where the two overlap.
9287169
Determinant Formulae and Unitarity for the N=2 Superconformal Algebras in Two-Dimensions or Exact Results on String Compactification
Determinant formulae are presented for the periodic, antiperiodic and twisted N = 2 superconformal algebras in two dimensions, and a classification is derived of the unitary highest weight representations. Physical realisations of several of these representations are discussed. In particular, it is noted that the unitarity constraints apply to string compactification, giving results which are nonperturbative in the compactification radius.
55379283
Chiral primaries in strange metals
Abstract It was suggested recently that the study of 1-dimensional QCD with fermions in the adjoint representation could lead to an interesting toy model for strange metals and their holographic formulation. In the high density regime, the infrared physics of this theory is described by a constrained free fermion theory with an emergent N = ( 2 , 2 ) superconformal symmetry. In order to narrow the choice of potential holographic duals, we initiate a systematic search for chiral primaries in this model. We argue that the bosonic part of the superconformal algebra can be extended to a coset chiral algebra of the form W N = SO ( 2 N 2 − 2 ) 1 / SU ( N ) 2 N . In terms of this algebra the spectrum of the low energy theory decomposes into a finite number of sectors which are parametrized by special necklaces. We compute the corresponding characters and partition functions and determine the set of chiral primaries for N ≤ 5 .
10140656
3d Higher-spin Gauge Theories with Matter †
This paper is a letter-type version of hep-th/9806236. We discuss properties of non-linear equations of motion which describe higher-spin gauge interactions for massive spin-0 and spin-1/2 matter fields in 2+1 dimensional anti-de Sitter space. The model is shown to have N = 2 supersymmetry and to describe higher-spin interactions of d3 N = 2 massive hypermultiplets. An integrating flow is found which reduces the full non-linear system to the free field equations via a non-local Bäcklund-Nicolai–type mapping.
118949332
The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
Abstract In this work we review recent progress in four-dimensional conformal quantum field theories and scaling dimensions of local operators. Here we consider the example of maximally supersymmetric gauge theory and present techniques to derive, investigate and apply the dilatation operator which measures the scaling dimensions. We construct the dilatation operator by purely algebraic means: Relying on the symmetry algebra and structural properties of Feynman diagrams we are able to bypass involved, higher-loop field theory computations. In this way we obtain the complete one-loop dilatation operator and the planar, three-loop deformation in an interesting subsector. These results allow us to address the issue of integrability within a planar four-dimensional gauge theory: We prove that the complete dilatation generator is integrable at one loop and present the corresponding Bethe ansatz. We furthermore argue that integrability extends to three loops and beyond. Assuming that it holds indeed, we finally construct a novel spin chain model at five loops and propose a Bethe ansatz which might be valid at arbitrary loop order!
73652073
The continuous orbifold of N$$ \mathcal{N} $$ = 2 minimal model holography
A bstractFor the N$$ \mathcal{N} $$ = 2 Kazama-Suzuki models that appear in the duality with a higher spin theory on AdS3 it is shown that the large level limit can be interpreted as a continuous orbifold of 2N free bosons and fermions by the group U(N ). In particular, we show that the subset of coset representations that correspond to the perturbative higher spin degrees of freedom are precisely described by the untwisted sector of this U(N ) orbifold. We furthermore identify the twisted sector ground states of the orbifold with specific coset representations, and give various pieces of evidence in favour of this identification.
15902919
Iterative structure of the = 4 SYM spin chain
We develop algebraic methods for finding loop corrections to the = 4 SYM dilatation generator, within the noncompact (1, 1|2) sector. This sector gives a 't Hooft coupling λ-dependent representation of (1, 1|2) × (1|1)2. At first working independently of the representation, we present an all-order algebraic ansatz for the λ-dependence of this Lie algebra's generators. The ansatz solves the symmetry constraints if an auxiliary generator, , satisfies certain simple commutation relations with the Lie algebra generators. Applying this to the (1, 1|2) sector leads to an iterative solution for the planar three-loop dilatation generator in terms of leading order symmetry generators and , which passes a thorough set of spectral tests. We argue also that this algebraic ansatz may be applicable to the nonplanar theory as well.