118845269
Supergravity at the boundary of AdS supergravity
We give a general analysis of AdS boundary conditions for spin-3/2 Rarita-Schwinger fields and investigate boundary conditions preserving supersymmetry for a graviton multiplet in AdS{sub 4}. Linear Rarita-Schwinger fields in AdS{sub d} are shown to admit mixed Dirichlet-Neumann boundary conditions when their mass is in the range 0{<=}|m|<1/2l{sub AdS}. We also demonstrate that mixed boundary conditions are allowed for larger masses when the inner product is 'renormalized' accordingly with the action. We then use the results obtained for |m|=1/l{sub AdS} to explore supersymmetric boundary conditions for N=1 AdS{sub 4} supergravity in which the metric and Rarita-Schwinger fields are fluctuating at the boundary. We classify boundary conditions that preserve boundary supersymmetry or superconformal symmetry. Under the AdS/CFT dictionary, Neumann boundary conditions in d=4 supergravity correspond to gauging the superconformal group of the three-dimensional CFT describing M2-branes, while N=1 supersymmetric mixed boundary conditions couple the CFT to N=1 superconformal topologically massive gravity.
123992482
Large N field theories, string theory and gravity
We describe the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions.
10865531
`Double-trace' deformations, boundary conditions and spacetime singularities
Double-trace deformations of the AdS/CFT duality result in a new perturbation expansion for string theory, based on a non-local worldsheet. We discuss some aspects of the deformation in the low energy gravity approximation, where it appears as a change in the boundary condition of fields. We relate unique features of the boundary of AdS to the worldsheet becoming non-local, and conjecture that non-local worldsheet actions may be generic in other classes of backgrounds.
119685686
Stability in Gauged Extended Supergravity
Extended supergravity theories with gauged SO(N) internal symmetry have, for N ≥ 4, scalar field potentials which are unbounded below. Nevertheless, it is argued that the theories have ground states with anti-de Sitter background geometry which are stable against fluctuations which vanish sufficiently fast at spatial infinity. Stability is implied because the appropriate conserved energy functional is positive for such fluctuations. Anti-de Sitter space is not globally hyperbolic, but the boundary conditions required for positive energy are also shown to give free field theories with well-defined Cauchy problem. New information on the particle representations of OSp(1, 4) supersymmetry is presented as part of the argument. Supersymmetry requires boundary conditions for spin 0 fields such that only the improved stress tensor leads to a conserved energy functional. Although the stability arguments support the view that gauged supergravity theories are acceptable quantum field theories, the problem of a large cosmological term in the Ads phase of the theories is still unsolved.
119993972
Positive Energy in anti-De Sitter Backgrounds and Gauged Extended Supergravity
The energy functional of a field theory with anti-de Sitter background geometry can be positive for scalar potentials which are unbounded below and for vacua corresponding to critical points which are maxima or saddle points.
17591901
Dynamics in non-globally-hyperbolic static spacetimes: III. Anti-de Sitter spacetime
In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a well-defined dynamics. Nevertheless, AdS spacetime is static, so the possible rules of dynamics for a field satisfying a linear wave equation are constrained by our previous general analysis—given in paper II—where it was shown that the possible choices of dynamics correspond to choices of positive, self-adjoint extensions of a certain differential operator, A. In the present paper, we reduce the analysis of electromagnetic and gravitational perturbations in AdS spacetime to scalar wave equations. We then apply our general results to analyse the possible dynamics of scalar, electromagnetic and gravitational perturbations in AdS spacetime. In AdS spacetime, the freedom (if any) in choosing self-adjoint extensions of A corresponds to the freedom (if any) in choosing suitable boundary conditions at infinity, so our analysis determines all the possible boundary conditions that can be imposed at infinity. In particular, we show that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbations, and depending on the number of spacetime dimensions and type of mode for electromagnetic and gravitational perturbations.
119113286
Supersymmetric multi-trace boundary conditions in AdS
Boundary conditions for massive fermions are investigated in AdSd for d ? 2. For fermion masses in the range 0 ? |m| < 1/2? with ? being the AdS length, the standard notion of normalizeability allows a choice of boundary conditions. As in the case of scalars at or slightly above the Breitenlohner?Freedman (BF) bound, such boundary conditions correspond to multi-trace deformations of any CFT dual. By constructing appropriate boundary superfields, for d = 3, 4, 5 we identify joint scalar/fermion boundary conditions which preserve either supersymmetry or superconformal symmetry on the boundary. In particular, we identify boundary conditions corresponding via AdS/CFT (at large N) to a 595-parameter family of double-trace marginal deformations of the low-energy theory of N M2-branes which preserve superconformal symmetry. We also establish that (at large N and large 't Hooft coupling ?) there are no marginal or relevant multi-trace deformations of 3+1 super Yang?Mills which preserve even supersymmetry.
5057213
Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry
We use a covariant phase space formalism to give a general prescription for defining Hamiltonian generators of bosonic and fermionic symmetries in diffeomorphism invariant theories, such as supergravities. A simple and general criterion is derived for a choice of boundary condition to lead to conserved generators of the symmetries on the phase space. In particular, this provides a criterion for the preservation of supersymmetries. For bosonic symmetries corresponding to diffeomorphisms, our prescription coincides with the method of Wald et al. We then illustrate these methods in the case of certain supergravity theories in d = 4. In minimal AdS supergravity, boundary conditions such that the supercharges exist as Hamiltonian generators of supersymmetry transformations are unique within the usual framework in which the boundary metric is fixed. In extended AdS supergravity, or more generally in the presence of chiral matter superfields, we find that there exist many boundary conditions preserving supersymmetry for which corresponding generators exist. These choices are shown to correspond to a choice of certain arbitrary boundary 'superpotentials', for suitably defined 'boundary superfields'. We also derive corresponding formulae for the conserved bosonic charges, such as energy, in those theories, and we argue that energy is always positive, for any supersymmetry-preserving boundary conditions. We finally comment on the relevance and interpretation of our results within the AdS/CFT correspondence.
117821436
Massive Spin 3/2 Theories in Three-dimensions
Abstract Topologically massive spin 3 2 theory in 3 spacetime dimensions, which is gauge invariant and involves second derivatives, is shown to be equivalent to the normal gauge variant first derivative massive Rarita-Schwinger model. The equivalence persists in arbitrary background geometries. In the particular anti-de Sitter space whose cosmological constant is minus the mass squared, the model effectively behaves like the massless theory in flat space: its degree of freedom disappears.
9491863
Note on the massive Rarita-Schwinger field in the AdS/CFT correspondence
Abstract We consider a massive Rarita-Schwinger field on the Anti-de Sitter space and solve the corresponding equations of motion. We show that appropriate boundary terms calculated on-shell give two-point correlation functions for spin-3/2 fields of the conformal field theory on the boundary. The relation between Rarita-Schwinger field masses and conformal dimensions of corresponding operators is established.
119344412
The massless gravitino and the AdS/CFT correspondence
We solve the Dirichlet boundary value problem for the massless gravitino on ${\mathrm{AdS}}_{d+1}$ space and compute the two-point function of the dual CFT supersymmetry currents using the AdS-CFT correspondence principle. We find analogously to the spinor case that the boundary data for the massless $(d+1)$-dimensional bulk gravitino field consists of only a $(d\ensuremath{-}1)$-dimensional gravitino.
7943400
Setting the boundary free in AdS/CFT
We describe a new class of boundary conditions for AdSd+1 under which the boundary metric becomes a dynamical field. The key technical point is to show that contributions from boundary counter-terms in the bulk gravitational action render such fluctuations normalizable. In the context of AdS/CFT, the simplest version of Neumann boundary conditions for AdS promotes the CFT metric to a dynamical field but adds no explicit gravitational dynamics; the gravitational dynamics is just that induced by the conformal fields. Other AdS boundary conditions couple the CFT to a gravity theory of choice. We use this correspondence to briefly explore the coupled CFT + gravity theories and, in particular, for d = 3 we show that coupling topologically massive gravity to a large N CFT preserves the perturbative stability of the theory with negative (three-dimensional) Newton's constant.
8659039
Gravitational duality transformations on (A)dS4
We discuss the implementation of electric-magnetic duality transformations in four-dimensional gravity linearized around Minkowski or (A)dS4 backgrounds. In the presence of a cosmological constant duality generically modifies the Hamiltonian, nevertheless the bulk dynamics is unchanged. We pay particular attention to the boundary terms generated by the duality transformations and discuss their implications for holography.
15613773
Dual gravitons in AdS 4 /CFT 3 and the holographic Cotton tensor
We argue that gravity theories in AdS4 are holographically dual to either of two three-dimensional CFT's: the usual Dirichlet CFT1 where the fixed graviton acts as a source for the stress-energy tensor, and a dual CFT2 with a fixed dual graviton which acts as a source for a dual stress-energy tensor. The dual stress-energy tensor is shown to be the Cotton tensor of the Dirichlet CFT. The two CFT's are related by a Legendre transformation generated by a gravitational Chern-Simons coupling. This duality is a gravitational version of electric-magnetic duality valid at any radius r, where the renormalized stress-energy tensor is the electric field and the Cotton tensor is the magnetic field. Generic Robin boundary conditions lead to CFT's coupled to Cotton gravity or topologically massive gravity. Interaction terms with CFT1 lead to a non-zero vev of the stress-energy tensor in CFT2 coupled to gravity even after the source is removed.
123585824
Quantum Gravity in Two Dimensions
Two dimensional induced quantum gravity is analyzed. By the use of light-cone gauge we derive a gravitational analogue of the Wess-Zumino action and discover its amazing connection with SL (2, ℝ) current algebra. The latter permits us to find differential equations for the correlation functions.
122809812
Cosmological Constant in Supergravity
We construct an extension of pure supergravity which contains a cosmological term and a masslike term for the spin-$\frac{3}{2}$ field. Unlike another recent model which incorporates these features, that presented here is constructed from the usual spin-2, spin-$\frac{3}{2}$ fields alone.
15186584
Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
Abstract: We develop a systematic method for renormalizing the AdS/CFT prescription for computing correlation functions. This involves regularizing the bulk on-shell supergravity action in a covariant way, computing all divergences, adding counterterms to cancel them and then removing the regulator. We explicitly work out the case of pure gravity up to six dimensions and of gravity coupled to scalars. The method can also be viewed as providing a holographic reconstruction of the bulk spacetime metric and of bulk fields on this spacetime, out of conformal field theory data. Knowing which sources are turned on is sufficient in order to obtain an asymptotic expansion of the bulk metric and of bulk fields near the boundary to high enough order so that all infrared divergences of the on-shell action are obtained. To continue the holographic reconstruction of the bulk fields one needs new CFT data: the expectation value of the dual operator. In particular, in order to obtain the bulk
metric one needs to know the expectation value of stress-energy tensor of the boundary theory. We provide completely explicit formulae for the holographic stress-energy tensors up to six dimensions. We show that both the gravitational and matter conformal anomalies of the boundary theory are correctly reproduced. We also obtain the conformal transformation properties of the boundary stress-energy tensors.
7861023
Holographic Renormalization
We systematically develop the procedure of holographic renormalization for RG flows dual to asymptotically AdS domain walls. All divergences of the on-shell bulk action can be cancelled by adding covariant local boundary counterterms determined by the near-boundary behavior of bulk fields. This procedure defines a renormalized action from which correlation functions are obtained by functional differentiation. The correlators are finite and well behaved at coincident points. Ward identities, corrected for anomalies, are satisfied. The correlators depend on parts of the solution of the bulk field equations which are not determined by near-boundary analysis. In principle a full nonlinear solution is required, but one can solve linearized fluctuation equations to define a bulk-to-boundary propagator from which 2-point correlation functions are easily obtained. We carry out the procedure explicitly for two known RG flows obtained from the maximal gauged D=5 supergravity theory, obtaining new results on correlators of vector currents and related scalar operators and giving further details on a recent analysis of the stress tensor sector. 1 M.Bianchi@damtp.cam.ac.uk 2 dzf@math.mit.edu kostas@feynman.princeton.edu
16882394
How to go with an RG flow
We apply the formalism of holographic renormalization to domain wall solutions of 5-dimensional supergravity which are dual to deformed conformal field theories in 4 dimensions. We carefully compute one- and two-point functions of the energy-momentum tensor and the scalar operator mixing with it in two specific holographic flows, resolving previous difficulties with these correlation functions. As expected, two-point functions have a 0-mass dilaton pole for the Coulomb branch flow in which conformal symmetry is broken spontaneously but not for the flow dual to a mass deformation in which it is broken explicitly. A previous puzzle of the energy scale in the Coulomb branch flow is explained.
13324104
D = 4 super Yang-Mills, D = 5 gauged supergravity and D = 4 conformal supergravity
Abstract We consider the role of N = 4 conformal supergravity in the duality relation between N = 4 SYM theory and D = 5 gauged supergravity expanded near the anti-de Sitter background. We discuss the structure of the SYM effective action in the conformal supergravity background, in particular, terms related to conformal anomaly. Solving the leading-order Dirichlet problem for the metric perturbation in AdS background we explicitly compute the bilinear graviton term in the D = 5 Einstein action, demonstrating its equivalence to the linearised Weyl tensor squared part of the gravitational effective action induced by SYM theory. We also compute the graviton-dilaton-dilaton three-point function which is found to have the form consistent with conformal invariance of the boundary theory.
18488178
Supersymmetry in the AdS/CFT correspondence
Abstract We study how local symmetry transformations of ( p , q ) anti de Sitter supergravities in three dimensions act on fields on the two-dimensional boundary. The boundary transformation laws are shown to be the same as those of two-dimensional ( p , q ) conformal supergravities for p , q ≤2. Weyl and super Weyl transformations are generated from three-dimensional general coordinate and super transformations.
2142061
On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory
We elaborate on the suggestion made in arXiv:0806.3498 that the 3d N = 8 superconformal SU(N) Chern-Simons-matter theory of “Lorentzian” Bagger-Lambert-Gustavson type (L-BLG) can be obtained by a scaling limit (involving sending the level k to infinity and redefining the fields) from the N = 6 superconformal U(N) × U(N) Chern-Simonsmatter theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We show that to implement such limit in a consistent way one is to extend the ABJM theory by an abelian “ghost” multiplet. The corresponding limit at the 3-algebra level also requires extending the non-antisymmetric Bagger-Lambert 3-algebra underlying the ABJM theory by a negative-norm generator. We draw analogy with similar scaling limits discussed previously for bosonic Chern-Simons theory and comment on some implications of this relation between the ABJM and L-BLG theories. Also at the Institute for Theoretical Physics and Modeling, Yerevan, Armenia Also at the Lebedev Institute, Moscow.
16987793
N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(N) and SU(N) × SU(N) which have explicit = 6 superconformal symmetry. Using brane constructions we argue that the U(N) × U(N) theory at level k describes the low energy limit of N M2-branes probing a C4/Zk singularity. At large N the theory is then dual to M-theory on AdS4 × S7/Zk. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS4 × CP3. For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) × SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.
14271261
AdS/CFT correspondence and geometry
In the first part of this paper we provide a short introduction to the AdS/CFT correspondence and to holographic renormalization. We discuss how QFT correlation functions, Ward identities and anomalies are encoded in the bulk geometry. In the second part we develop a Hamiltonian approach to the method of holographic renormalization, with the radial coordinate playing the role of time. In this approach regularized correlation functions are related to canonical momenta and the near-boundary expansions of the standard approach are replaced by covariant expansions where the various terms are organized according to their dilatation weight. This leads to universal expressions for counterterms and one-point functions (in the presence of sources) that are valid in all dimensions. The new approach combines optimally elements from all previous methods and supersedes them in efficiency.
122074708
The Mass Spectrum of Supergravity on the Round Seven Sphere
Abstract We derive the mass spectrum of supergravity compactified on the round seven-sphere. The final result may be arrived at either by employing harmonic expansions on S7 or by using properties of Osp(8,4).
8750172
Trace anomaly driven inflation
This paper investigates Starobinsky's model of inflation driven by the trace anomaly of conformally coupled matter fields. This model does not suffer from the problem of contrived initial conditions that occurs in most models of inflation driven by a scalar field. The universe can be nucleated semiclassically by a cosmological instanton that is much larger than the Planck scale provided there are sufficiently many matter fields. There are two cosmological instantons: the four sphere and a new ``double bubble'' solution. This paper considers a universe nucleated by the four sphere. The AdS/CFT correspondence is used to calculate the correlation function for scalar and tensor metric perturbations during the ensuing de Sitter phase. The analytic structure of the scalar and tensor propagators is discussed in detail. Observational constraints on the model are discussed. Quantum loops of matter fields are shown to strongly suppress short scale metric perturbations, which implies that short distance modifications of gravity would probably not be observable in the cosmic microwave background. This is probably true for any model of inflation provided there are sufficiently many matter fields. This point is illustrated by a comparison of anomaly driven inflation in four dimensions and in a Randall-Sundrum brane-world model.
121024024
1/N Expansion and Renormalization in Quantum Gravity
Gravity coupled to N massless fermions is expanded in powers of 1N, keeping κ2N fixed. The resulting lowest order graviton propagator has (k4log k2)−1 asymptotic behavior, and no tachyon or unphysical real bound state poles. There are, however, complex conjugate poles on the physical sheet. This leads to a unitary, and renormalizable, though “non-analytical” S-matrix.
121842378
A Chern-Simons Action for Three-Dimensional anti-De Sitter Supergravity Theories
Abstract We construct the (p,q)-type anti-de Sitter (adS) supergravity theories associated with the three-dimensional adS supergroups OSp (p|2; R )⊗ OSp (q|2; R ) . They are distinguished, for N=p+q, by the gravitini mass-matrix, which has signature p−q. We show that the action can be written as the integral of the Chern-Simons three-form associated with the (adS) supergroup.
2695861
Variational methods in AdS/CFT correspondence
We prove that the AdS/CFT calculation of 1-point functions can be drastically simplified by using variational arguments. We give a simple proof, valid for any theory that can be derived from a Lagrangian, that the large radius divergencies in 1-point functions can always be renormalized away (at least in the semiclassical approximation). The renormalized 1-point functions then follow by a simple variational problem involving only finite quantities. Several examples, a massive scalar, gravity, and renormalization flows, are discussed. Our results are general and can thus be used for dualities beyond AdS/CFT.
122315136
TOPOLOGICALLY MASSIVE SUPERGRAVITY
Abstract The locally supersymmetric extension of three-dimensional topologically massive gravity is constructed. Its fermionic part is the sum of the (dynamically trivial) Rarita-Schwinger action and a gauge-invariant topological term, of second derivative order, analogous to the gravitational one. It is ghost free and represents a single massive spin 3/2 excitation. The fermion-gravity coupling is minimal and the invariance is under the usual supergravity transformations. The system's energy, as well as that of the original topological gravity, is therefore positive.
2874311
The general supersymmetric solution of topologically massive supergravity
We find the general fully nonlinear solution of topologically massive supergravity admitting a Killing spinor. It is of plane-wave type, with a null Killing vector field. Conversely, we show that all solutions with a null Killing vector are supersymmetric for one or the other choice of sign for the Chern–Simons coupling constant μ. If μ does not take the critical value, μ = ±1, these solutions are asymptotically regular on a Poincare patch, but do not admit a smooth global compactification with boundary . In the critical case, the solutions have a logarithmic singularity on the boundary of the Poincare patch. We derive a Nester–Witten identity, which allows us to identify the associated charges, but we conclude that the presence of the Chern–Simons term prevents us from making a statement about their positivity. The Nester–Witten procedure is applied to the BTZ black hole.
507883
Restrictions imposed by superconformal invariance on quantum field theories
We derive unitarity restrictions on the scaling dimensions of primary operators in a superconformal quantum field theory, in d=3,4,5,6.
5240874
Comments on Unparticles
Abstract We comment on several points concerning unparticles which have been overlooked in the literature. One regards Mack's unitarity constraint lower bounds on CFT operator dimensions, e.g., d V ⩾ 3 for primary, gauge invariant, vector unparticle operators. We correct the results in the literature to account for this, and also for a needed correction in the form of the propagator for vector and tensor unparticles. We show that the unitarity constraints can be directly related to unitarity requirements on scattering amplitudes of particles, e.g., those of the Standard Model, coupled to the CFT operators. We also stress the existence of explicit Standard Model contact terms, which are generically induced by the coupling to the CFT (or any other hidden sector), and are subject to LEP bounds. Barring an unknown mechanism to tune away these contact interactions, they can swamp interference effects generated by the CFT. We illustrate these points in the context of a weakly coupled CFT example. A significant amount of the unparticle literature should be reconsidered or revised in light of the observations in this note.
14108777
Dyonic AdS black holes from magnetohydrodynamics
We use the AdS/CFT correspondence to argue that large dyonic black holes in anti-de Sitter spacetime are dual to stationary solutions of the equations of relativistic magnetohydrodynamics on the conformal boundary of AdS. The dyonic Kerr-Newman-AdS4 solution corresponds to a charged diamagnetic fluid not subject to any net Lorentz force, due to orthogonal magnetic and electric fields compensating each other. The conserved charges, stress tensor and R-current of the fluid are shown to be in exact agreement with the corresponding quantities of the black hole. Furthermore, we obtain stationary solutions of the Navier-Stokes equations in four dimensions, which yield predictions for (yet to be constructed) charged rotating black strings in AdS5 carrying nonvanishing momentum along the string. Finally, we consider Scherk-Schwarz reduced AdS gravity on a circle. In this theory, large black holes and black strings are dual to lumps of deconfined plasma of the associated CFT. We analyze the effects that a magnetic field introduces in the Rayleigh-Plateau instability of a plasma tube, which is holographically dual to the Gregory-Laflamme instability of a magnetically charged black string.
11351404
Supersymmetric hydrodynamics from the AdS/CFT correspondence
We compute holographically the dispersion relation for a hydrodynamic mode of fluctuation (the phonino) of the density of supersymmetry current in = 4 SYM at strong coupling. The mode appears as a pole at low frequency and momentum in the correlator of supercurrents. It has a wave-like propagation, and we find its speed and coefficient of attenuation.