Holography of 3d-3d correspondence at large N (original) (raw)
Related papers
Prepared for submission to JHEP Holography of 3d-3d correspondence at Large N
2016
Abstract: We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one hand, it leads to the 3d-3d correspondence which maps an N = 2 superconformal field theory to a pure Chern-Simons theory on the 3-manifold. On the other hand, it leads to a warped AdS4 geometry in M-theory holographically dual to the superconformal field theory. Combining the holographic duality and the 3d-3d correspon-dence, we propose a conjecture for the large N limit of the perturbative free energy of a Chern-Simons theory on hyperbolic 3-manifold. The conjecture claims that the tree, one-loop and two-loop terms all share the same N3 scaling behavior and are proportional to the volume of the 3-manifold, while the three-loop and higher terms are suppressed at large N. Under mild assumptions, we prove the tree and one-loop parts of the conjecture. For the two-loop part, we test the conjecture numerically in a number of examples and find precise agreement. We also confirm the su...
Holography of wrapped M5-branes and Chern–Simons theory
Physics Letters B, 2014
We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern-Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N limit. We check the correspondence numerically in a number of examples, and confirm the N 3 scaling with precise coefficients.
𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
Journal of High Energy Physics, 2008
We construct three dimensional Chern-Simons-matter theories with gauge groups U (N ) ×U (N ) and SU (N ) ×SU (N ) which have explicit N = 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 C 4 /Z k singularity. At large N the theory is then dual to M-theory on AdS 4 × S 7 /Z k . 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 AdS 4 × CP 3 . 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.
Holographic duals of D = 3 $ \mathcal{N} = 4 $ superconformal field theories
Journal of High Energy Physics, 2011
We find the warped AdS 4 K type-IIB supergravity solutions holographically dual to a large family of three dimensional N = 4 superconformal field theories labeled by a pair (ρ,ρ) of partitions of N. These superconformal theories arise as renormalization group fixed points of three dimensional mirror symmetric quiver gauge theories, denoted by T ρ ρ (SU(N)) and Tρ ρ (SU(N)) respectively. We give a supergravity derivation of the conjectured field theory constraints that must be satisfied in order for these gauge theories to flow to a non-trivial supersymmetric fixed point in the infrared. The exotic global symmetries of these superconformal field theories are precisely realized in our explicit supergravity description.
Holographic flavor in 𝒩 = 4 gauge theories in 3d from wrapped branes
Journal of High Energy Physics, 2009
We study the addition of flavor to the gravity dual of N = 4 three-dimensional gauge theories obtained by wrapping N c D4-branes on a two-cycle of a non-compact Calabi-Yau two-fold. In this setup the flavor is introduced by adding another set of D4-branes that are extended along the non-compact directions of the Calabi-Yau which are normal to the cycle which the color branes wrap. The analysis is performed both in the quenched and unquenched approximations. In this latter case we compute the backreacted metric and we show that it reproduces the running of the gauge coupling. The meson spectrum and the behavior of Wilson loops are also discussed and the holographic realization of the Higgs branch is analyzed. Other aspects of this system studied are the entanglement entropy and the non-relativistic version of our backgrounds.
AdS 4 /CFT 3 duals from M2-branes at hypersurface singularities and their deformations
Journal of High Energy Physics, 2009
We construct three-dimensional N = 2 Chern-Simons-quiver theories which are holographically dual to the M-theory Freund-Rubin solutions AdS 4 × V 5,2 /Z k (with or without torsion G-flux), where V 5,2 is a homogeneous Sasaki-Einstein seven-manifold. The global symmetry group of these theories is generically SU (2) × U (1) × U (1) R , and they are hence non-toric. The field theories may be thought of as the n = 2 member of a family of models, labelled by a positive integer n, arising on multiple M2-branes at certain hypersurface singularities. We describe how these models can be engineered via generalized Hanany-Witten brane constructions. The AdS 4 × V 5,2 /Z k solutions may be deformed to a warped geometry R 1,2 ×T * S 4 /Z k , with self-dual G-flux through the four-sphere. We show that this solution is dual to a supersymmetric mass deformation, which precisely modifies the classical moduli space of the field theory to the deformed geometry.
Intersecting D3-branes and holography
Physical Review D, 2003
We study a defect conformal field theory describing D3-branes intersecting over two spacetime dimensions. This theory admits an exact Lagrangian description which includes both two-and four-dimensional degrees of freedom, has (4, 4) supersymmetry and is invariant under global conformal transformations. Both two-and four-dimensional contributions to the action are conveniently obtained in a two-dimensional (2, 2) superspace. In a suitable limit, the theory has a dual description in terms of a probe D3-brane wrapping an AdS 3 × S 1 slice of AdS 5 × S 5 . We consider the AdS/CFT dictionary for this set-up. In particular we find classical probe fluctuations corresponding to the holomorphic curve wy = cα ′ . These fluctuations are dual to defect fields containing massless two-dimensional scalars which parameterize the classical Higgs branch, but do not correspond to states in the Hilbert space of the CFT. We also identify probe fluctuations which are dual to BPS superconformal primary operators and to their descendants. A non-renormalization theorem is conjectured for the correlators of these operators, and verified to order g
Perturbative Approach to Integrability in Three-Dimensional Chern-Simons Theories
2013
One of the most fascinating discoveries of contemporary Theoretical Physics is the AdS/CFT correspondence relating gauge theories to gravity theories. Soon after its formulation, tremendous developments allowed to obtain a deep comprehension of the four-dimensional N = 4 SYM theory and, in particular, led to the discovery of integrable structures both in the gauge theory itself and in its string counterpart. In the last few years, much attention was devoted to the study of supersymmetric ChernSimons-matter theories in three dimensions. In this class of theories a distinguished role is played by the N = 6 ABJM model which is a U(N)k×U(N)−k superconformal gauge theory with Chern-Simons level k. Indeed, in the large N limit, the ABJM theory has been conjectured to be the AdS/CFT dual description of M-theory on an AdS4 × S/Zk background and, for k ≪ N ≪ k, of a type IIA string theory on AdS4 × CP. For this reason, soon after its discovery the ABJM model has quickly become the ideal thre...
Journal of High Energy Physics, 2015
Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A K−1 superconformal field theory (SCFT) on AdS 5 ×S 1 , with equal radii for AdS 5 and for S 1 . We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS 5 × S 5 /Z K . On R 4,1 × S 1 , this six-dimensional theory has a 5(K − 1)dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS 5 × S 1 , the theory has a 2(K − 1)-dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS 5 whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS 5 . Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional N = 2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the six-dimensional N = (2, 0) theory on AdS 5 × S 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2 JHEP03(2015)121 quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories' on AdS 5 × S 1 .