N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
TL;DR: In this paper, the authors constructed three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(n) and SU(N), SU(2) × SU (2) which have explicit = 6 superconformal symmetry.
Abstract: 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.
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TL;DR: In this paper, the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter were computed using localization techniques, and the path-integral reduces to a non-Gaussian matrix model.
Abstract: We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N = 2 theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.
1,154 citations
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TL;DR: In this article, two generalizations of the = 6 superconformal Chern-Simons-matter theories with gauge group U(n) × U(N) have been considered, and they are conjectured to describe M−N| fractional M2-branes localized at the orbifold singularity.
Abstract: We consider two generalizations of the = 6 superconformal Chern-Simons-matter theories with gauge group U(N) × U(N). The first generalization is to = 6 superconformal U(M) × U(N) theories, and the second to = 5 superconformal O(2M) × USp(2N) and O(2M+1) × USp(2N) theories. These theories are conjectured to describe M2-branes probing C4/Zk in the unitary case, and C4/k in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as |M−N| fractional M2-branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals.
764 citations
Cites background or methods or result from "N=6 superconformal Chern-Simons-mat..."
...The first generalization we consider is to U(M)k×U(N)−k Chern-Simons-matter theories, with the same matter content and interactions as in [5], but with M 6= N ....
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...In [5] we suggested an alternative route to studying M2-branes....
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...It is straightforward to generalize the field theory construction of [5] to supersymmetric U(M)k × U(N)−k Chern-Simons matter theories....
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...We will use the description of these theories in [5], in which they are written as special cases of N = 3 supersymmetric Chern-Simons-matter theories that happen to have enhanced supersymmetry....
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...In this paper we generalize the construction of [5] in two directions, both of which break the parity symmetry of the original construction....
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TL;DR: In this paper, the three sphere partition function of three dimensional theories with four supercharges and an R-symmetry is computed using localization, resulting in a matrix integral over the Cartan of the gauge group.
Abstract: The three sphere partition function, Z , of three dimensional theories with four supercharges and an R-symmetry is computed using localization, resulting in a matrix integral over the Cartan of the gauge group. There is a family of couplings to the curved background, parameterized by a choice of R-charge, such that supersymmetry is preserved; Z is a function of those parameters. The magnitude of the result is shown to be extremized for the superconformal R-charge of the infrared conformal field theory, in the absence of mixing of the R-symmetry with accidental symmetries. This exactly determines the IR superconformal R-charge.
744 citations
Additional excerpts
... put to impressive use by Drukker, Marino, and Putrov [11] (see also [18, 30]), who found the famous N3/2 scaling of the entropy of multiple M2 branes directly in the IR N = 6 conformal field 1 theory [1] on NM2 branes. Recall that in three dimensions, there are no anomalies in the trace of the stress energy tensor, and thus no obvious analogues of the cand aanomaly coefficients of four dimensional theo...
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TL;DR: In this paper, the S-duality of boundary conditions is closely related to mirror symmetry of three-dimensional gauge theories, and the IR behavior of large classes of quiver gauge theories.
Abstract: By analyzing brane configurations in detail, and extracting general lessons, we develop methods for analyzing S-duality of supersymmetric boundary conditions in N=4 super Yang-Mills theory. In the process, we find that S-duality of boundary conditions is closely related to mirror symmetry of three-dimensional gauge theories, and we analyze the IR behavior of large classes of quiver gauge theories.
711 citations
TL;DR: In this article, a new class of non-Fermi liquids in (2+1)-dimensions were identified via the response functions of composite fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence.
Abstract: We report on a potentially new class of non-Fermi liquids in (2+1)-dimensions. They are identified via the response functions of composite fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence. We find strong evidence of Fermi surfaces: gapless fermionic excitations at discrete shells in momentum space. The spectral weight exhibits novel phenomena, including particle-hole asymmetry, discrete scale invariance, and scaling behavior consistent with that of a critical Fermi surface postulated by Senthil.
670 citations
References
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TL;DR: In this article, it was shown that the large-N limits of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes, spheres, and other compact manifolds.
Abstract: 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.
15,567 citations
CERN1
TL;DR: In this article, it was shown that only planar diagrams with the quarks at the edges dominate; the topological structure of the perturbation series in 1/N is identical to that of the dual models, such that the number 1/n corresponds to the dual coupling constant.
4,449 citations
"N=6 superconformal Chern-Simons-mat..." refers background in this paper
...However, in the large N limit with N/k fixed, as in the ’t Hooft limit of standard gauge theories with adjoints and bifundamentals [18], there is an expansion in 1/N(2) (whose leading order is given by planar diagrams), and the effective coupling constant in the planar diagrams is the ’t Hooft coupling λ ≡ N/k....
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TL;DR: The correspondence between supergravity and string theory on AdS space and boundary conformal eld theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamic properties of Schwarzschild black holes in Anti-de Sitter space as mentioned in this paper.
Abstract: The correspondence between supergravity (and string theory) on AdS space and boundary conformal eld theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic connement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale \holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.
4,209 citations
TL;DR: In this paper, the expectation values of an operator similar to the Wilson loop in the large $N$ limit of field theories were calculated for supersymmetric Yang-Mills theory.
Abstract: We propose a method to calculate the expectation values of an operator similar to the Wilson loop in the large $N$ limit of field theories. We consider $N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4$ $(3+1)$-dimensional supersymmetric Yang-Mills theory. The prescription involves calculating the area of a fundamental string world sheet in certain supergravity backgrounds. We also consider the case of coincident $M$-theory five-branes where one is led to calculating the area of $M$-theory two-branes. We briefly discuss the computation for $(2+1)$-dimensional supersymmetric Yang-Mills theory with 16 supercharges which is nonconformal. In all of these cases, we calculate the energy of a quark-antiquark pair.
2,117 citations
TL;DR: In this paper, a macroscopic string-anti-quark pair configuration is proposed as a physical realization of a heavy quark Wilson loop, and the potentials of the BPS string are derived from the strong 't Hooft coupling limit.
Abstract: We study some aspects of Maldacena's large-N correspondence between \({\cal N}=4\) superconformal gauge theory on the D3-brane and maximal supergravity on AdS\(_5 \times S_5\) by introducing macroscopic strings as heavy (anti-) quark probes. The macroscopic strings are semi-infinite Type IIB strings ending on a D3-brane world-volume. We first study deformation and fluctuation of D3-branes when a macroscopic BPS string is attached. We find that both dynamics and boundary conditions agree with those for the macroscopic string in anti-de Sitter supergravity. As a by-product we clarify how Polchinski's Dirichlet and Neumann open string boundary conditions arise dynamically. We then study the non-BPS macroscopic string–anti-string pair configuration as a physical realization of a heavy quark Wilson loop. We obtain the \(Q \bar Q\) static potential from the supergravity side and find that the potential exhibits non-analyticity of the square-root branch cut in the 't Hooft coupling parameter. We put forward non-analyticity as a prediction for large-N gauge theory in the strong 't Hooft coupling limit. By turning on the Ramond–Ramond zero-form potential, we also study the \(\theta\) vacuum angle dependence of the static potential. We finally discuss the possible dynamical realization of the heavy N-prong string junction and of the large-N loop equation via a local electric field and string recoil thereof. Throughout comparisons of the AdS–CFT correspondence, we find that a crucial role is played by “geometric duality” between the UV and IR scales in directions perpendicular to the D3-brane and parallel ones, explaining how the AdS\(_5\) spacetime geometry emerges out of four-dimensional gauge theory at strong coupling.
1,637 citations
"N=6 superconformal Chern-Simons-mat..." refers background in this paper
...This is related to the fact that Wilson lines with k fundamentals under one gauge group can be screened, since as usual in AdS/CFT [48] in the ’t Hooft limit we can identify the Wilson lines with fundamental strings in the bulk....
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...As in other cases of the AdS/CFT correspondence [51], the finite temperature behavior is governed in the gravitational description by an AdS black hole....
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...Presumably, the difference between the U(N) × U(N) theory and the theory that we find lies (as in other examples of the AdS/CFT correspondence) in the behavior of the subtle “singleton” modes that live on the boundary of AdS space [57], since the bulk physics arising from a brane configuration with U(N) gauge symmetry typically captures only the SU(N) dynamics (see, e.g. [58])....
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...This is related to the fact that Wilson lines with k fundamentals under one gauge group can be screened, since as usual in AdS/CFT [55] in the ’t Hooft limit we can identify the Wilson lines with fundamental strings in the bulk....
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