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Journal ArticleDOI

Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions

06 Dec 2012-Journal of High Energy Physics (Springer-Verlag)-Vol. 2012, Iss: 12, pp 28
TL;DR: In this article, the authors considered the conformal field theory of N complex massless scalars coupled to a U(N) Chern-Simons theory at level k, and they showed that the theory is equivalent to the Legendre transform of the theory of k fermions coupled to the U(k)
Abstract: We consider the conformal field theory of N complex massless scalars in 2 + 1 dimensions, coupled to a U(N) Chern-Simons theory at level k. This theory has a ’t Hooft large N limit, keeping fixed λ ≡ N/k. We compute some correlation functions in this theory exactly as a function of λ, in the large N (planar) limit. We show that the results match with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have high-spin symmetries in the large N limit. It has been suggested in the past that this theory is dual (in the large N limit) to the Legendre transform of the theory of fermions coupled to a Chern-Simons gauge field, and our results allow us to find the precise mapping between the two theories. We find that in the large N limit the theory of N scalars coupled to a U(N) k Chern-Simons theory is equivalent to the Legendre transform of the theory of k fermions coupled to a U(k) N Chern-Simons theory, thus providing a bosonization of the latter theory. We conjecture that perhaps this duality is valid also for finite values of N and k, where on the fermionic side we should now have (for N f flavors) a $ \mathrm{U}{(k)_{{{{{N-{N_f}}} \left/ {2} \right.}}}} $ theory. Similar results hold for real scalars (fermions) coupled to the O(N) k Chern-Simons theory.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment, are highlighted, highlighting how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as searches for physics beyond the Standard Model.
Abstract: We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

433 citations

Journal ArticleDOI
TL;DR: In this article, a web of dualities in 2 + 1 dimensions is presented, which generalize the known particle/vortex duality. But it is not clear how time reversal is realized in these dualities.

405 citations

Journal ArticleDOI
TL;DR: In this article, a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents is presented.
Abstract: This paper is mainly a review of the dualities between Vasiliev’s higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

313 citations

Journal ArticleDOI
TL;DR: In this article, a supersymmetric and parity violating version of Vasiliev's higher spin gauge theory in AdS4 admits boundary conditions that preserve or 6 supersymmetries.
Abstract: We demonstrate that a supersymmetric and parity violating version of Vasiliev’s higher spin gauge theory in AdS4 admits boundary conditions that preserve or 6 supersymmetries. In particular, we argue that the Vasiliev theory with U(M) Chan–Paton and boundary condition is holographically dual to the 2+1 dimensional U(N)k × U(M)−k ABJ theory in the limit of large N, k and finite M. In this system all bulk higher spin fields transform in the adjoint of the U(M) gauge group, whose bulk t’Hooft coupling is M/N. Analysis of boundary conditions in Vasiliev theory allows us to determine exact relations between the parity breaking phase of Vasiliev theory and the coefficients of two and three point functions in Chern–Simons vector models at large N. Our picture suggests that the supersymmetric Vasiliev theory can be obtained as a limit of type IIA string theory in AdS, and that the non-Abelian Vasiliev theory at strong bulk ’t Hooft coupling smoothly turn into a string field theory. The fundamental string is a singlet bound state of Vasiliev’s higher spin particles held together by U(M) gauge interactions. This is illustrated by the thermal partition function of free ABJ theory on a two sphere at large M and N even in the analytically tractable free limit. In this system the traces or strings of the low temperature phase break up into their Vasiliev particulate constituents at a U(M) deconfinement phase transition of order unity. At a higher temperature of order Vasiliev’s higher spin fields themselves break up into more elementary constituents at a U(N) deconfinement temperature, in a process described in the bulk as black hole nucleation.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

275 citations

Journal ArticleDOI
TL;DR: In this article, level/rank duality in three-dimensional Chern-Simons theories and various related dualities in 3D ChernSimons-matter theories are discussed in detail.
Abstract: We discuss in detail level/rank duality in three-dimensional Chern-Simons theories and various related dualities in three-dimensional Chern-Simons-matter theories. We couple the dual Lagrangians to appropriate background fields (including gauge fields, spin c connections and the metric). The non-trivial maps between the currents and the line operators in the dual theories is accounted for by mixing of these fields. In order for the duality to be valid we must add finite counterterms depending on these background fields. This analysis allows us to resolve a number of puzzles with these dualities, to provide derivations of some of them, and to find new consistency conditions and relations between them. In addition, we find new level/rank dualities of topological Chern-Simons theories and new dualities of Chern-Simons-matter theories, including new boson/boson and fermion/fermion dualities.

249 citations

References
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Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: In this article, it was shown that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of the super Yang-Mills theory in four dimensions.
Abstract: 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.

14,084 citations

Journal ArticleDOI
TL;DR: In this paper, a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory is introduced to obtain certain Green's functions in 3+1-dimensional N = 4 supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory.

11,887 citations


"Correlation functions of large N Ch..." refers background in this paper

  • ... duals. All the theories discussed above have a good 1=Nexpansion (see [1] for a review), so it is natural to suggest that they could have classical gravitational duals (by the AdS/CFT correspondence [2,3,4]) at large N, living on AdS4. These duals should have massless high spin elds, to match with the eld theory spectrum. Indeed, it was suggested in [5,6] (see also [7,8,9]) that the bosonic theories are...

    [...]

Posted Content
TL;DR: In this article, a correspondence between conformal field theory observables and those of supergravity was proposed, where correlation functions in conformal fields are given by the dependence of the supergravity action on the asymptotic behavior at infinity.
Abstract: 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 $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

8,751 citations


"Correlation functions of large N Ch..." refers background in this paper

  • ...All the theories discussed above have a good 1/N expansion (see [1] for a review), so it is natural to suggest that they could have classical gravitational duals (by the AdS/CFT correspondence [2, 3, 4]) at large N , living on AdS4....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the modern formulation of the renormalization group is explained for both critical phenomena in classical statistical mechanics and quantum field theory, and the expansion in ϵ = 4−d is explained [ d is the dimension of space (statistical mechanics) or space-time (quantum field theory)].

3,882 citations