Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit

A class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. In particular we study a case where the matrix model potential has 1/N correction and give a general solution thereof up to the order of 1/N^2. We confirm that the general solution correctly reproduces the past exact result of the free energy up to the order in the case of pure Chern-Simons theory. We also apply to the matrix model of N=2 Chern-Simons theory with arbitrary numbers of fundamental chiral multiplets and anti-fundamental ones, which does not admit the Fermi gas analysis in general.Comment: 1+29 pages, 2 figures, v2: some improvements, figures added, v3: genus half loop equation solved, calculation for confirmation of the solution, further discussion, improvements, references added, v4: minor improvements, a new example, a reference added, published versio

Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models

We present exact large N calculus of four point function in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, unusual crossing relation and non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to Chern-Simons theory interacting with free fermions.Comment: 1+28 pages, 5 figures, v2: minor correction

More on BPS States in N=4 Supersymmetric Yang-Mills Theory on R x S3

We perform a systematic analysis on supersymmetric states in N=4 supersymmetric Yang-Mills theory (SYM) on R x S^3. We find a new set of 1/16 BPS equations and determine the precise configuration of the supersymmetric states by solving all 1/16 BPS equations when they are valued in Cartan subalgebra of a gauge group and the fermionic fields vanish. We also determine the number of supersymmetries preserved by the supersymmetric states varying the parameters of the BPS solutions. As a byproduct we present the complete set of such supersymmetric states in N=8 SYM on R x S^2 by carrying out dimensional reduction.Comment: 37 pages, v2: typos corrected, comments and Acknowledgements adde

Superconformal index for large N quiver Chern-Simons theories

We investigate the N=2 superconformal index for supersymmetric quiver Chern-Simons theories with large N gauge groups. After general arguments about the large N limit, we compute the first few terms in the series expansion of the index for theories proposed as dual theories to homogeneous spaces V^{5,2}, Q^{1,1,1}, Q^{2,2,2}, M^{1,1,1}, and N^{0,1,0}. We confirm that the indices have symmetries expected from the isometries of dual manifolds.Comment: 27 pages, 7 figures; v2: typos corrected, Sec.6 modified; v3: explanation improved, minor corrections, version published in JHE

Chern Simons Bosonization along RG Flows

It has previously been conjectured that the theory of free fundamental scalars minimally coupled to a Chern Simons gauge field is dual to the theory of critical fundamental fermions minimally coupled to a level rank dual Chern Simons gauge field. In this paper we study RG flows away from these two fixed points by turning on relevant operators. In the t' Hooft large N limit we compute the thermal partition along each of these flows and find a map of parameters under which the two partition functions agree exactly with each other all the way from the UV to the IR. We conjecture that the bosonic and fermionic RG flows are dual to each other under this map of parameters. Our flows can be tuned to end at the gauged critical scalar theory and gauged free fermionic theories respectively. Assuming the validity of our conjecture, this tuned trajectory may be viewed as RG flow from the gauged theory of free bosons to the gauged theory of free fermions.Comment: 21 pages, v2: new subsection 3.3 added, typos corrected, version accepted in JHE

AdS geometry from CFT on a general conformally flat manifold

We construct an anti-de-Sitter (AdS) geometry from a conformal field theory (CFT) defined on a general conformally flat manifold via a flow equation associated with the curved manifold, which we refer to as the primary flow equation. We explicitly show that the induced metric associated with the primary flow equation becomes AdS whose boundary is the curved manifold. Interestingly, it turns out that such an AdS metric with conformally flat boundary is obtained from the usual Poincare AdS by a simple bulk diffeomorphism transformation. We also demonstrate that the emergence of such an AdS space is guaranteed only by the conformal symmetry at boundary, which converts to the AdS isometry after quantum averaging, as in the case of the flat boundary.Comment: 16 pages, no figur

Twisted Sectors in Gravity Duals of N=4 Chern-Simons Theories

We study Kaluza-Klein modes of a d=7, N=2 vector multiplet in AdS_4 x S^3. Such modes arise in the context of AdS/CFT as dual objects of a class of gauge invariant operators in N=4 Chern-Simons theories. We confirm that the Kaluza-Klein modes precisely reproduce the BPS spectrum of the operators.Comment: 21 pages, v2: Eqs. (32), (33), (34), and (35) are correcte

Complete factorization in minimal N=4 Chern-Simons-matter theory

We investigate an N=4 U(N)_k x U(N+M)_{-k} Chern-Simons theory coupled to one bifundamental hypermultiplet by employing its partition function, which is given by 2N+M dimensional integration via localization. Surprisingly, by performing the integration explicitly we find that the partition function completely factorizes into that of the pure Chern-Simons theory for two gauge groups and an analogous contribution for the bifundamental hypermultiplet. Using the factorized form of the partition function we argue the level/rank duality, which is also expected from the Hanany-Witten transition in the type IIB brane realization. We also present the all order 't Hooft expansion of the partition function and comment on the connection to the higher-spin theory.Comment: 1+20 pages, 5 figures, v2: comments on the convergence and regularization of the partition function, one figure, references added, some other minor improvements, v3: typos corrected, published versio