373 research outputs found
Interacting fermions and N=2 Chern-Simons-matter theories
The partition function on the three-sphere of N=3 Chern-Simons-matter
theories can be formulated in terms of an ideal Fermi gas. In this paper we
show that, in theories with N=2 supersymmetry, the partition function
corresponds to a gas of interacting fermions in one dimension. The large N
limit is the thermodynamic limit of the gas and it can be analyzed with the
Hartree and Thomas-Fermi approximations, which lead to the known large N
solutions of these models. We use this interacting fermion picture to analyze
in detail N=2 theories with one single node. In the case of theories with no
long-range forces we incorporate exchange effects and argue that the partition
function is given by an Airy function, as in N=3 theories. For the theory with
g adjoint superfields and long-range forces, the Thomas-Fermi approximation
leads to an integral equation which determines the large N, strongly coupled
R-charge.Comment: 29 pages, 4 figure
Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification
We consider N=3 supersymmetric Chern-Simons (CS) theories that contain
product U(N) gauge groups and bifundamental matter fields. Using the matrix
model of Kapustin, Willett and Yaakov, we examine the Euclidean partition
function of these theories on an S^3 in the large N limit. We show that the
only such CS theories for which the long range forces between the eigenvalues
cancel have quivers which are in one-to-one correspondence with the simply
laced affine Dynkin diagrams. As the A_n series was studied in detail before,
in this paper we compute the partition function for the D_4 quiver. The D_4
example gives further evidence for a conjecture that the saddle point
eigenvalue distribution is determined by the distribution of gauge invariant
chiral operators. We also see that the partition function is invariant under a
generalized Seiberg duality for CS theories.Comment: 20 pages, 3 figures; v2 refs added; v3 conventions in figure 3
altered, version to appear in JHE
Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories
We give further support for our conjecture relating eigenvalue distributions
of the Kapustin-Willett-Yaakov matrix model in the large N limit to numbers of
operators in the chiral ring of the corresponding supersymmetric
three-dimensional gauge theory. We show that the relation holds for
non-critical R-charges and for examples with {\mathcal N}=2 instead of
{\mathcal N}=3 supersymmetry where the bifundamental matter fields are
nonchiral. We prove that, for non-critical R-charges, the conjecture is
equivalent to a relation between the free energy of the gauge theory on a three
sphere and the volume of a Sasaki manifold that is part of the moduli space of
the gauge theory. We also investigate the consequences of our conjecture for
chiral theories where the matrix model is not well understood.Comment: 27 pages + appendices, 5 figure
The large N limit of M2-branes on Lens spaces
We study the matrix model for N M2-branes wrapping a Lens space L(p,1) =
S^3/Z_p. This arises from localization of the partition function of the ABJM
theory, and has some novel features compared with the case of a three-sphere,
including a sum over flat connections and a potential that depends
non-trivially on p. We study the matrix model both numerically and analytically
in the large N limit, finding that a certain family of p flat connections give
an equal dominant contribution. At large N we find the same eigenvalue
distribution for all p, and show that the free energy is simply 1/p times the
free energy on a three-sphere, in agreement with gravity dual expectations.Comment: 28 pages, 4 figure
Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
We provide a non-trivial check of the AdS_4/CFT_3 correspondence recently
proposed in arXiv:1106.4253 by verifying the GKPW relation in the large N
limit. The CFT free energy is obtained from the previous works
(arXiv:1105.2551, arXiv:1105.4390) on the S^3 partition function for
3-dimensional N=4 SCFT T[SU(N)]. This is matched with the computation of the
type IIB action on the corresponding gravity background. We unexpectedly find
that the leading behavior of the free energy at large N is 1/2 N^2 ln N. We
also extend our results to richer theories and argue that 1/2 N^2 ln N is the
maximal free energy at large N in this class of gauge theories.Comment: 20 pages, 3 figure
The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
We compute the large N limit of the localized three dimensional free energy
of various field theories with known proposed AdS duals. We show that
vector-like theories agree with the expected supergravity results, and with the
conjectured F-theorem. We also check that the large N free energy is preserved
by the three dimensional Seiberg duality for general classes of vector like
theories. Then we analyze the behavior of the free energy of chiral-like
theories by applying a new proposal. The proposal is based on the restoration
of a discrete symmetry on the free energy before the extremization. We apply
this procedure at strong coupling in some examples and we discuss the results.
We conclude the paper by proposing an alternative geometrical expression for
the free energy.Comment: 40 pages, 7 figures, using jheppub.sty, references adde
Relation between the 4d superconformal index and the S^3 partition function
A relation between the 4d superconformal index and the S^3 partition function
is studied with focus on the 4d and 3d actions used in localization. In the
case of vanishing Chern-Simons levels and round S^3 we explicitly show that the
3d action is obtained from the 4d action by dimensional reduction up to terms
which do not affect the exact results. By combining this fact and a recent
proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a
formula which gives the partition function depending on the Weyl weight of
chiral multiplets, real mass parameters, FI parameters, and a squashing
parameter as a limit of the index of a parent 4d theory.Comment: 20 pages, LaTeX; v2: comments added; v3: minor corrections, version
published in JHE
Refined Checks and Exact Dualities in Three Dimensions
We discuss and provide nontrivial evidence for a large class of dualities in
three-dimensional field theories with different gauge groups. We match the full
partition functions of the dual phases for any value of the couplings to
underpin our proposals. We focus on two classes of models. The first class,
motivated by the AdS/CFT conjecture, consists of necklace U(N) quiver gauge
theories with non chiral matter fields. We also consider orientifold
projections and establish dualities among necklace quivers with alternating
orthogonal and symplectic groups. The second class consists of theories with
tensor matter fields with free theory duals. In most of these cases the
R-symmetry mixes with IR accidental symmetries and we develop the prescription
to include their contribution into the partition function and the extremization
problem accordingly.Comment: 38 pages, 3 figure, using jheppu
The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
We consider N = 3 supersymmetric Chern-Simons gauge theories with product
unitary and orthosymplectic groups and bifundamental and fundamental fields. We
study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov
matrix model. The saddlepoint equations in a large N limit lead to a constraint
that the long range forces between the eigenvalues must cancel; the resulting
quiver theories are of affine Dynkin type. We introduce a folding/unfolding
trick which lets us, at the level of the large N matrix model, (i) map quivers
with orthosymplectic groups to those with unitary groups, and (ii) obtain
non-simply laced quivers from the corresponding simply laced quivers using a
Z_2 outer automorphism. The brane configurations of the quivers are described
in string theory and the folding/unfolding is interpreted as the
addition/subtraction of orientifold and orbifold planes. We also relate the
U(N) quiver theories to the affine ADE quiver matrix models with a
Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in
2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.Comment: 30 pages, 5 figure
From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
The matrix model of Kapustin, Willett, and Yaakov is a powerful tool for
exploring the properties of strongly interacting superconformal Chern-Simons
theories in 2+1 dimensions. In this paper, we use this matrix model to study
necklace quiver gauge theories with {\cal N}=3 supersymmetry and U(N)^d gauge
groups in the limit of large N. In its simplest application, the matrix model
computes the free energy of the gauge theory on S^3. The conjectured F-theorem
states that this quantity should decrease under renormalization group flow. We
show that for a simple class of such flows, the F-theorem holds for our
necklace theories. We also provide a relationship between matrix model
eigenvalue distributions and numbers of chiral operators that we conjecture
holds more generally. Through the AdS/CFT correspondence, there is therefore a
natural dual geometric interpretation of the matrix model saddle point in terms
of volumes of 7-d tri-Sasaki Einstein spaces and some of their 5-d
submanifolds. As a final bonus, our analysis gives us the partition function of
the T(U(N)) theory on S^3.Comment: 3 figures, 41 pages; v2 minor improvements, refs adde
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