1,475 research outputs found
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
Integrability on the Master Space
It has been recently shown that every SCFT living on D3 branes at a toric
Calabi-Yau singularity surprisingly also describes a complete integrable
system. In this paper we use the Master Space as a bridge between the
integrable system and the underlying field theory and we reinterpret the
Poisson manifold of the integrable system in term of the geometry of the field
theory moduli space.Comment: 47 pages, 20 figures, using jheppub.st
p-wave Holographic Superconductors and five-dimensional gauged Supergravity
We explore five-dimensional and
SO(6) gauged supergravities as frameworks for condensed matter applications.
These theories contain charged (dilatonic) black holes and 2-forms which have
non-trivial quantum numbers with respect to U(1) subgroups of SO(6). A question
of interest is whether they also contain black holes with two-form hair with
the required asymptotic to give rise to holographic superconductivity. We first
consider the case, which contains a complex two-form potential
which has U(1) charge . We find that a slight
generalization, where the two-form potential has an arbitrary charge , leads
to a five-dimensional model that exhibits second-order superconducting
transitions of p-wave type where the role of order parameter is played by
, provided . We identify the operator that condenses
in the dual CFT, which is closely related to Super Yang-Mills
theory with chemical potentials. Similar phase transitions between R-charged
black holes and black holes with 2-form hair are found in a generalized version
of the gauged supergravity Lagrangian where the two-forms have
charge .Comment: 35 pages, 14 figure
N=1 Chern-Simons theories, orientifolds and Spin(7) cones
We construct three dimensional N=1 Chern-Simons theories living on M2 branes
probing Spin(7) cones. We consider Spin(7) manifolds obtained as quotients of
Calabi-Yau four-folds by an anti-holomorphic involution, following a
construction by Joyce. The corresponding Chern-Simons theories can be obtained
from N=2 theories by an orientifolding procedure. These theories are
holographically dual to M theory solutions AdS_4 \times H, where the weak G_2
manifold H is the base of the Spin(7) cone.Comment: 26 pages, 3 figures, reference added
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
Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
The localization formula of Chern-Simons quiver gauge theory on nicely
reproduces the geometric data such as volume of Sasaki-Einstein manifolds in
the large- limit, at least for vector-like models. The validity of
chiral-like models is not established yet, due to technical problems in both
analytic and numerical approaches. Recently Gulotta, Herzog and Pufu suggested
that the counting of chiral operators can be used to find the eigenvalue
distribution of quiver matrix models. In this paper we apply this method to
some vector-like or chiral-like quiver theories, including the triangular
quivers with generic Chern-Simons levels which are dual to in-homogeneous
Sasaki-Einstein manifolds . The result is consistent
with AdS/CFT and the volume formula. We discuss the implication of our
analysis.Comment: 23 pages; v2. revised version; v3. corrected typos and clarified
argument
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
M5 spikes and operators in the HVZ membrane theory
In this note we study some aspects of the so-called dual ABJM theory
introduced by Hanany, Vegh & Zaffaroni. We analyze the spectrum of chiral
operators, and compare it with the spectrum of functions on the mesonic moduli
space M=C^2\times C^2/Z_k, finding expected agreement for the coherent branch.
A somewhat mysterious extra branch of dimension N^2 opens up at the orbifold
fixed point. We also study BPS solutions which represent M2/M5 intersections.
The mesonic moduli space suggests that there should be two versions of this
spike: one where the M5 lives in the orbifolded C^2 and another where it lives
in the unorbifolded one. While expectedly the first class turns out to be like
the ABJM spike, the latter class looks like a collection of stacks of M5 branes
with fuzzy S^3 profiles. This shows hints of the appearance of the global SO(4)
at the non-abelian level which is otherwise not present in the bosonic
potential. We also study the matching of SUGRA modes with operators in the
coherent branch of the moduli space. As a byproduct, we present some formulae
for the laplacian in conical CY_4 of the form C^n\times CY_{4-n}.Comment: 22 pages, 1 figure. Published version with corrected typos
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
Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence
We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3
correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of
the boundary conditions for vector fields in AdS_4 allows for a choice where
wrapped M5 brane states carrying non-zero charge under such symmetries can be
considered. We begin by focusing on isolated toric singularities without
vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary
conditions considered are dual to a CFT where the gauge group is U(1)^2 x
SU(N)^4. We find agreement between the spectrum of gauge-invariant
baryonic-type operators in this theory and wrapped M5 brane states. Moreover,
the physics of vacua in which these symmetries are spontaneously broken
precisely matches a dual gravity analysis involving resolutions of the
singularity, where we are able to match condensates of the baryonic operators,
Goldstone bosons and global strings. We also argue more generally that theories
where the resolutions have six-cycles are expected to receive non-perturbative
corrections from M5 brane instantons. We give a general formula relating the
instanton action to normalizable harmonic two-forms, and compute it explicitly
for the Q^{222} example. The holographic interpretation of such instantons is
currently unclear.Comment: 92 pages, 10 figure
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