241 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
Z-extremization and F-theorem in Chern-Simons matter theories
The three dimensional exact R symmetry of N=2 SCFTs extremizes the partition
function localized on a three sphere. Here we verify this statement at weak
coupling. We give a detailed analysis for two classes of models. The first one
is an SU(N)_k gauge theory at large k with both fundamental and adjoint matter
fields, while the second is a flavored version of the ABJ theory, where the CS
levels are large but they do not necessarily sum up to zero. We study in both
cases superpotential deformations and compute the R charges at different fixed
points. When these fixed points are connected by an RG flow we explicitly
verify that the free energy decreases at the endpoints of the flow between the
fixed points, corroborating the conjecture of an F-theorem in three dimensions.Comment: 28 pages, 3 figures, JHEP.cls, minor corrections, references adde
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
Probing the Space of Toric Quiver Theories
We demonstrate a practical and efficient method for generating toric Calabi-Yau quiver theories, applicable to both D3 and M2 brane world-volume physics. A new analytic method is presented at low order parametres and an algorithm for the general case is developed which has polynomial complexity in the number of edges in the quiver. Using this algorithm, carefully implemented, we classify the quiver diagram and assign possible superpotentials for various small values of the number of edges and nodes. We examine some preliminary statistics on this space of toric quiver theories
Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
For 3-dimensional field theories with {\cal N}=2 supersymmetry the Euclidean
path integrals on the three-sphere can be calculated using the method of
localization; they reduce to certain matrix integrals that depend on the
R-charges of the matter fields. We solve a number of such large N matrix models
and calculate the free energy F as a function of the trial R-charges consistent
with the marginality of the superpotential. In all our {\cal N}=2
superconformal examples, the local maximization of F yields answers that scale
as N^{3/2} and agree with the dual M-theory backgrounds AdS_4 x Y, where Y are
7-dimensional Sasaki-Einstein spaces. We also find in toric examples that local
F-maximization is equivalent to the minimization of the volume of Y over the
space of Sasakian metrics, a procedure also referred to as Z-minimization.
Moreover, we find that the functions F and Z are related for any trial
R-charges. In the models we study F is positive and decreases along RG flows.
We therefore propose the "F-theorem" that we hope applies to all 3-d field
theories: the finite part of the free energy on the three-sphere decreases
along RG trajectories and is stationary at RG fixed points. We also show that
in an infinite class of Chern-Simons-matter gauge theories where the
Chern-Simons levels do not sum to zero, the free energy grows as N^{5/3} at
large N. This non-trivial scaling matches that of the free energy of the
gravity duals in type IIA string theory with Romans mass.Comment: 66 pages, 10 figures; v2: refs. added, minor improvement
The a-theorem and conformal symmetry breaking in holographic RG flows
We study holographic models describing an RG flow between two fixed points
driven by a relevant scalar operator. We show how to introduce a spurion field
to restore Weyl invariance and compute the anomalous contribution to the
generating functional in even dimensional theories. We find that the
coefficient of the anomalous term is proportional to the difference of the
conformal anomalies of the UV and IR fixed points, as expected from anomaly
matching arguments in field theory. For any even dimensions the coefficient is
positive as implied by the holographic a-theorem. For flows corresponding to
spontaneous breaking of conformal invariance, we also compute the two-point
functions of the energy-momentum tensor and the scalar operator and identify
the dilaton mode. Surprisingly we find that in the simplest models with just
one scalar field there is no dilaton pole in the two-point function of the
scalar operator but a stronger singularity. We discuss the possible
implications.Comment: 50 pages. v2: minor changes, added references, extended discussion.
v3: we have clarified some of the calculations and assumptions, results
unchanged. v4: published version in JHE
Metastable Vacua and the Backreacted Stenzel Geometry
We construct an M-theory background dual to the metastable state recently
discussed by Klebanov and Pufu, which corresponds to placing a stack of anti-M2
branes at the tip of a warped Stenzel space. With this purpose we analytically
solve for the linearized non-supersymmetric deformations around the warped
Stenzel space, preserving the SO(5) symmetries of the supersymmetric
background, and which interpolate between the IR and UV region. We identify the
supergravity solution which corresponds to a stack of backreacting
anti-M2 branes by fixing all the 12 integration constants in terms of
. While in the UV this solution has the desired features to describe
the conjectured metastable state of the dual (2+1)-dimensional theory, in the
IR it suffers from a singularity in the four-form flux, which we describe in
some details.Comment: 33 pages, 3 figure
Non-singlet Baryons in Less Supersymmetric Backgrounds
We analyze the holographic description of non-singlet baryons in various
backgrounds with reduced supersymmetries and/or confinement. We show that they
exist in all AdS_5xY_5 backgrounds with Y_5 an Einstein manifold bearing five
form flux, for a number of quarks 5N/8< k< N, independently on the
supersymmetries preserved. This result still holds for gamma_i deformations. In
the confining Maldacena-Nunez background non-singlet baryons also exist,
although in this case the interval for the number of quarks is reduced as
compared to the conformal case. We generalize these configurations to include a
non-vanishing magnetic flux such that a complementary microscopical description
can be given in terms of lower dimensional branes expanding into fuzzy baryons.
This description is a first step towards exploring the finite 't Hooft coupling
region.Comment: 36 Pages, 1 figure, Latex, v2: few minor changes, JHEP versio
Aspects of ABJM orbifolds with discrete torsion
We analyze orbifolds with discrete torsion of the ABJM theory by a finite
subgroup of . Discrete torsion is implemented by
twisting the crossed product algebra resulting after orbifolding. It is shown
that, in general, the order of the cocycle we chose to twist the algebra by
enters in a non trivial way in the moduli space. To be precise, the M-theory
fiber is multiplied by a factor of in addition to the other effects that
were found before in the literature. Therefore we got a
action on the fiber. We present a general
analysis on how this quotient arises along with a detailed analysis of the
cases where is abelian
F-Theorem without Supersymmetry
The conjectured F-theorem for three-dimensional field theories states that
the finite part of the free energy on S^3 decreases along RG trajectories and
is stationary at the fixed points. In previous work various successful tests of
this proposal were carried out for theories with {\cal N}=2 supersymmetry. In
this paper we perform more general tests that do not rely on supersymmetry. We
study perturbatively the RG flows produced by weakly relevant operators and
show that the free energy decreases monotonically. We also consider large N
field theories perturbed by relevant double trace operators, free massive field
theories, and some Chern-Simons gauge theories. In all cases the free energy in
the IR is smaller than in the UV, consistent with the F-theorem. We discuss
other odd-dimensional Euclidean theories on S^d and provide evidence that
(-1)^{(d-1)/2} \log |Z| decreases along RG flow; in the particular case d=1
this is the well-known g-theorem.Comment: 34 pages, 2 figures; v2 refs added, minor improvements; v3 refs
added, improved section 4.3; v4 minor improvement
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