23 research outputs found
High-Temperature Asymptotics of the 4d Superconformal Index.
This dissertation contains a study of certain four-dimensional superconformal field theories (4d SCFTs). Any 4d SCFT has a spectrum of local operators. Some of these operators sit in short representations of the 4d N=1 superconformal group SU(2,2|1), and can be quantified using a partition function known as the 4d superconformal index. The superconformal index I(b,beta) is a function of two positive real parameters: the squashing parameter b, and the inverse temperature
beta. Our study in the present dissertation is focused on the temperature- (or beta-) dependence of the superconformal index of 4d SCFTs.
The superconformal index of a typical Lagrangian 4d SCFT is given by a complicated special function known as an elliptic hypergeometric integral (EHI). The high-temperature limit of the index corresponds to the hyperbolic limit of the EHI. The hyperbolic limit of certain special EHIs has been analyzed by Eric Rains around 2006; extending Rains’s techniques, we discover a surprisingly rich structure in the high-temperature limit of a (rather large) class of EHIs that arise as the superconformal index of unitary Lagrangian 4d SCFTs with non-chiral matter content. Our result has implications for N=1 dualities, the AdS/CFT correspondence, and supersymmetric gauge dynamics on R^3 x S^1.
We also investigate the high-temperature asymptotics of the large-N limit of the superconformal index of a class of holographic 4d SCFTs (described by toric quiver gauge theories with SU(N) nodes). We show that from this study a rather general solution to the problem of holographic Weyl anomaly in AdS5/CFT4 at the subleading order (in the 1/N expansion) emerges.
Most of this dissertation is based on published works by Jim Liu, Phil Szepietowski, and the author. We include here a few previously unpublished results though, one of which is the high-temperature asymptotics of the superconformal index of puncture-less SU(2) class-S theories.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133352/1/ardehali_1.pd
On Exactly Marginal Deformations Dual to -Field Moduli of IIB Theory on SE
The complex dimension of the space of exactly marginal deformations for
quiver CFTs dual to IIB theory compactified on is known to be
generically three. Simple general formulas already exist for two of the exactly
marginal directions in the space of couplings, one of which corresponds to the
sum of the (inverse squared of) gauge couplings, and the other to the
-deformation. Here we identify the third exactly marginal direction,
which is dual to the modulus on the gravity side. This
identification leads to a relation between the field theory gauge couplings and
the vacuum expectation value of the gravity modulus that we further support by
a computation related to the chiral anomaly induced by added fractional branes.
We also present a simple algorithm for finding similar exactly marginal
directions in any CFT described by brane tiling, and demonstrate it for the
quiver CFTs dual to IIB theory compactified on and the Suspended
Pinch Point.Comment: 28 pages, JHEP style. v2: minor corrections, added references and
acknowledgements. v3: a number of speculative comments regarding the
application of the Konishi anomaly equation to our problem are removed. v4:
the proposal in Eq. (2.4) added back as a conjectur
Central charges from the superconformal index
We present prescriptions for obtaining the central charges, and , of a
four dimensional superconformal quantum field theory from the superconformal
index. At infinite , for holographic theories dual to Sasaki-Einstein
5-manifolds the prescriptions give the parts of the central
charges. This allows us, among other things, to show the exact AdS/CFT matching
of and for arbitrary toric quiver CFTs without adjoint matter that are
dual to smooth Sasaki-Einstein 5-manifolds. In addition, we include evidence
from non-holographic theories for the applicability of these results outside of
a holographic setting and away from the large- limit.Comment: 4+1 pages. v2: minor revisions and added acknowledgements. v3:
improved presentatio
Modified supersymmetric indices in AdS/CFT
We consider the AdS/CFT dualities proposed by
Eberhardt, where the bulk geometry is AdS, and the CFT is a deformation of the symmetric orbifold of
the supersymmetric sigma model (with ). The
elliptic genera of the two sides vanish due to fermionic zero modes, so for
microstate counting applications one must consider modified supersymmetric
indices. In an analysis similar to that of Maldacena, Moore, and Strominger for
the standard case of , we study the appropriate
helicity-trace index of the boundary CFTs. We encounter a strange phenomenon
where a saddle-point analysis of our indices reproduces only a fraction
(respectively ) of the
Bekenstein-Hawking entropy of the associated macroscopic black branes.Comment: v2: an outline added in the introductio
1/N^2 corrections to the holographic Weyl anomaly
We compute the O(1) contribution to holographic c-a for IIB supergravity on
AdS_5 x S^5/Z_n and on AdS_5 x T^{1,1}/Z_n. In both cases, we find agreement
with the dual field theory results, thus providing 1/N^2 checks of AdS/CFT with
reduced supersymmetry. Since the holographic computation involves a sum over
shortened multiplets in the KK tower, we provide some details on the S^5 and
T^{1,1} spectra in a form that is convenient when considering their Z_n
orbifolds. The computation for the even Z_n orbifolds of S^5 includes a sum
over the multiplets in the twisted sector that is essential for obtaining
agreement with the dual field theory.Comment: 23 pages, 2 figures. v2: minor corrections and references adde
from the superconformal index
We present a prescription for obtaining the difference of the central
charges, c-a, of a four dimensional superconformal quantum field theory from
its single-trace index. The formula is derived from a one-loop holographic
computation, but is expected to be valid independent of holography. We
demonstrate the prescription with several holographic and non-holographic
examples. As an application of our formula, we show the AdS/CFT matching of c-a
for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth
Sasaki-Einstein 5-manifolds.Comment: 19 pages. v2: minor changes, reference added. v3: minor
clarifications, published version. v4: a typo in Table 2 fixe
High-Temperature Expansion of Supersymmetric Partition Functions
Di Pietro and Komargodski have recently demonstrated a four-dimensional
counterpart of Cardy's formula, which gives the leading high-temperature
() behavior of supersymmetric partition functions
. Focusing on superconformal theories, we elaborate on the
subleading contributions to their formula when applied to free chiral and U(1)
vector multiplets. In particular, we see that the high-temperature expansion of
terminates at order . We also demonstrate how
their formula must be modified when applied to SU() toric quiver gauge
theories in the planar () limit. Our method for
regularizing the one-loop determinants of chiral and vector multiplets helps to
clarify the relation between the 4d superconformal index and
its corresponding supersymmetric partition function obtained by
path-integration.Comment: 15 pages plus appendices; v2: minor modifications and a "Note added";
v3: presentation improved and minor errors in app B correcte