244 research outputs found
Modular Constraints on Superconformal Field Theories
We constrain the spectrum of and
superconformal field theories in two-dimensions by requiring the NS-NS sector
partition function to be invariant under the congruence
subgroup of the full modular group . We employ semi-definite
programming to find constraints on the allowed spectrum of operators with or
without charges. Especially, the upper bounds on the twist gap for the
non-current primaries exhibit interesting peaks, kinks, and plateau. We
identify a number of candidate rational (S)CFTs realized at the numerical
boundaries and find that they are realized as the solutions to modular
differential equations associated to . Some of the candidate
theories have been discussed by H\"ohn in the context of self-dual extremal
vertex operator (super)algebra. We also obtain bounds for the charged operators
and study their implications to the weak gravity conjecture in AdS.Comment: 50 pages, 16 figure
On the Holography of Free Yang-Mills
We study the AdS/CFT duality where the boundary CFT is free
Yang-Mills theory with gauge group SU(N). At the planar level we use the
spectrum and correlation functions of the boundary theory to explicate features
of the bulk theory. Further, by computing the one-loop partition function of
the bulk theory using the methods of arXiv:1603.05387, we argue that the bulk
coupling constant should be shifted to from . Similar conclusions
are reached by studying the dualities in thermal AdS with
boundary.Comment: 44 pages, version to appear in JHE
Monster Anatomy
We investigate the two-dimensional conformal field theories (CFTs) of
, and `dual' to the critical Ising
model, the three state Potts model and the tensor product of two Ising models,
respectively. We argue that these CFTs exhibit moonshines for the double
covering of the baby Monster group, , the triple covering of
the largest Fischer group, and multiple-covering of
the second largest Conway group, . Various
twined characters are shown to satisfy generalized bilinear relations involving
Mckay-Thompson series. We also rediscover that the `self-dual' two-dimensional
bosonic conformal field theory of has the Conway group
as an automorphism group.Comment: 23 pages, revised according to suggestions from JHEP refere
Exploring Free Matrix CFT Holographies at One-Loop
We extend our recent study on the duality between stringy higher spin
theories and free CFTs in the adjoint representation to other matrix
models namely the free and adjoint models as well as the free
bi-fundamental and bi-vector models. After
determining the spectrum of the theories in the planar limit by Polya counting,
we compute the one loop vacuum energy and Casimir energy for their respective
bulk duals by means of the CIRZ method that we have introduced recently. We
also elaborate on possible ambiguities in the application of this method.Comment: 37 pages, 7 figure
Modular Constraints on Conformal Field Theories with Currents
We study constraints coming from the modular invariance of the partition
function of two-dimensional conformal field theories. We constrain the spectrum
of CFTs in the presence of holomorphic and anti-holomorphic currents using the
semi-definite programming. In particular, we find the bounds on the twist gap
for the non-current primaries depend dramatically on the presence of
holomorphic currents, showing numerous kinks and peaks. Various rational CFTs
are realized at the numerical boundary of the twist gap, saturating the upper
limits on the degeneracies. Such theories include Wess-Zumino-Witten models for
the Deligne's exceptional series, the Monster CFT and the Baby Monster CFT. We
also study modular constraints imposed by -algebras of various
type and observe that the bounds on the gap depend on the choice of
-algebra in the small central charge region.Comment: 49 pages, 23 figure
Rademacher Expansions and the Spectrum of 2d CFT
A classical result from analytic number theory by Rademacher gives an exact
formula for the Fourier coefficients of modular forms of non-positive weight.
We apply similar techniques to study the spectrum of two-dimensional unitary
conformal field theories, with no extended chiral algebra and . By
exploiting the full modular constraints of the partition function we propose an
expression for the spectral density in terms of the light spectrum of the
theory. The expression is given in terms of a Rademacher expansion, which
converges for spin . For a finite number of light operators the
expression agrees with a variant of the Poincare construction developed by
Maloney, Witten and Keller. With this framework we study the presence of
negative density of states in the partition function dual to pure gravity, and
propose a scenario to cure this negativity.Comment: 30 pages, 5 figure
Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds
We study the twisted index of 4d = 2 class S theories on a
closed hyperbolic 3-manifold . Via 6d picture, the index can be written in
terms of topological invariants called analytic torsions twisted by irreducible
flat connections on the 3-manifold. Using the topological expression, we
determine the full perturbative 1/N expansion of the twisted index. The leading
part nicely matches the Bekestein-Hawking entropy of a magnetically charged
black hole in the holographic dual with near-horizon.Comment: 10 pages, v2: minor corrections and references adde
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