This series consists of talks in the area of Superstring Theory.
Warped AdS3 has isometry SL(2,R) x U(1). It is closed
related to Kerr/CFT, non local dipole theories and AdS/CMT. In this talk I will
derive the spectrum of string theory on
Warped AdS3. This is possible because the worldsheet theory can be
mapped to the worldsheet on AdS3 by a nonlocal field redefinition.
In this talk, I will
relate moduli stabilization in AdS or de Sitter space to basic properties of
the Wilsonian action in the holographic dual theory living on dS (of one lower
dimension): the single-trace terms in the action have vanishing beta
functions, and higher-trace couplings are determined purely from lower-trace
ones (a property we refer to as the iterative structure of RG). In the dS
case, this encodes the maximal symmetry of the bulk spacetime in a quantity
which is accessible within a single observer's patch.
Chern-Simons contact terms constitute new
observables in three-dimensional quantum field theory. In N=2 supersymmetric
theories with an R-symmetry, they lead to a superconformal anomaly. This
understanding clarifies several puzzles surrounding the S3 partition function
of these theories. In particular, it leads to a proof of the F-maximization
principle. Chern-Simons contact terms
can be computed exactly using localization and lead to new tests of proposed
dualities.
The existence of a
positive linear functional acting on the space of (differences between)
conformal blocks has been shown to rule out regions in the parameter space of
conformal field theories (CFTs). We argue that at the boundary of the allowed
region the extremal functional contains, in principle, enough information to
determine the dimensions and OPE coefficients of an infinite number of
operators appearing in the correlator under analysis. Based on this idea we
develop the Extremal Functional Method (EFM), a numerical procedure for
I will present recent developments in the computation of
three point functions in the AdS4/CFT3 correspondence. More specifically I will
consider two different computations for three point functions of operators
belonging to the SU(2)XSU(2) sector of ABJM. I
will discuss first the generalization of the
determinant representation, found by Foda for the three-point functions of
the SU(2) sector of N = 4 SYM, to the ABJM theory and
I will discuss recent progress in the study of
anomaly-induced transport, focusing on the chiral vortical effect in 3+1 dimensions.
Most of my discussion will be framed in light of a larger story, namely
progress in making exact statements about finite-temperature quantum field
theory, for which the chiral magnetic and vortical effects are instructive
prototypes.
Recently techniques have been developed to compute the
partition functions of 3d theories with N=2 supersymmetry on curved, compact
spaces, in particular S^3 and S^2xS^1 (the latter giving a supersymmetric
index). I will discuss how both of these partition functions can be decomposed
as products of more fundamental, universal "holomorphic blocks." For
3d gauge theories arising from (auxiliary) 3-manifolds M, these holomorphic
blocks are specific Chern-Simons partition functions on M.
String-like objects arise in many quantum field theories.
Well known examples include flux tubes in QCD and cosmic strings. To a first approximation,
their dynamics is governed by the Nambu-Goto action, but for QCD flux tubes
numerical calculations of the energy levels of these objects have become so
accurate that a systematic understanding of corrections to this simple
description is desirable.
The entanglement entropy S(R) across a circle of radius R
has been invoked recently in deriving general constraints on renormalization
group flow in three-dimensional field theory.
At conformal fixed points, the negative of the finite part of the
entanglement entropy, which is called F, is equal to the free energy on the
round three-sphere. The F-theorem states that F decreases under RG flow.
Integrability has been successfully used to compute the
non-perturbative spectrum, Wilson loops and scattering amplitudes in the
AdS/CFT correspondence. Most of these results apply to N=4, D=4 SYM / strings
on AdS(5)xS(5). Strings on AdS(3)xM, where M is either