This series consists of talks in the area of Quantum Fields and Strings.
I will discuss the chiral algebra W_infty which is obtained from the Virasoro algebra by adding fields of spin 3, 4, .... Via a non-local non-linear map one can show that it is equivalent to Tsymbaliuk's Yangian of affine u(1). In this way we find an infinite number of commuting conserved charges. Diagonalizing these, the representation theory reduces to combinatorial study of plane partitions, 3-dimensional generalization of the Young diagrams. Tsymbaliuk's presentation can be derived from RTT relations using Maulik-Okounkov's free boson R-matrix.
Recently a boundary energy-momentum tensor Tzz has been constructed from the soft graviton operator for any 4D quantum theory of gravity in asymptotically flat space. Up to an "anomaly" which is one-loop exact, Tzz generates a Virasoro action on the 2D celestial sphere at null infinity. Here we show by explicit construction that the effects of the IR divergent part of the anomaly can be eliminated by a one-loop renormalization that shifts Tzz.
The subject of quantum field theory in mixed states of quantum matter is an old and rich one. The natural setting to discuss field theory in a mixed state is the Schwinger-Keldysh formalism. The subject of this talk is the set of peculiar symmetries that arise in Schwinger-Keldysh theories, and how they may be accounted for in effective field theory. In particular, when the mixed state is thermal, the effective description is constrained by two BRST-like supercharges which, at low energies, generate an algebra akin to minimal supersymmetric quantum mechanics.
The conformal bootstrap aims to calculate scaling dimensions and correlation functions in various theories, starting from general principles such as unitarity and crossing symmetry. I will explain that local operators are not independent of each other but organize into analytic functions of spin, and I will present a formula which quantifies the consequences of this fact. This will include a controlled approximation to the operator spectrum at large spin, as well as new bounds over the strength of bulk higher-derivative interactions in large-N theories with a sparse spectrum.
We study the eigenstate thermalization hypothesis in chaotic conformal ﬁeld theories (CFTs) of arbitrary dimensions by computing the reduced density matrices of small size in energy eigenstates. We show that in the inﬁnite volume limit this operator is well-approximated by a “universal” density matrix which is its projection to the primary operators that have nonzero thermal one-point functions. These operators in all two-dimensional CFTs and holographic higher-dimensional CFTs are the polynomials of stress tensor.
I will discuss a new class of supersymmetric Wilson loop operators in pure N=2 Yang-Mills-Chern-Simons theory. These Wilson loops preserve one supercharge on-shell and wrap arbitrary Legendrian knots in the standard contact R^3. I will also explain a relation, motivated by a global picture of contact three-manifolds, between these loop operators and chiral current algebra in two dimensions. This talk is directly related to, but independent of, my preceding Friday talk in the Mathematical Physics seminar.
In this talk I will discuss a new use for conformal field theory crossing equation in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. I will revisit this problem and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N^2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders.
In the first part of the talk, I will explain how the lengths of non-minimal geodesics in AdS3 conical defect backgrounds can be interpreted as the entanglement entropy of certain subalgebras in the dual CFT. This part will be based on 1608.02040. In the second part of the talk, I will discuss how the Ryu-Takayanagi area term seems to be the analog of a certain edge term for EE in a gauge theory, and how one might try to test this. This part is more speculative.
The moduli space of vacua of 3d N=4 gauge theories splits essentially into two ``branches”: the Higgs branch parametrised by the vevs of hypermultiplet scalars and the Coulomb branch parametrised by the vevs of dressed monopole operators. They can be described as complex algebraic varieties. I will present a new approach to the analysis of the Higgs and Coulomb branches based on the type IIB brane realisation of the gauge theory.
1. The notion of wall-crossing structure (as defined by Maxim Kontsevich and myself in arXiv: 1303.3253)
provides the universal framework for description of different types of wall-crossing formulas (e.g. Cecotti-Vafa in 2d or KSWCF in 4d). It also gives
a language and tools for proving algebraicity and analyticity of arising generating series (e.g. for BPS invariants).