Conference

I will discuss the interplay between 2d de Sitter and supersymmetry in two concrete supergravity models coupled to superconformal field theories. Upon fixing a supersymmetric analogue of the Weyl gauge these theories can be viewed as supersymmetric extensions of timelike Liouville theory with N=1 and N=2 supersymmetry respectively. Supersymmetric timelike Liouville is well behaved in the UV and combines supersymmetry with a positive cosmological constant and a de Sitter saddle. The theory is amenable to a variety of techniques including systematic loop expansions and localization methods.

In this talk we will analyze renormalization group flows on d-dimensional planar defects, embedded in a D-dimensional conformal field theory. This general setup includes the case of quantum field theory with no defects ($D=d$), as well as defects of different dimensionality that are of interest in high energy and condensed matter physics. Using methods from quantum information theory, we will establish the irreversibility of renormalization group flows for defect dimensions $d \le 4$, and for all $D$. The main ingredients in the proof are strong subadditivity of the entanglement entropy, the Markov property of the conformal vacuum, and the quantum null energy condition.

I will review some recent developments that attempt to put modern mathematical tools and structural insights to effective use in physics. The focus will be on two such tools. The first is a perspective on superspace geometry that leads to powerful structural analogies between twisted theories (which encode the dynamics of particular BPS subsectors) and their untwisted parents. The second deals with generalizations of typical field theories akin to the generalization from symplectic to Poisson phase spaces. As an application, one obtains an object with N=(2,0) superconformal symmetry in six dimensions. Working at the holomorphic level on flat space, this object becomes the current algebra of the exceptional simple superalgebra E(3|6), which localizes to the W_2 algebra and dimensionally reduces to sl(2) super Yang-Mills theory. This is a mixture of joint work with numerous collaborators, in particular Hahner, Raghavendran, and Williams.

I will explain a new 2d gravity/matrix model duality. The bulk theory can be defined as a minimal string theory whose matter sector is given by timelike Liouville theory instead of a minimal model. The theory admits a dual description in terms of a double-scaled matrix integral whose leading density of states is given by the universal Cardy density of states in a 2d CFT of central charge c, thus motivating us to call the bulk theory the Virasoro minimal string. The duality can be derived by exploiting a certain relation to 3d gravity compactified on a circle. For large central charge, it reduces to the duality between JT-gravity and the corresponding double-scaled matrix integral. Based on work in collaboration with Scott Collier, Beatrix Mühlmann and Victor Rodriguez.

Richard Feynman's last blackboard at Caltech contains a number of tantalizing inscriptions about Bethe Ansatz in quantum integrable models, which fascinated him in the last years of his life. After reviewing some basic examples, I will present a modern perspective on the subject, linking it to dualities in QFT and String Theory, as well as the Langlands duality in mathematics. I will then discuss some recent developments that lend support to Feynman's intuition that these ideas could be useful in the study of 4d gauge theory, and formulate some open questions.