Talks

I will present some results on three-dimensional gauge theory from the point of view of extended topological field theory. In this setting a theory is specified by describing its collection of boundary conditions - in our case, a collection of categories (standing in for 2d TFTs) with a prescribed symmetry group G. We will apply ideas from Seiberg-Witten geometry to construct a new commutative algebra of symmetries for categorical representations (or line operators in the gauge theory) -  a categorification of Kostant's description of the center of the enveloping algebra. (Joint with Sam Gunningham and David Nadler)

I will talk about the relation between non-local theories and gravity. The main thesis is that non-local field theories naturally induce gravity, even at the classical level. Supporting this idea, I will study bi-local scalar field theories, which involve minimal deviations from locality. We will treat them both, bi-local theories and gravity perturbatively. We will see that bi-local theories encode gravity together with higher spin fields.

We classify quantum states proximate to the semiclassical Neel state of the spin S=1/2 square lattice antiferromagnet with two-spin near-neighbor and four-spin ring exchange interactions. Motivated by a number of recent experiments on the cuprates and the iridates, we examine states with Z_2 topological order, an order which is not present in the semiclassical limit. Some of the states break one or more of reflection, time-reversal, and lattice rotation symmetries, and can account for the observations. We discuss implications for the pseudogap phase.

An overview will be given of recently discovered connection between asymptotic symmetries in general relativity  and soft theorems in quantum field theory together with their implications for the black hole information paradox.

We study the boundary conditions in the topologically twisted Chern-Simons matter theories with the Lie 3-algebraic structure. We find that the supersymmetric boundary conditions and the gauge invariant boundary conditions can be unified as the complexified gauge invariant boundary conditions which lead to the supergroup WZW models. We examine the BPS indices of the supergroup WZW models which may describe certain junctions of M2-branes and M5-branes by identifying the vacuum configurations of the brane system with the weight diagrams of the associated Lie superalgebras. For the case arising from the BLG model an explicit expression can be given in terms of a mock modular form. We will also consider the alternative matrix quantum mechanical descriptions of the supergroup WZW models. The talk will be based on recent works arXiv:1512.06646, arXiv:1612.07565 and ongoing research.