Calendar

Kapustin and Witten have studied a one-parameter family of topological twists of 4d N=4 super Yang–Mills. They have shown that the categories of boundary conditions on a surface are exactly the categories participating in the geometric Langlands program of Beilinson and Drinfeld. Moreover, S-duality is manifested as a quantum geometric Langlands duality after the topological twist. In this talk I will describe some mathematical formalizations of Hilbert spaces of states on a 3-manifold. I will outline an equivalence between two such possible formalizations: complexified Floer homology of Abouzaid–Manolescu and skein modules. This is a report on work in progress joint with Sam Gunningham.

Zoom: https://harvard.zoom.us/j/94717938264

I will discuss the conditions under which Higgs and confining regimes in gauge theories with fundamental representation matter fields can be sharply distinguished. It is widely believed that these regimes are smoothly connected unless they are distinguished by the realization of global symmetries. However, I will show that when a U(1) global symmetry is spontaneously broken in both the confining and Higgs regimes, the two phases can be separated by a phase boundary. The phase transition between the two regimes may be detected by a novel topological vortex order parameter. I’ll illustrate these ideas by explicit calculations in gauge theories in three spacetime dimensions, and then explain the generalization to four dimensions. One important implication of our results is that nuclear matter and quark matter are sharply distinct phases of QCD with an approximate SU(3) flavor symmetry.

Zoom: https://harvard.zoom.us/j/977347126