I will discuss constructions of supersymmetric interfaces in quantum field theories with eight supercharges, both within one theory and between different theories, that provide physical realizations of certain geometric constructions in the context of quiver varieties (such as stable envelopes and actions of Yangians/quantum loop/quantum elliptic algebras). The basic building blocks are supersymmetric Janus interfaces that realize stable envelopes introduced … Read More
I will discuss supergroup gauge theory with emphasis on the following aspects: instanton counting, Seiberg-Witten geometry, brane construction, realization in topological string and intersecting defects, Bethe/Gauge correspondence, and quantum algebraic structure. Based on joint works with H.-Y. Chen, N. Lee, F. Nieri, V. Pestun, and Y. Sugimoto (mostly summarized in https://arxiv.org/abs/2012.11711).
For the most up to date information, see:http://www.birs.ca/events/2021/5-day-workshops/21w5105/schedule
Khovanov showed, more than 20 years ago, that Jones polynomial emerges as an Euler characteristic of a homology theory. The knot categorification problem is to find a uniform description of this theory, for all gauge groups, which originates from physics, or from geometry. In these lectures, I will describe two solutions to this problem, which originate in string theory, and … Read More
Khovanov showed, more than 20 years ago, that Jones polynomial emerges as an Euler characteristic of a homology theory. The knot categorification problem is to find a uniform description of this theory, for all gauge groups, which originates from physics, or from geometry. In these lectures, I will describe two solutions to this problem, which originate in string theory, and … Read More
Khovanov showed, more than 20 years ago, that Jones polynomial emerges as an Euler characteristic of a homology theory. The knot categorification problem is to find a uniform description of this theory, for all gauge groups, which originates from physics, or from geometry. In these lectures, I will describe two solutions to this problem, which originate in string theory, and … Read More
Khovanov showed, more than 20 years ago, that Jones polynomial emerges as an Euler characteristic of a homology theory. The knot categorification problem is to find a uniform description of this theory, for all gauge groups, which originates from physics, or from geometry. In these lectures, I will describe two solutions to this problem, which originate in string theory, and … Read More
We introduce the notions of (G,q)-opers and Miura (G,q)-opers, where G is a simply-connected complex simple Lie group, and prove some general results about their structure. We then establish a one-to-one correspondence between the set of (G,q)-opers of a certain kind and the set of nondegenerate solutions of a system of Bethe Ansatz equations. Additionally we associate to a (G,q)-oper … Read More
Abstract: In the “Euclidean” approach to quantum gravity, it sometimes seems useful to include complex saddle points. But what class of complex spacetime metrics is physically sensible? That will be the topic of this lecture.