Sixtieth Meeting of the North British Mathematical Physics Seminar

The sixtieth meeting of the North British Mathematical Physics Seminar was held via Zoom on Tuesday 24th November 2020.

These were the participants at the meeting.

Programme

14:00-14:45
Sylvain LACROIX (University of Hamburg)
Integrable sigma-models: new examples and renormalisation

I will present recent developments in the study of integrable sigma models. After reviewing the definition of a coupled integrable model on an arbitrary number of copies of a Lie group, I will discuss its underlying geometry and its one-loop renormalisation group flow, leading to a conjecture for the renormalisation of a general class of integrable sigma models. I will then present the construction of new integrable sigma models defined on the quotient of copies of a Lie group by a well-chosen diagonal subgroup and their applications to \(T^{1,1}\) manifolds.

14:45-15:30
Madalena LEMOS (Durham University)
Superconformal surface defects and vertex operator algebras

We will motivate and introduce the study of conformal defects in superconformal field theories (SCFTs). We will show how symmetries constrain the anomaly coefficients of BPS defects. In the case of N=(2,2) surface defects in four-dimensional N=2 SCFTs these anomaly coefficients can be computed by studying a protected subsector captured by a vertex operator algebra, or two-dimensional chiral algebra.

15:30-15:45
Short Break
15:45-16:30
Tudor DIMOFTE (University of Edinburgh)
Categorifying the Schur Index

The Schur index of a 4d N=2 theory counts local operators in the cohomology of a particular supercharge Q. In superconformal theories, it was shown to coincide with the character of an associated VOA. I will discuss some current work with Wenjun Niu that goes in a (literally) orthogonal direction, explaining how local operators in Q-cohomology arise from a geometric description of the category of line operators in 4d N=2 theories (due to Kapustin and Cautis-Williams), and how this idea generalizes to operators at junctions of Wilson-'t Hooft lines, bound to surface defects, and in the presence of boundary conditions (half-indices). Mathematically, derived algebraic geometry plays a key role throughout.

16:30-17:00
Vincenzo MAROTTA (Heriot-Watt University)
Born Geometry and Generalised T-duality

I will briefly introduce the notion of para-Hermitian geometry and how to define a compatible generalised metric. This allows the construction of a sigma-model associated with these structures. Then I will discuss the reduction of such metric to the leaf space of a para-Hermitian manifold via a Lie algebroid gauging, thus obtaining a reduced sigma-model. I will also show how para-Hermitian morphisms play the role of generalised T-dualities and their relation with ordinary T-duality.

17:00--1800

Post-meeting Virtual Pub discussions.


Douglas Smith
Last modified: 1 December 2020