Sixty-Third Meeting of the North British Mathematical Physics Seminar

The sixty-third meeting of the North British Mathematical Physics Seminar was held on Saturday 13th November 2021 in Durham, in Room MCS0001 (the Scott Logic lecture theatre) in the Department of Mathematical Sciences and on Zoom. These were the participants at the meeting.

Provisional Programme

11:00-11:30
Tea/Coffee
11:30-12:30
Andreas BRAUN (Durham University)
The fate of higher form symmetries in string compactification

Theories of quantum gravity not only require the absence of ordinary global symmetries, but also of higher form symmetries. We study theories of quantum gravity using F-Theory compactification in which such symmetries are manifestly absent, but can exist in decompactification limits. By examining how the resulting non-compact geometries are glued to the original compact one, we find that there can be unbroken 2-form symmetries even in a compact setting. In a theory of quantum gravity these must hence be gauged. We give further evidence for this proposal using dual perspectives in which gauged 2-form symmetries are mapped to the global structure of the gauge group.

12:30-13:00
Gabriele DIAN (Durham University)
Amplituhedron-Like Geometries and the Product of Amplitudes

The on-shell superspace formulation of N=4 SYM allows the writing of all possible scattering processes in one compact object called the super-amplitude. Famously, the super-amplitude integrand can be extracted from generalized polyhedra called the amplituhedron. In this talk, I review this construction and present a natural generalization of the amplituhedron that we proved at tree level and conjectured at loop level to correspond to the product of two parity conjugate superamplitudes. The sum of all parity conjugate amplitudes corresponds to a particular limit of the supercorrelator through the Wilson Loop/Amplitude duality. I will conclude by discussing this connection from a geometrical point of view. This talk is based on the recent work arXiv:2106.09372.

13:00-14:00
Lunch
14:00-15:00
Clare DUNNING (University of Kent)
On Wronskians of orthogonal polynomials and applications

Wronskians of certain orthogonal polynomials arise in a variety of areas including integrable systems, random matrix theory, supersymmetric quantum mechanics and are associated with rational solutions of certain Painleve equations. As well as showing that they play a key role in an example of the ODE/IM correspondence, I'll describe how the combinatorics of the underlying partitions play a curious role in properties of Wronskian polynomials.

15:00-15:30
Daniele FAROTTI (University of Surrey)
Supersymmetry Enhancement of Heterotic Horizons

The supersymmetry of near-horizon geometries in heterotic supergravity is considered. A necessary and sufficient condition for a solution to preserve more than the minimal \(\mathcal{N} = 2\) supersymmetry is obtained. A supersymmetric near-horizon solution is constructed which is a \(U(1)\) fibration of \(AdS_3\) over a particular Aloff-Wallach space. It is proven that this solution preserves the conditions required for \(\mathcal{N} = 2\) supersymmetry, but does not satisfy the necessary condition required for further supersymmetry enhancement. Hence, there exist supersymmetric near-horizon heterotic solutions preserving exactly \(\mathcal{N} = 2\) supersymmetry.

15:30-16:00
Tea/Coffee
16:00-17:00
Ben HOARE (Durham University)
The relation between Yang-Baxter deformations and perturbations of gauged WZW models

In recent years there has been a proliferation of new integrable sigma-models. Many of these have come from new organisational frameworks and exploiting the tools of deformations and dualities. To retain control of the landscape of models, it helps to understand the relations between them. In this talk we will review two such deformations, the Yang-Baxter deformation of the SSSM and parafermion deformations of the gauged WZW model, and explore how they are related by both duality transformations and scaling limits.

17:00--
Post-meeting discussions in pub and/or over dinner. All are welcome.

Douglas Smith
Last modified: 21 November 2021