71st North British Mathematical Physics Seminar

Abstract: In this talk I will introduce holomorphic higher Chern-Simons theory (based on 2-Lie algebras). This is an example of a higher gauge theory in five-dimensions with a disorder defect which allows boundary localisation to a three-dimensional theory. The resulting model is integrable and its symmetry algebra can be understood as a homotopical generalisation of the affine Kac Moody algebra. This suggest that the three dimensional theory could be understood as a higher-dimensional analogue of WZW. This talk is based on joint work [arXiv:2405.18625] with Hank Chen.

Abstract: Holomorphic Chern-Simons theory on twistor has received significant interest in recent years due to its profound role in generating lower dimensional integrable field theories, making use of the Ward transform and symmetry reduction to do so. In this talk, we will display recent work in extending the framework of holomorphic Chern-Simons theory to encompass lower dimensional integrable theories that exhibit gauge symmetry. Indeed, gauging integrable field theories is a subtle art, with most naive attempts at gauging rendering the resulting gauged theory non-integrable. We will show that this problem can be easily navigated when formulating a theory using a local action on twistor space.

Abstract: The Nambu-Goto action can be related to an integrable deformation of a free theory. The scattering of excitations on the two-dimensional worldsheet of the string is then very simple, given by a pure phase. In this talk I will consider the setup of a membrane in flat space. I will analyse the dynamics of excitations on the three-dimensional worldvolume of the membrane, and also compactify the theory on a circle. I will present the perturbative S-matrix, compare with the Nambu-Goto case, and discuss the integrability of the model.

Abstract: In the context of rational conformal field theories (RCFT) we review the concept of a fusing matrix and look at the fusing matrices that arise when a topological defect is attached to a conformal boundary condition. We call such junctions open topological defects. One type of fusing matrices arises when two open defects fuse while another arises when an open defect passes through a boundary operator. We will briefly describe our procedure of calculating these matrices for any given RCFT based on the topological field theory approach to RCFTs. Finally, we explore applications mainly to boundary renormalisation group flows for the rational free boson theories.

Abstract: A myriad of generalisations and extensions of the BMS3 algebra have seen a surge interest in the recent years due to their relations to various areas of physics, such as flat-space holography, tensionless strings, ambitwistor strings, soft-theorems, AdS3 gravity etc. In this talk, the construction of the BRST complexes of these algebras resulting from studying their semi-infinite cohomology using VOA techniques is discussed. Some embedding theorems and their formulation in terms of twisted N=2 SCFTs are also presented, along with a few preliminary implications of our findings to special cases of these algebras that are of interest.

Practical Information

Limited funds are available to help with travel expenses of those with no other source of funding, especially postgraduate students and postdocs. Please book early to take advantage of the cheaper advance-purchase train fares. For how to claim please see the main NBMPS page.

Zoom invitations will be sent out to the NBMPS list and the local groups closer to the meeting.

If you have any questions, please email the local organiser, Benoit Vicedo. There is no need to notify us in order to attend.

71st North British Mathematical Physics Seminar

Programme

Practical Information