Triangle Seminars

Abstract:
https://indico.global/event/14913/

Abstract:
String theory was arguably born with a scattering amplitude in 1968, and the formula came before its derivation. I will review the many aspects of scattering amplitudes in string theory with the aim of illustrating some of the recent advances. These combine insights from physics and mathematics and shine new light on these central observables and how they connect with quantum field theory

Abstract:
I will review the motivation and aims of symmetric mass generation (SMG), whereby fermions are gapped while preserving a chiral but necessarily non-anomalous symmetry. A simple model of SMG will be described, which leverages strongly-coupled gauge dynamics. I will then use CFT tools alongside bosonisation to derive the phase diagrams of a series of 2d Abelian gauge theories, including the 2d SMG model, in doing so establishing its validity. I will finally comment on the application of such constructions to symmetry-preserving boundary conditions and fermion-monopole scattering in 4d gauge theory.

Abstract:
In this talk we introduce the notion of generalized/categorical families of QFTs. These families of theories have a structure which is analogous to the categorical symmetries in Lagrangian QFTs and may be thought of as the family structure that arises when a categorical symmetry is explicitly broken by deformations of the action. After describing this structure, we will explain the anomalies of these families and their implications. We will then use this structure to study some higher dimensional deformations of 4d N=1 SUSY gauge theories.

Abstract:
A colouring of a graph with \(k\) colours is an assignment of colours to vertices so that no edge is monochromatic. As it is well-known colouring with 2 colours is in P while colouring with \(k > 2\) colours is NP-complete. This dichotomy was extended to the *graph homomorphism problem*, also called \(H\)-colouring, by Hell and Nešetřil [J. Comb. Theory B, 48(1):92-110, 1990]. More precisely, they proved that deciding whether there is a graph homomorphism from a given graph to a fixed graph \(H\) is in P if \(H\) is bipartite (or contains a self-loop), and is NP-complete otherwise. This dichotomy served as an important test-case for the Feder–Vardi dichotomy conjecture, and Bulatov–Zhuk dichotomy of complexity of finite-template CSPs.

In the talk, I will present a new proof of this theorem using tools from topological combinatorics based on ideas of Lovász [J. Comb. Theory, Ser. A, 25(3):319-324, 1978] and Brower’s fixed-point theorem. This is joint work with Sebastian Meyer (TU Dresden).

Abstract:
I will present some recent results on quantum integrable systems, such as the Gaudin model, the XXZ model, and their generalizations to all affine Kac-Moody algebras and their quantum deformations (quantum affine algebras). I will also explain how the problem of finding the spectra of the Hamiltonians in these models is connected to the geometric Langlands correspondence and the theory of q-characters of quantum affine algebras. This gives a new perspective on (and substitutes) the old method for finding these spectra, the Bethe Ansatz.

Abstract:
The SU(N) theory with 2N fundamental matter multiplets, in the vicinity of the so-called special vacuum - where the vacuum expectation values of the Higgs field are arranged near the vertices of a regular N-gon - is known to possess ⌊N/2⌋ effective coupling constants. I will show, however, that with the diameter of the polygon tending to infinity, a single effective coupling constant emerges. Moreover, this unique effective coupling enters the Zamolodchikov-like recurrence relation for the instanton partition function that remains valid for arbitrary vacuum expectation values, and is therefore meaningful beyond the special vacuum. By reconstructing the coupling matrix with simple symmetry and dimensional arguments, I will clarify the origin of this unique effective coupling. Finally, I will present the complete set of ⌊N/2⌋ effective couplings and discuss their modular properties, as well as the corrections induced by the masses of the matter multiplets.