Sixty-Ninth Meeting of the North British Mathematical Physics Seminar

In this talk, I will describe an intricate interplay between Calabi-Yau geometry and black hole physics. In particular, I will show how 5d supergravity theories, constructed by compactifications of M-theory on a Calabi-Yau threefold, are a useful testing ground for the Weak Gravity Conjecture. In the process, I will describe how the physics of 5d supergravity can be used to generate the full Kahler moduli space and the effective cone of a Calabi-Yau threefold.

As in Minkowskian QFT, for each unitary free field theory in D-dimensional de Sitter (dS) space, one can construct a `dictionary’ between the corresponding one-particle Hilbert space and a Unitary Irreducible Representation of the dS algebra, so(D,1). Such a dictionary for bosonic fields of any spin has been constructed by Higuchi. However, the dictionary for fermionic higher-spin fields is absent from the literature. In this talk, we will make a first attempt to fill this gap in the case of the spin-3/2 field. Remarkably, we find that 4-dimensional dS space plays a distinguished role in the unitarity of the massless spin-3/2 field (i.e. gravitino). In particular, this field theory cannot be unitary unless D=4. This talk is based on https://doi.org/10.1007/JHEP05(2023)015.

Wetterich equations are renormalisation group equations that find applications in many physical problems, notably including the asymptotic safety approach to quantum gravity. They were traditionally formulated in the Euclidean signature on flat spacetime. In a recent paper with d'Angelo, Drago and Pinamonti, we have formulated a Lorentzian analog thereof, which can be applied in QFT on curved spacetimes.

‘t Hooft anomaly matching is an important tool to probe the IR physics of a given gauge theory. When we place a theory on a torus, we can get new ‘t Hooft anomalies associated to generalized fractional fluxes. In a new class of chiral gauge theories, we will discuss these generalized anomalies we call CFU (Colour-Flavour-U(1)) anomalies and the possible ways they could be matched in the IR.

Chiral magnets exhibit 2-dimensional localised topological soliton excitations coined magnetic skyrmions. There is currently significant interest in developing techniques to control these particle like excitations in the lab. I will argue, that taking a more geometric approach to their dynamics, governed by the first order Landau–Lifshitz–Gilbert equation, offers additional insight into their properties. In the first part of my talk, I will reframe known results about breather solutions in terms of symplectic flow. In particular, I will describe breather solutions as coupled modes that form symplectic pairs. I will then use this geometric viewpoint to consider their more complicated current driven dynamics. In particular, by expanding the standard Thiele approximation, I will show that the symplectic pairs that couple to the current depend intrinsically on the skyrmion’s symmetry and topology. I will then compare the approximation with full numeric simulations of the LLG equation. This is based on ongoing work in collaboration with Bernd Schroers at the University of Edinburgh.

Generalised Eisenstein series are modular-invariant functions that satisfy a Laplace eigenvalue equation with a source-term that is bilinear in ordinary non-holomorphic Eisenstein series. These functions appear in a variety of contexts related to string theory and N=4 super Yang-Mills theory, where, in particular, they encode non-perturbative information. In this talk I will look at certain resurgent properties these functions have and discuss a construction of spectra that are relevant for physical applications. The non-trivial zeros of the Riemann zeta function also make an unexpected appearance.