Fifty-First Meeting of the North British Mathematical Physics Seminar

Three-dimensional QCD theories flow towards strong coupling, leading to interesting low energy phases with conformal invariance or spontaneously broken flavour symmetry, depending on the number of colours and flavours. With supersymmetry each theory has degenerate vacua, and the low energy physics also depends on which vacuum is chosen. In this talk I will focus on three dimensional superQCD with eight supercharges, which strike a perfect balance between rich low energy physics and theoretical control. I will explain how the recent understanding of their Coulomb branch of vacua allows us to determine their infrared physics for any number of colours and flavours and any vacuum. This is joint work with Benjamin Assel (CERN).

The AdS/CFT correspondence can be used to solve quantum field theory problems using string theory frameworks, and vice versa. While initially focusing on solely on the relationship between Conformal Field Theories and string theories in the Anti-de Sitter spacetime, similar techniques have proved to have far wider applications. Recent work has show that these techniques can be used to successfully model mesons. In particular, the combination of this method and the instanton method shows particular promise in calculating meson decay rates. I will present the background of this technique, beginning with introducing a toy 2 dimensional model. I will then present my more recent work on a more realistic model using the Sakai-Sugimoto spacetime in for the string picture.

In order to study the weakly coupled regime of some given quantum theory we often make use of perturbative expansions of the physical quantities of interest. But such expansions are often divergent, and defined only as asymptotic series. This divergence is connected to the existence of nonperturbative contributions, i.e. instanton effects not captured by a perturbative analysis. The theory of resurgence perfectly captures this connection and its consequences. Moreover, it allows us to construct a full non-perturbative solution from perturbative data.

In this talk, I will analyse essential role of resurgence theory in a variety of problems appearing in gauge and string theories. I will focus in how to effectively use the resurgent properties and exponentially accurate numerical methods to go beyond the perturbative results and obtain (analytically and numerically) nonperturbative data. I will exemplify how these techniques can be applied to a wide range of problems, from hydrodynamic theories mimicking the existence of black brane quasinormal modes appearing on the gravity dual description of a $\mathcal{N}=4$ SYM plasma, to the large-N resurgent dynamics of certain matrix models.

We analyse the energy cost of building or demolishing a wall for a massless Dirac field in (1+1)-dimensional Minkowski spacetime and the response of an Unruh-DeWitt particle detector to the generated radiation. For any smoothly evolving wall, both the field's energy density and the detector's response are finite. In the limit of rapid wall creation or demolition, the energy density displays a delta function squared divergence but, within first order perturbation theory, the detector's response diverges only logarithmically in the duration of the wall evolution. The results add to the evidence that a localised matter system may not be as sensitive to the divergence in local expectation values of field observables such as the energy density. This disparity has potential interest for quantum information preservation scenarios.

Generalised geometry is an extension of (pseudo-)Riemannian geometry which provides an elegant geometrical description of the supergravity theories underlying string theory and M theory. After a brief introduction to these topics, I will describe recent developments showing that general supersymmetric flux backgrounds can be described as the analogue of special holonomy manifolds in this new geometry. The Killing superalgebra, which has a neat manifestation in this language, plays a key role in the proof of the result for N > 2 supersymmetry and we are able to fix its form explicitly using this technology. If time allows I will also briefly discuss the corresponding picture for supersymmetric AdS solutions.

In this talk I will consider transport of conserved charges in strongly coupled quantum systems with broken translations, using holographic techniques. Such systems are relevant in condensed matter physics in the context of spontaneous symmetry breaking as well as in the context of momentum relaxation through a lattice. In this setup of reduced symmetry, I will give the precise identification of the relevant hydrodynamic modes that diffuse heat and electric charge.