Edinburgh Mathematical Physics Group Seminars

Cutting rules for diagrams in QED in a strong background field
Arseny Mironov (Ecole Polytechnique)
2:45pm-3:45pm

Rates and cross-sections of elementary particle scattering processes can change significantly in a strong background. This happens, for example, near compact stars or in experiments where high-energy particles encounter an intense field. It is common to study such effects within QED using the strong-field method. It suggests calculating scattering amplitudes in the so-called Furry picture, when particle states are fully dressed in an interaction with the external field, and the interaction with the quantised part of the gauge field is considered perturbatively. The downside of this non-perturbative technique is a significant increase in the computational complexity of amplitudes. For example, tree-level scattering process rates are generally unknown beyond the second order. As some results on higher-order loop amplitudes are available in the literature (for specific background models), it is tempting to introduce the cutting rules and apply them to extract such rates directly. In this talk, I will discuss how the cutting rules can be formulated for QED in a plane-wave background. After discussing the general approach, I will consider an example of one relevant process beyond the leading order: Cutting a two-loop electron elastic scattering amplitude in order to extract the rate of a trident process (creation of an electron-positron pair by an electron in an external field). One of the non-trivial aspects brought by the external field is the splitting of this amplitude into two parts: the one- and two-step contributions, which are mediated by an off- and on-shell photon, respectively. I will discuss how this feature is recovered when we apply the cut.

Many-body chaos, hydrodynamics and horizon symmetries
Mike Blake (Bristol)
4:00pm-5:00pm

I will describe recent connections between two naively distinct aspects of the dynamics of finite-temperature quantum field theories. These are many-body chaos (as probed through OTOCs of local operators) and hydrodynamics (an effective description of conserved quantities, specifically energy density). I will first review a proposal that in maximally chaotic systems the exponential growth of OTOCs can be understood as arising from exponential zero modes of a hydrodynamic effective action. I will then describe recent work in which we explicitly derive hydrodynamic actions using the AdS/CFT correspondence. In this setting it has been argued that the conjectured exponential zero modes of hydrodynamics are associated with certain horizon symmetries – that is infrared diffeomorphisms that preserve certain structures of the horizon. I will present our explicit constructions of hydrodynamic actions dual to black holes with bulk dimensions d=2,3,4, as well as a general argument for how to identify gravitational horizon symmetries with zero modes of hydrodynamic actions. For d=2,3, the hydrodynamic actions we construct explicitly realise a form of horizon symmetries argued for by Knysh, Liu and Pinzani-Fokeeva.