73rd North British Mathematical Physics Seminar

Abstract: I will review homotopy algebras, and show how they can simultaneously play a role in two different gauge-gravity duality frameworks. In the context of flat space holography, they seem to precisely encode the required fall-off for fields at null infinity. In the context of the double copy programme, they allow us to find novel kinematic algebras in spacetime slices close to null infinity.  

Abstract: Equivariant localization is a powerful method for performing integrals using fixed point theorems. Recently it has been applied to compute various holographic observables in supergravity without the need for solving any of the supergravity field equations. I will discuss applications of these techniques in 4d gauged supergravity. In particular the on-shell action takes a particularly simple form depending only on topological data.

Abstract: In this talk I aim to give a gentle review of cosmic inflation and the motivation for considering cosmological correlators. I’ll then look at the “shadow formalism” for calculating such objects before delving into the cosmological dressing rules that we have developed, which enable one to recast the correlators as flat-space Feynman diagrams “dressed” with auxiliary propagators. If time permits, I may briefly discuss an extension to the spinning case which is in progress.

Abstract: In a first part I will deduce scaling dimensions by matching the chirally broken gauge theory to the pion effective theory. Consistency with soft theorems, the lattice and N=1 supersymmetric gauge theories will be discussed. In a second part, I will consider how the interpretation extends to include a dilaton, the Goldstone due to spontaneous scale symmetry breaking. The Gross-Neveu-Yukawa (GNY) theory in d=3 will serve as a proof of principle template that an RG-flow and a genuine dilaton are compatible. Definite signatures can be found in gravitational form factors which we discuss in the GNY theory and QCD where there is activity due to their experimental accessibility.

Abstract: In this talk, I present our recent work towards general theory of higher principal bundles with connection. In particular, we developed the notion of principal groupoid-bundles with connection using a new framework that is suitable for generalization. In this setup, principal bundles with connections are principal bundles without connection in a different category, namely the category of dg-manifolds.