62nd North British Mathematical Physics Seminar

Abstract: I will describe higher dimensional (multivariable) analogs of the Virasoro and affine Kac—Moody symmetries that exist in chiral conformal field theory. In four dimensions these appear in twists of supersymmetric field theories as enhancements of superconformal and global symmetries, respectively. I will discuss a few works in progress including using these algebras to make refined checks of Seiberg duality and their appearances in higher dimensional Wakimoto realization.

Abstract: On a bosonic background of a supergravity theory, supersymmetries that preserve the background are described by geometric objects known as Killing spinors. These spinors generate a Lie superalgebra known as the Killing superalgebra, and recent work on the algebraic structure of these objects has provided a method of obtaining Killing spinor equations via purely algebraic means, namely by a homological computation on the Poincaré superalgebra. This allows Killing spinors to be defined without knowing any of the details of the supergravity theory a priori and gives an explicit description of the structure of the Killing superalgebra. Further information about the supergravity theory, such as the bosonic field equations, can often be recovered via geometric calculations. In some cases, the definition of Killing spinors obtained is more general than that of supergravity and provides hints of as-yet-unknown supersymmetric field theories on curved backgrounds which are not related to supergravity (eg. via Festuccia-Seiberg). I will discuss the general picture and highlight some results from recent work in minimal 5-dimensional supersymmetry. Based on [arXiv:2105.05775].

Abstract: BV formalism is a powerful tool used in quantization of gauge theories. In particular, it can be implemented in the framework of perturbative algebraic quantum field theory, where it provides a unified setting for describing dynamics, symmetries and, in its BV-BFV variant, the boundary data for a given theory.

Abstract: In this talk, I present a Feynman integral approach to understanding the three level interactions of N = 4 SYM theory, and compare it to the BCFW approach of the Amplituhedron. In particular, in the Feynman integral approach, the geometry decomposes nicely in $Gr_{\geq 0}(k,n)$ for n-particle N^kMHV tree level interactions, a property that is only conjectured for the Amplituhedron. I will present several barriers to generalizing this structure to understanding the geometry of the Amplituhedron, as well as new mathematical questions that have been uncovered by the exploration of N=4 SYM theory in this manner.