Are We Already Living on a Supermanifold?

by Apostolos Pilaftsis (University of Manchester (GB))

Thursday 25 Nov 2021, 13:30 → 14:30 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

For more than half a century, covariant and differential geometric methods have been playing a central role in the development of Quantum Field Theory (QFT).  After a brief historic overview of the major scientific achievements using these methods, I will focus on the covariant and differential geometric formalism originally proposed by Vilkovisky and DeWitt (VDW).  I will discuss recent developments made in addressing the uniqueness of the path-integral measure of the VDW effective action, and so address the problem of quantum frame dependence in cosmologically relevant scalar-tensor theories beyond the classical approximation.  I will then turn my attention to a long-standing problem concerning the obstacles that the VDW formalism is facing from its original conception in describing generic QFTs that include fermions. I will show how in addition to bosons the VDW effective action can be extended to supermanifolds to include fermions.  The so-extended formulation appears to be very promising for a complete geometrisation of realistic theories of micro-cosmos, such as the Standard Model and its gravitational sector.