Exact Methods for Quantum Fields

This project focuses on the relation between quantum fields and geometry in diverse regimes.

The dynamics of supersymmetric field theories is very interesting because it displays phenomena, like confinement, that occur in nature. We will establish new exact results in supersymmetric QFT at strong coupling. In the past I have constructed a general framework to understand supersymmetry in curved spaces.

I will build on these ideas to devise new exact probes of the dynamics of QFT:Obj I: Use localization techniques to study supersymmetric field theories on general curved backgrounds and to understand how the properties of these theories reflects the geometry of the backgrounds.

We will also study the relations between these theories in different number of dimensions.Obj II: Study the conformal field theories encoding the dynamics of strongly coupled supersymmetric systems at low energies.

In particular we will devise new ways to compute protected quantities that characterize these theories.Besides providing new tools to study QFTs, these results could lead to new cross-disciplinary developments connecting Physics and Mathematics. Additionally a deeper understanding of QFT, through holography, offers a window on quantum gravity.

The grant will sustain my research group with a postdoc and a student with whom I will tackle the objectives above during four years.