Higher-spin symmetry and duality in (super)conformal field theory

Conformal symmetry is the maximal spacetime symmetry in relativistic quantum field theory. Such a symmetry is also realised in condensed matter systems at second order phase transitions.

Conformal field theories possessing higher-spin and/or duality symmetries, along with their supersymmetric extensions, have recently been the focus of enormous interest worldwide. This proposal puts forward a research program to explore the dynamics and quantum aspects of such theories.

Using recent advances in group theoretic formalism to compute correlation functions, the project aims to develop novel, manifestly supersymmetric techniques used for comprehensive analysis of three-point functions for conserved higher-spin current multiplets in superconformal field theories in Minkowski and Anti-de Sitter backgrounds – both playing pivotal roles in deciphering celebrated dualities between quantum field and gravity theories.

Another goal is to study, for the first time, the quantum properties of the recently discovered Modified Maxwell (ModMax) theory. The latter is a unique non-linear extension of Maxwell's electrodynamics which is conformal and duality invariant. It has opened new avenues, all to be discovered, to study new classes of non-analytic conformal field theories.

The project outcomes will advance our knowledge of scattering amplitudes and their relation to anomalies of superconformal field theories on curved backgrounds, while at the same time giving new insight into the field of non-linear electrodynamics.

These results will be of major significance for a wide range of areas of modern mathematical and theoretical high-energy physics including string theory, gravity, cosmology and condensed matter.