Superconformal symmetry and higher-derivative Lagrangians

TL;DR

This paper explores the construction of higher-derivative supergravity actions using superconformal methods, focusing on their role in understanding finiteness and anomalies in supergravity theories.

Contribution

It demonstrates how to construct all-order Dirac--Born--Infeld actions with Volkov--Akulov supersymmetries, advancing the understanding of higher-derivative supergravity actions.

Findings

Constructed all-order Dirac--Born--Infeld actions with Volkov--Akulov supersymmetries

Provided insights into higher-derivative supergravity actions and their symmetries

Discussed implications for finiteness and anomalies in supergravity theories

Abstract

Superconformal methods are useful to build invariant actions in supergravity. We have a good insight in the possibilities of actions that are at most quadratic in spacetime derivatives, but insight in general higher-derivative actions is missing. Recently higher-derivative actions got more attention for several applications. One of these is the understanding of finiteness of loop computations in supergravities. Divergences can only occur if invariant counterterms or anomalies exist. One can wonder whether conformal symmetry might also play a role in this context. In order to construct higher-derivative supergravities with the conformal methods, one should first get more insight in such rigid supersymmetric actions with extra fermionic symmetries. We show how Dirac--Born--Infeld actions with Volkov--Akulov supersymmetries can be constructed in all orders.