N=2 Supergravity Counterterms, Off and On Shell

TL;DR

This paper investigates the structure of N=2 supergravity with higher derivative deformations, revealing how off-shell supersymmetry is preserved while on-shell counterterms break some supersymmetry components.

Contribution

It provides a detailed analysis of supersymmetric completions of R^4 terms in N=2 supergravity using the off-shell superconformal framework, highlighting differences with on-shell approaches.

Findings

Deformation of supersymmetry rules includes higher derivative terms like λ ∂^4 F^3.

The deformed action resembles a Born-Infeld type with higher derivatives.

On-shell counterterms in superspace break N=2 local supersymmetry.

Abstract

We study N=2 supergravity deformed by a genuine supersymmetric completion of the $\lambda R^4$ term, using the underlying off shell N=2 superconformal framework. The gauge-fixed superconformal model has unbroken local supersymmetry of N=2 supergravity with higher derivative deformation. Elimination of auxiliary fields leads to the deformation of the supersymmetry rules as well as to the deformation of the action, which becomes a Born-Infeld with higher derivative type action. We find that the gravitino supersymmetry deformation starts from $\lambda \, \pa^4 {\cal F}^3$ and has higher graviphoton couplings. In the action there are terms $\lambda^2 \pa^8 {\cal F}^{6}$ and higher, in addition to original on shell counterterm deformation. These deformations are absent in the on shell superspace and in the candidate on shell counterterms of N=4,~8 supergravities, truncated down to N=2. We conclude therefore that the undeformed on shell superspace candidate counterterms break the N=2 part of local supersymmetry.