New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term

TL;DR

This paper introduces a new class of N=2 supergravity invariants involving higher derivatives, specifically extending the Gauss-Bonnet term supersymmetrically, and addresses key open questions in the field.

Contribution

It constructs novel supersymmetric invariants based on logarithms of chiral superfields, linking them to the Gauss-Bonnet term and resolving two major open questions.

Findings

Constructed supersymmetric invariants involving R^2 terms.

Connected invariants to dimensional reduction of 5D Chern-Simons terms.

Explained the role of pure Gauss-Bonnet in black hole entropy calculations.

Abstract

A new class of N=2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to R_{\mu\nu}^2 - 1/3*R^2, which equals the non-conformal part of the Gauss-Bonnet term. Upon combining one such invariant with the known supersymmetric version of the square of the Weyl tensor, one obtains the supersymmetric extension of the Gauss-Bonnet term. The construction is carried out in the context of both conformal superspace and the superconformal multiplet calculus. The new class of supersymmetric invariants resolves two open questions. The first concerns the proper identification of the 4D supersymmetric invariants that arise from dimensional reduction of the 5D mixed gauge-gravitational Chern-Simons term. The second is why the pure Gauss-Bonnet term without supersymmetric completion has reproduced the correct result in calculations of the BPS black hole entropy in certain models.