Supersymmetry Constraints in Holographic Gravities

TL;DR

This paper investigates the constraints imposed by supersymmetry on higher derivative gravity theories in the context of holography, identifying which terms can be supersymmetrized without obstruction in seven dimensions.

Contribution

It formulates a necessary condition for supersymmetrizing higher derivative gravitational terms and shows quadratic Riemann terms are compatible, unlike more complex higher order terms.

Findings

Quadratic Riemann terms do not obstruct supersymmetrization.

Generic higher order terms face obstructions to supersymmetrization.

The analysis is specific to seven-dimensional theories using Weyl anomaly coefficients.

Abstract

Supersymmetric higher derivative gravities define superconformal field theories via the AdS/CFT correspondence. From the boundary theory viewpoint, supersymmetry implies a relation between the coefficients which determine the three point function of the stress energy tensor which can be tested in the dual gravitational theory. We use this relation to formulate a necessary condition for the supersymmetrization of higher derivative gravitational terms. We then show that terms quadratic in the Riemann tensor do not present obstruction to supersymmetrization, while generic higher order terms do. For technical reasons, we restrict the discussion to seven dimensions where the obstruction to supersymmetrization can be formulated in terms of the coefficients of Weyl anomaly, which can be computed holographically.