Curvature squared invariants in six-dimensional ${\cal N} = (1,0)$ supergravity

TL;DR

This paper constructs and analyzes supersymmetric curvature-squared invariants in six-dimensional ${ m N}=(1,0)$ supergravity, exploring their properties, including the Gauss-Bonnet term, and their implications for string theory compactifications.

Contribution

It provides the first off-shell supersymmetric completions of all three pure curvature-squared invariants in 6D supergravity and introduces a new higher-derivative invariant with applications to (A)dS solutions.

Findings

Constructed off-shell supersymmetric Riemann, Ricci, and scalar curvature squared invariants.

Presented the supersymmetric completion of the Gauss-Bonnet term.

Analyzed the spectrum of Einstein-Gauss-Bonnet supergravity around ${ m AdS}_3 imes { m S}^3$.

Abstract

We describe the supersymmetric completion of several curvature-squared invariants for ${\cal N}=(1,0)$ supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matter couplings. In the case of minimal off-shell Poincar\'e supergravity based on the dilaton-Weyl multiplet coupled to a linear multiplet as a conformal compensator, we describe off-shell supersymmetric completions for all the three possible purely gravitational curvature-squared terms in six dimensions: Riemann, Ricci, and scalar curvature squared. A linear combination of these invariants describes the off-shell completion of the Gauss-Bonnet term, recently presented in arXiv:1706.09330. We study properties of the Einstein-Gauss-Bonnet supergravity, which plays a central role in the effective low-energy description of $\alpha^\prime$-corrected string theory compactified to six dimensions, including a detailed analysis of the spectrum about the ${\rm AdS}_3\times {\rm S}^3$ solution. We also present a novel locally superconformal invariant based on a higher-derivative action for the linear multiplet. This invariant, which includes gravitational curvature-squared terms, can be defined both coupled to the standard-Weyl or dilaton-Weyl multiplet for conformal supergravity. In the first case, we show how the addition of this invariant to the supersymmetric Einstein-Hilbert term leads to a dynamically generated cosmological constant and non-supersymmetric (A)dS$_6$ solutions. In the dilaton-Weyl multiplet, the new off-shell invariant includes Ricci and scalar curvature-squared terms and possesses a nontrivial dependence on the dilaton field.