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#### Curvature squared invariants in six-dimensional N = (1,0) supergravity

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1808.00459.pdf

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Butter2019_Article_CurvatureSquaredInvariantsInSi.pdf

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##### Citation

Butter, D., Novak, J., Ozkan, M., Pang, Y., & Tartaglino-Mazzucchelli, G. (2019).
Curvature squared invariants in six-dimensional N = (1,0) supergravity.* Journal of high energy physics:
JHEP,* *2019*(04): 013. doi:10.1007/JHEP04(2019)013.

Cite as: https://hdl.handle.net/21.11116/0000-0001-FA33-C

##### 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.

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.