Bimetric, Conformal Supergravity and its Superstring Embedding

Abstract

We discuss the connection between Weyl${}^2$ supergravity and superstrings and further discuss holography between 4-dimensional, $\mathcal{N}=4$ superconformal Weyl${}^2$ supergravity and $\mathcal{N}=8$, higher spin-four theory on $Ad{S}_5$. The Weyl${}^2$ plus Einstein supergravity theory is a special kind of a bimetric gravity theory and consists of a massless graviton multiplet plus an additional massive spin-two supermultiplet. Here, we argue that the additional spin-two field and its superpartners originate from massive excitations in the open string sector; just like the $\mathcal{N}=4$ super Yang-Mills gauge fields, they are localized on the world volume of D3-branes. The ghost structure of the Weyl action should be considered as an artifact of the truncation of the infinitely many higher derivative terms underlying the massive spin 2 action. In field theory, $\mathcal{N}=4$ Weyl${}^2$ supergravity exhibits superconformal invariance in the limit of vanishing Planck mass. In string theory the additional spin-two fields become massless in the tensionless limit. Therefore low string scale scenarios with large extra dimensions provide (almost) superconformal field theories with almost massless open string spin-two fields. The full $\mathcal{N}=4$ scalar potential including the Yang-Mills matter multiplets is presented and the supersymmetric vacua of Einstein Supergravity are shown, as expected, to be vacua of massive Weyl supergravity. Other vacua are expected to exist which are not vacua of Einstein supergravity. Finally, we identify certain spin-four operators on the 4-dimensional boundary theory that could be the holographic duals of spin-four fields in the bulk.

33 pages, revised version with corrected typos and references added

References in corpus (10)

• Massive Gravity in Three Dimensions
• Quadratic Gravity
• The LHC String Hunter's Companion
• New Energy Definition for Higher Curvature Gravities
• Direct Production of Lightest Regge Resonances
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Cited by in corpus (10)

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• Scattering Massive String Resonances through Field-Theory Methods
• Extracting Bigravity from String Theory
• On the Ghost Problem of Conformal Gravity
• Spin-2 and the Weak Gravity Conjecture
• Emergent gravity from hidden sectors and TT deformations
• Conformal Renormalization of topological black holes in AdS${}_6$
• Massive AdS Supergravitons and Holography
• Supersymmetric Massive Gravity
• Goldstino condensation at large N