Bimetric, Conformal Supergravity and its Superstring Embedding

TL;DR

This paper explores the connection between Weyl$^2$ supergravity, superstring theory, and holography, revealing how massive spin-two fields originate from string excitations and their implications for superconformal theories and higher spin dualities.

Contribution

It establishes a link between Weyl$^2$ supergravity and superstrings, analyzing the emergence of massive spin-two fields from string excitations and their role in holography and superconformal invariance.

Findings

Massive spin-two fields originate from open string excitations on D3-branes.

In the tensionless limit, these fields become massless, leading to superconformal theories.

Identification of boundary operators dual to bulk spin-four fields.

Abstract

We discuss the connection between Weyl$^2$ supergravity and superstrings and further discuss holography between 4-dimensional, ${\cal N}=4$ superconformal Weyl$^2$ supergravity and ${\cal N}=8$, higher spin-four theory on $AdS_5$. 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 ${\cal N}=4$ 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, ${\cal N}=4$ 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 ${\cal N}=4$ 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.