Higher Spin Double Field Theory : A Proposal

TL;DR

This paper proposes a double field theory framework that incorporates higher spin fields and symmetries, unifying aspects of Vasiliev's equations with T-duality and diffeomorphism invariance.

Contribution

It introduces a novel double field theory coupled to higher spin fields, utilizing semi-covariant geometry to unify various symmetries and derive Vasiliev's equations as special solutions.

Findings

Constructed a covariant functional with full symmetry invariance.

Derived a linear dilaton vacuum as a solution.

Reduced BPS-like conditions to bosonic Vasiliev equations.

Abstract

We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to $\mathbf{O}(4,4)$ T-duality, doubled diffeomorphisms, $\mathbf{Spin}(1,3)$ local Lorentz symmetry and, separately, $\mathbf{HS}(4)$ higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.