Embedding Unimodular Gravity in String Theory

TL;DR

This paper explores how Unimodular Gravity can be embedded within string theory, demonstrating that both Diff and WTDiff invariance principles are valid for describing string spectrum excitations.

Contribution

It provides the first explicit analysis of embedding Unimodular Gravity into string theory, clarifying the role of gauge invariances in string spectra.

Findings

Both Diff and WTDiff invariance principles are valid for string massless modes.

Unimodular Gravity can be consistently embedded in string theory.

No significant differences are expected in other string theories.

Abstract

Unimodular Gravity is a theory displaying Weyl rescalings of the metric and transverse (volume-preserving) diffeomorphisms as gauge symmetries, as opposed to the full set of diffeomorphisms displayed by General Relativity. Recently, we presented a systematic comparison of both theories, concluding that both of them are equivalent in everything but the behaviour of the cosmological constant under radiative corrections. A careful study of how Unimodular Gravity can be embedded in the string theory framework has not been provided yet and was not analyzed there in detail. In this article, we provide such an explicit analysis, filling the gap in the literature. We restrict ourselves to the unoriented bosonic string theory in critical dimension for the sake of simplicity, although we argue that no differences are expected for other string theories. Our conclusions are that both a Diff and a WTDiff invariance principle are equally valid for describing the massless excitations of the string spectrum.