A unimodular-like string effective description

TL;DR

This paper demonstrates that the vanishing of string sigma-model beta-functions at tree level can be derived from a universal effective action with a non-dynamical field combination, linking string theory conditions to unimodular gravity concepts.

Contribution

It introduces a universal effective action framework that reproduces string beta-function conditions using a non-dynamical field combination, connecting string theory to unimodular gravity.

Findings

Beta-function vanishing conditions derived from a universal effective action.

The non-dynamical field combination is identified as f0ge9e^{-2f4}

Cosmological constant appears as an integration constant, similar to unimodular gravity.

Abstract

We show that vanishing of the sigma-model beta-functions for the metric $g_{\mu\nu}$, antisymmetric tensor $B_{\mu\nu}$ and dilaton $\Phi$ of any string-theory model in $D$ dimensions at tree level can be obtained from a universal effective action, provided that the field combination $\sqrt{-g}e^{-2\Phi}$ is non-dynamical. The central-charge deficit term is omitted from the action and appears as an integration constant at the level of the field equations. The analysis is done at leading order in $\alpha'$, i.e. at the two-derivative level in the effective description. It can be extended to incorporate higher order string-loop corrections, Ramond-Ramond forms and moduli fields. In all cases, the non-dynamical field combination turns out to be $\sqrt{-g}\, U$, where $U$ is the effective potential. When certain fluxes are fixed and the moduli fields are stabilized, no cosmological term will arise in the action. Instead, the cosmological constant will appear as an integration constant as in unimodular modifications of general relativity.