A Background-Independent Closed String Action at Tree Level

TL;DR

This paper introduces a novel off-shell bosonic string action that is background-independent and free of spurious solutions, enabling broader deformations of the worldsheet theory and providing insights into the structure of string theory.

Contribution

It presents a new string action that removes previous constraints, allowing for arbitrary irrelevant deformations and analyzing non-perturbative properties and gauge redundancies.

Findings

The action removes the renormalization window constraint.

Non-minimal Ricci couplings act as gauge redundancies.

Identifies non-smooth behavior in the Zamolodchikov C-function.

Abstract

We propose an off-shell bosonic string action that removes the renormalization window constraint of [1]. To all orders in conformal perturbation theory, this action allows for deformations of the worldsheet theory by any primary or descendant irrelevant deformation. Non-perturbatively, this action has no spurious solutions on the space of all worldsheet theories with a unitary matter sector that flows from a UV fixed point. We find that non-minimal couplings dressed with more than one factor of the Ricci curvature behave as gauge redundancies. As part of our investigation of this action, we find non-smooth behavior in the Zamolodchikov $C$-function. Our results mostly apply to Euclidean-signature target spaces, but can be extended to Lorentzian backgrounds which are invariant under time translations and CTO symmetry.