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arXiv · 2410.11938

A Background-Independent Closed String Action at Tree Level

Amr Ahmadain·Alexander Frenkel·Aron C. Wall
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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.

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Amr Ahmadain, Alexander Frenkel, Aron C. Wall. 2025-10-04. A Background-Independent Closed String Action at Tree Level. https://arxiv.org/abs/2410.11938

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