Bosonic String in Affine-Metric Curved Space
Vasily E.Tarasov
TL;DR
This paper calculates two-loop counterterms for the bosonic string sigma model on affine-metric manifolds, exploring conditions for ultraviolet finiteness and providing examples of nonflat nonRiemannian manifolds with trivial beta-functions.
Contribution
It presents the explicit calculation of two-loop metric counterterms for the nonlinear sigma model with affine-metric target spaces, advancing understanding of string theory in non-Riemannian geometries.
Findings
Two-loop counterterms for affine-metric manifolds are derived.
Conditions for ultraviolet finiteness are analyzed.
Examples of nonflat nonRiemannian manifolds with trivial beta-functions are provided.
Abstract
The sigma model approach to the closed bosonic string on the affine-metric manifold is considered. The two-loop metric counterterms for the nonlinear two-dimensional sigma model with affine-metric target manifold are calculated. The correlation of the metric and affine connection is considered as the result of the ultraviolet finiteness (or beta-function vanishing) condition for the nonlinear sigma model. The examples of the nonflat nonRiemannian manifolds resulting in the trivial metric beta-function are suggested.
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