Covariant calculation of the partition function of the two-dimensional sigma model on compact two-surfaces

TL;DR

This paper develops a covariant method for calculating the partition function of the 2D sigma model on various compact surfaces, emphasizing measure regularization, with explicit computations on sphere, disk, and torus.

Contribution

It introduces a covariant perturbative approach for the 2D sigma model's partition function, addressing measure regularization and providing explicit results for key 2-manifolds.

Findings

Partition function computed for sphere, disk, and torus

Highlights importance of measure regularization in path integrals

Provides a covariant framework aligned with string theory

Abstract

Motivated by string theory connection, a covariant procedure for perturbative calculation of the partition function of the two-dimensional generalized $\sigma$-model is considered. The importance of a consistent regularization of the measure in the path integral is emphasized. The partition function is computed for a number of specific 2-manifolds: sphere, disk and torus.