An Effective Superstring Spectral Action

TL;DR

This paper demonstrates that the superstring partition function can be interpreted as a spectral action within noncommutative geometry, linking supersymmetric theories to geometric frameworks.

Contribution

It introduces a novel application of the spectral action principle to superstring theory, deriving a generalized Dirac operator in supersymmetric non-linear sigma models.

Findings

Superstring partition function is a spectral action.

Derived a generalized loop space Dirac operator.

Connected supersymmetric models with noncommutative geometry.

Abstract

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma model and derive an expression for the generalized loop space Dirac operator, in presence of a general background, using canonical quantization. The spectral action principle is used to show that the superstring partition function is also a spectral action valid for the fluctuations of the string modes.