The Sigma Model on Complex Projective Superspaces

TL;DR

This paper non-perturbatively determines the spectrum of the sigma model on complex projective superspaces CP^{S-1|S} using both continuum and numerical methods, revealing detailed spectral properties across parameters.

Contribution

It provides a closed-form formula for the partition function and verifies the spectrum through a novel spin chain regularization, advancing understanding of supersymmetric conformal field theories.

Findings

Exact partition function formula derived and tested.

Numerical spectrum matches continuum predictions.

Spin chain model effectively captures boundary conditions.

Abstract

The sigma model on complex projective superspaces CP^{S-1|S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle \theta. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we propose a spin chain regularization of the CP^{S-1|S} model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis.