Vanishing Theorems for the Self-Dual N=2 String

TL;DR

This paper proves specific vanishing theorems for amplitudes in the self-dual N=2 string in four-dimensional spacetime, identifying which amplitudes are non-zero at various loop levels.

Contribution

It establishes new vanishing theorems for momentum-dependent and independent amplitudes, using a topological approach and supersymmetric non-renormalization principles.

Findings

Only tree-level two and three-point functions are non-vanishing for momentum-dependent amplitudes.

One-loop partition function and certain tree-level functions are the only non-vanishing momentum-independent amplitudes.

Vanishing theorems are based on relationships between zero-momentum dilaton and axion.

Abstract

It is proven that up to possible surface terms, the only non-vanishing momentum-dependent amplitudes for the self-dual N=2 string in $R^{2,2}$ are the tree-level two and three-point functions, and the only non-vanishing momentum-independent amplitudes are the one-loop partition function and the tree-level two and four-point functions. The calculations are performed using the topological prescription developed in an earlier paper with Vafa. As in supersymmetric non-renormalization theorems, the vanishing proof is based on a relationship between the zero-momentum dilaton and axion.