Six-loop divergences in the supersymmetric Kahler sigma model

TL;DR

This paper investigates the six-loop divergences in the two-dimensional supersymmetric Kähler sigma model, revealing that unlike at five loops, the six-loop beta function cannot be made to vanish, indicating persistent divergences.

Contribution

The study demonstrates that the six-loop beta function in the supersymmetric Kähler sigma model remains non-zero regardless of renormalisation scheme choices.

Findings

Six-loop beta function is non-zero.

Divergences persist at six loops.

Scheme independence of six-loop divergence.

Abstract

The two-dimensional supersymmetric $\s$-model on a K\"ahler manifold has a non-vanishing $\b$-function at four loops, but the $\b$-function at five loops can be made to vanish by a specific choice of renormalisation scheme. We investigate whether this phenomenon persists at six loops, and conclude that it does not; there is a non-vanishing six-loop $\b$-function irrespective of renormalisation scheme ambiguities.