On the symmetries of special holonomy sigma models

TL;DR

This paper investigates the extended symmetries of special holonomy sigma models, revealing their algebraic structures and challenges in quantization due to field-dependent structure functions.

Contribution

It demonstrates the linearization of superconformal algebras with extra symmetries on special holonomy manifolds, except for G_2 and SU(3).

Findings

Superconformal algebras extend with symmetries from covariantly constant forms.

These extended algebras form W-algebras with field-dependent structure functions.

Linearization of algebras is possible in finite steps, except for G_2 and SU(3).

Abstract

In addition to superconformal symmetry, (1,1) supersymmetric two-dimensional sigma models on special holonomy manifolds have extra symmetries that are in one-to-one correspondence with the covariantly constant forms on these manifolds. The superconformal algebras extended by these symmetries close as W-algebras, i.e. they have field-dependent structure functions. It is shown that it is not possible to write down cohomological equations for potential quantum anomalies when the structure functions are field-dependent. In order to do this it is necessary to linearise the algebras by treating composite currents as generators of additional symmetries. It is shown that all cases can be linearised in a finite number of steps, except for G_2 and SU(3). Additional problems in the quantisation procedure are briefly discussed.