On the symmetries of special holonomy sigma models

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.

arXiv comment16 pages. Abstract improved and a few typographical errors corrected

References in corpus (7)

• Antibracket, Antifields and Gauge-Theory Quantization
• Holonomy groups and W-symmetries
• A note on the extended superconformal algebras associated with manifolds of exceptional holonomy
• String and M-theory Deformations of Manifolds with Special Holonomy
• The Topological G2 String
• Quantising Higher-spin String Theories
• Gauging Conformal Algebras with Relations between the Generators

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• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• Two-Dimensional Supersymmetric Sigma Models on Almost-Product Manifolds and Non-Geometry
• Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations