Superconformal Selfdual Sigma-Models

Abstract

A range of bosonic models can be expressed as (sometimes generalized) $\sigma$-models, with equations of motion coming from a selfduality constraint. We show that in D=2, this is easily extended to supersymmetric cases, in a superspace approach. In particular, we find that the configurations of fields of a superconformal $\mathfrak{G}/\mathfrak{H}$ coset models which satisfy some selfduality constraint are automatically solutions to the equations of motion of the model. Finally, we show that symmetric space $\sigma$-models can be seen as infinite-dimensional $\tfG/\tfH$ models constrained by a selfduality equation, with $\tfG$ the loop extension of $\mathfrak{G}$ and $\tfH$ a maximal subgroup. It ensures that these models have a hidden global $\tfG$ symmetry together with a local $\tfH$ gauge symmetry.

21 pages; v2 few corrections and references added; v3 exposition changes

References in corpus (13)

• Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities
• Kac-Moody Symmetries of IIB Supergravity
• Conformal internal symmetry of $2d$ $\sigma$-models coupled to gravity and a dilaton
• Massive IIA Supergravity as a Non-linear Realisation
• Isomonodromic Quantization of Dimensionally Reduced Gravity
• Integrability and Canonical Structure of d=2, N=16 Supergravity
• Classical Symmetries of Some Two-Dimensional Models Coupled to Gravity
• Quantization of coset space sigma-models coupled to two-dimensional gravity
• Yangian Symmetry in Integrable Quantum Gravity
• Non-local charges and quantum integrability of sigma models on the symmetric spaces SO(2n)/SO(n)xSO(n) and Sp(2n)/Sp(n)xSp(n)
• Twisted Self-Duality of Dimensionally Reduced Gravity and Vertex Operators
• New Linear Systems for 2D Poincare Supergravities
• On the sigma-model structure of type IIA supergravity action in doubled field approach

Cited by in corpus (1)

• Selfduality of d=2 Reduction of Gravity Coupled to a Sigma-Model