Journal article

Takiff superalgebras and conformal field theory

Andrei Babichenko, David Ridout

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | IOP PUBLISHING LTD | Published : 2013

Abstract

A class of non-semisimple extensions of Lie superalgebras is studied. They are obtained by adjoining to the superalgebra its adjoint representation as an Abelian ideal. When the superalgebra is of affine KacMoody type, a generalization of Sugawaras construction is shown to give rise to a copy of the Virasoro algebra and so, presumably, to a conformal field theory. Evidence for this is detailed for the extension of the affinization of the superalgebra gl(1|1): its highestweight irreduciblemodules are classified using spectral flow, the irreducible supercharacters are computed and a continuum version of the Verlinde formula is verified to give non-negative integer structure coefficients. Inter..

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University of Melbourne Researchers

Grants

Awarded by UK EPSRC


Awarded by Australian Research Council Discovery Project


Awarded by Engineering and Physical Sciences Research Council


Funding Acknowledgements

AB would like to thank Maria Gorelik for interesting discussions and the Einstein Center of Weizmann Institute for support. He thanks also the University of York for hospitality where this work was finished, and support from UK EPSRC grant number EP/H000054/1. DR's research is supported by the Australian Research Council Discovery Project DP1093910. We would also like to thank Thomas Quella, Volker Schomerus and Jan Troost for discussions related to the work reported here and gratefully acknowledge the Institut Henri Poincare and, in particular, the organizers of the recent trimestre 'Advanced Conformal Field Theory and Applications', for hospitality during a phase of this project.