Towards a loop representation of connection theories defined over a super Lie algebra

Details Towards a loop representation of connection theories defined over a super Lie algebra Towards a loop representation of connection theories defined over a super Lie algebra

1996-08-30

arxiv.org/abs/hep-th/9609001v1

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, LATEX, aipproc style Based on the lectures given at the Fifth Workshop on Particles and Fields, Puebla, Nov. 1995

Scientific paper

10.1063/1.49736

The purpose of this contribution is to review some aspects of the loop space formulation of pure gauge theories having the connection defined over a Lie algebra. The emphasis is focused on the discussion of the Mandelstam identities, which provide the basic constraints upon both the classical and the quantum degrees of freedom of the theory. In the case where the connection is extended to be valued on a super Lie algebra, some new results are presented which can be considered as first steps towards the construction of the Mandelstam identities in this situation, which encompasses such interesting cases as supergravity in $3+1$ dimensions together with $2+1$ super Chern-Simons theories, for example. Also, these ideas could be useful in the loop space formulation of fully supersymmetric theories.

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