Short Distance Operator Product Expansion of the 1D, N = 4 Extended GR Super Virasoro Algebra by Use of Coadjoint Representations

TL;DR

This paper constructs and analyzes the short distance operator product expansions of a deformed 1D, N=4 extended Super Virasoro algebra using coadjoint representations, highlighting the effects of Levi-Civita tensor modifications.

Contribution

It introduces a new approach to derive OPEs for a deformed superalgebra using coadjoint orbits and compares it with Clifford algebra methods.

Findings

Deformation with Levi-Civita tensor alters super-commutation relations.

Coadjoint orbit method effectively computes OPEs without invariant Lagrangians.

Clifford algebra approach provides an alternative derivation.

Abstract

Using the previous construction of the geometrical representation (GR) of the centerless 1D, N = 4 extended Super Virasoro algebra, we construct the corresponding Short Distance Operation Product Expansions for the deformed version of the algebra. This algebra differs from the regular algebra by the addition of terms containing the Levi-Civita tensor. How this addition changes the super-commutation relations and affects the Short Distance Operation Product Expansions (OPEs) of the associated fields is investigated. The Method of Coadjoint Orbits, which removes the need first to find Lagrangians invariant under the action of the symmetries, is used to calculate the expansions. Finally, an alternative method involving Clifford algebras is investigated for comparison.