Non-Abelian Sugawara construction and theq-deformedN= 2 superconformal algebra

Abstract

The construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of U q ( su(2)) quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to U q ( su(N + 1)) is also proposed.

Deformed fields and Moyal construction of deformed super Virasoro algebra

“…The deformed Virasoro algebras proposed in an early stage [1]- [5] have recently become more suitable to be examined in physical connections. These algebras were studied originally from the purely mathematical motivation to seek a q-analogue of the Virasoro algebra in the context of quantum groups.…”

FFZ realization of the deformed super Virasoro algebra – Chaichian–Prešnajder type

“…Nearly a decade ago, a series of q-analogues of the Virasoro algebra were investigated through analyzing an infinite set of q-deformed differential operators [1,2]. Some of these algebras can be organized as a N = 1 supersymmetric algebra [3,4], and there exists a N = 2 extension as well [5]. As to the nonsupersymmetric parts, the following things are known.…”