gl(4|4) current superalgebra: Free field realization and screening currents

Abstract

The gl(4|4) current algebra at general level k is investigated. Its free field representation and corresponding energy-momentum tensor are constructed. Seven screening currents of the first kind are also presented.

Free field realization of current superalgebra gl(m∣n)k

“…15 for n =0 ͑i.e., in the bosonic case͒, and recover those in Ref. 21 for m = n = 4, thus providing a complete proof of the results in that paper.…”

“…18 and 19͒. We demonstrated this by working out the differential realization of gl͑4 ͉ 4͒ in Ref. 21. Here we provide the complete results of gl͑m ͉ n͒ for any m and n. This paper is organized as follows.…”

Finite dimensional irreducible representations of Lie superalgebra D (2, 1; α)

“…To obtain a shift operator [22] of D(2, 1; α), one needs to construct the differential operator representations [23][24][25][26][27][28][29][30][31] of the Lie superalgebra D(2, 1; α). Let 〈Λ| be the highest weight vector in the representation of D(2, 1; α) with the highest weights λ i , satisfying the following conditions:…”

Free-field realization of the exceptional current superalgebra $\widehat{D(2,1;\alpha )}_k$

“…To obtain a free-field realization of the D(2, 1; α) currents, one needs [19][20][21][23][24][25][26][27][28] firstly to construct the differential operator representation of the corresponding finite-dimensional superalgebra D(2, 1; α). Let | be the lowest weight vector in a representation of D(2, 1; α), satisfying the following conditions:…”

“…Free-field realization [18][19][20][21][22][23][24][25][26][27][28] has been proven to be a powerful method in analyzing CFTs such as WZNW models. In this paper, motivated by its potential applications, we obtain the free-field realization of the current superalgebra underlying the D(2, 1; α) WZNW model.…”