On gl 2|2 with hat ⁽²⁾ _k Current Superalgebra and Twisted Conformal Field Theory

Abstract

Motivated by the recently discovered hidden symmetry of the type IIB Green–Schwarz superstring on certain background, the non-semisimple Kac–Moody twisted superalgebra gl(2)k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformal Field Theory (CFT) has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U(1) factor and an outer automorphism operator, we get the free field representation of psl(2)k, which is the algebra of gl(2)k modulo the ℤ4-outer automorphism, the CFT has central charge -2.