q-Virasoro algebra, q-conformal dimensions and and free q-superstring Original Research Article

The commutators of standard Virasoro generators and fields generate various representations of the centreless Virasoro algebra depending on a conformal dimension J of the field in question (J is related to the Bargman index of SU(1, 1) generated by Lm, m = 0, ±1). We introduce the notion of q-conformal dimension for various oscillator realizations of q-deformed Virasoro (super) algebras proposed earlier. We use the field theoretical approach introduced recently in which the q-Virasoro currents Lα(z) are expressed as Schwinger-like point-split normally ordered quadratic expressions in elementary fields We extend this approach and probe the elementary fields A(z) (the q-superstring coordinate, momentum and fermionic field) and their powers by the 1-Virasoro generators Lmα (i.e. we calculate the commutators [Lmα, A(z)]) and show that to all of them can be assigned just the standard non-deformed conformal dimension.