\(q\)-Virasoro algebra, \(q\)-conformal dimensions and free \(q\)-superstring. (English) Zbl 0974.81507
Summary: 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 Bargmann index of SU\((1,1)\) generated by \(L_m, m=0,\pm 1)\). 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 \(L^{\alpha } (z)\) 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 \(q\)-Virasoro generators \(L^{\alpha}_m\) (i.e. we calculate the commutators \([L^{\alpha}_m ,A(z)])\) and show that to all of them can be assigned just the standard non-deformed conformal dimension.
MSC:
81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
Keywords:
Bargmann index; oscillator realizations; field theory; Schwinger-like quadratic expressions; quantum groups; point splitting regularizationReferences:
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