arXiv subjects
Publications and source records attributed to J. Panvel.
The two-dimensional supersymmetric $\s$-model on a Kähler manifold has a non-vanishing $\b$-function at four loops, but the $\b$-function at five loops can be made to vanish by a specific choice of renormalisation scheme. We investigate whether this phenomenon persists at six loops, and conclude that it does not; there is a non-vanishing six-loop $\b$-function irrespective of renormalisation scheme ambiguities.
We derive an explicit, exactly conformally invariant form for the action for the non-abelian Toda field theory. We demonstrate that the conformal invariance conditions, expressed in terms of the $β$-functions of the theory, are satisfied to all orders, and we use our results to obtain a value for the central charge agreeing with previous calculations.
We construct a quantum Hamiltonian operator for the Wess-Zumino-Witten (WZW) model in terms of the Casimir operator. This facilitates the discussion of the reduction of the WZW model to Toda field theory at the quantum level and provides a very straightforward derivation of the quantum central charge for the Toda field theory.
Proposals that $O(d,d)$ boosts of trivial backgrounds lead to non-trivial conformally invariant backgrounds are checked to two loop order. We find that conformal invariance can be achieved by adding simple higher order corrections to the metric and dilaton.
We show that Witten's two-dimensional string black hole metric is exactly conformally invariant in the supersymmetric case. We also demonstrate that this metric, together with a recently proposed exact metric for the bosonic case, are respectively consistent with the supersymmetric and bosonic $σ$-model conformal invariance conditions up to four-loop order.