We derive the current algebra of supersymmetric principal chiral models with a Wess-Zumino term. At the critical point one obtains two commuting super Kac-Moody algebra as expected, but in general there are intertwining fields connecting both right and left sectors, analogously to the bosonic case. Moreover, in the present supersymmetric extension we have a quadratic algebra, rather than an aff...

The most general four-dimensional non-linear sigma-model, having the second-order derivatives only and interacting with a background metric and an antisymmetric tensor field, is constructed. Despite its apparent non-renormalizability, just imposing the one-loop UV-finiteness conditions determines the unique model, which may be finite to all orders of the quantum perturbation theory. This model ...

We study logarithmic operators in Coulomb gas models, and show that they occur when the “puncture” operator of the Liouville theory is included in the model. We also consider WZNW models for SL(2,R), and for SU(2) at level 0, in which we find logarithmic operators which form Jordan blocks for the current as well as the Virasoro algebra. e-mail: [email protected] e-mail: a.lewis1@phy...

We briefly review the possible Poisson structures on the chiral WZNW phase space and discuss the associated Poisson-Lie groupoids. Many interesting dynamical r-matrices appear naturally in this framework. Particular attention is paid to the special cases in which these r-matrices satisfy the classical dynamical Yang-Baxter equation or its PoissonLie variant. Talk presented at the Workshop on In...

The two-dimensional (2d) manifestly locally supersymmetric actions describing the N=2 and N=4 extended super-Liouville theory coupled to the N=2 and N=4 conformal supergravity, respectively, are constructed in superspace. It is shown that the N=4 super-Liouville multiplet is described by the improved twisted-II scalar mul-tiplet TM-II, whose kinetic terms are given by the SU(2) ⊗ U(1) WZNW model.

The G/G gauged supergroup valued WZNW theory is considered. It is shown that for G = OSP (1, 2), the G/G theory tensoring a (b, c, β, γ) system is equivalent to the non-critical fermionic theory. The relation between integral or half integral moded affine superalgebra and its reduced theory, the NS or R superconformal algebra, is discussed in detail. The physical state space, i.e. the BRST semi...

Abstract We give a mathematical definition of irregular conformal blocks in the genus-zero WZNW model for any simple Lie algebra, using coinvariants modules affine algebras whose parameters match up with those moduli spaces meromorphic connections: open de Rham spaces. The Segal–Sugawara representation Virasoro algebra is used to show that assemble into flat vector bundle over space isomonodrom...