Jonathan Bagger

Gauging N=2 sigma models in harmonic superspace

Abstract We construct the general minimal coupling of N = 2 Yang-Mills fields to N = 2 sigma models in flat and curved harmonic superspace. We show that the complete symmetry group of the matter action can always be gauged in curved space. In flat space, we find that the gauging can be blocked by a local obstruction. We give a number of examples based on homogeneous quaternionic spaces and on quaternionic generalizations of the Taub-NUT and Eguchi-Hanson metrics.

Bosons, fermions and Thirring strings

Abstract All toroidal compactifications of string theories are described in terms of two-dimensional fermions. The compactification parameters (the metric, the antisymmetric tensor and the gauge field) are incorporated into four-Fermi Thirring-like interactions on the world sheet. An alternative formulation removes the Thirring interactions and considers free fermions with twisted boundary conditions. In this description, there are several twisted sectors, and a generalized GSO projection is necessary for modular invariance.

Minimal Model Correlation Functions on the Torus

Abstract We generalize the Feigin-Fuchs construction to the torus, and propose an ansatz for certain correlation functions of the minimal conformal models. Our ansatz is periodic, modular-covariant and has the correct short-distance behavior. As an example, we compute the one-point function of the Ising-model energy operator on the torus.

Coulomb-gas representation on higher-genus surfaces

Abstract In this paper we use the Coulomb-gas approach to construct the minimal-model conformal blocks of higher-genus Riemann surfaces. We define the higher-genus blocks by sewing, and write them in terms of the rational blocks of a compactified scalar field. We show that spurious states decouple, which implies that the blocks degenerate correctly. As an example, we compute the genus-two partition function, and verify modular invariance for the subset of minimal models which only require one type of screening charge.

Gauging the supersymmetric sigma model with a goldstone field

Abstract We gauge the supersymmetric nonlinear sigma model in superspace. We show that the additional terms satisfy a set of Wess-Zumino consistency conditions, and that the vector superfield V plays the role of a Goldstone boson.

Coulomb-Gas Construction on Higher-Genus Riemann Surfaces

The Coulomb-gas construction provides a powerful tool for computing correlation functions in the minimal series of two-dimensional conformai field theories. The basic idea is to replace the irreducible highest-weight representations of the Virasoro algebra with the simpler Fock space of a free scalar field. It has been known for some time [1] that on such Fock spaces one can construct representations of the Virasoro algebra with arbitrary central charge.