International Journal of Modern Physics A

We review electric–magnetic duality in N=4 (and certain N=2) globally supersymmetric gauge theories and show how this duality, which relates strong to weak coupling, follows as a consequence of a string—string duality. Black holes, 11 dimensions and supermembranes also have a part to play in the big picture.

In the thermodynamic Bethe ansatz approach to 2D integrable, ADE-related quantum field theories, one derives a set of algebraic functional equations (a Y system) which play a prominent role. This set of equations is mapped onto the problem of finding finite triangulations of certain 3D manifolds. This mapping allows us to find a general explanation of the periodicity of the Y system. For the A_N related theories, and more generally for the various restrictions of the fractionally supersymmetric sine—Gordon models, we find an explicit, surprisingly simple solution of such functional equations in terms of a single unknown function of the rapidity. The recently found dilogarithm functional equations associated to the Y system simply express the invariance of the volume of a manifold for deformations of its triangulations.

The higher spin properties of non-Abelian bosonization in the classical theory are investigated. Both the symmetry transformation algebra and the classical current algebra for the non-Abelian free-fermionic model are linear Gel’fand–Dickey type algebras. However, for the corresponding WZNW model these algebras are different. There exist symmetry transformations whose algebra remains the linear Gel’fand-Dickey algebra, while in the corresponding current algebra nonlinear terms arise. Moreover, this algebra is closed (in Casimir form) only in an extended current space in which nonlinear currents are included. In the affine sector, it is necessary to include higher isotopic spin current too. As a result we have a triple extended algebra.

In this paper, the relationship between the sine-Gordon model with an integrable boundary condition and the Thirring model with boundary is discussed and the reflection R matrix for the massive Thirring model, which is related to the physical boundary parameters of the sine—Gordon model, is given. The relationship between the boundary parameters and the two formal parameters appearing in the work of Ghoshal and Zamolodchikov is also discussed.

We compute the effective action and correlators of the Polyakov loop operator in the Schwinger model at finite temperature and discuss the realization of the discrete symmetries that occur there. We show that, due to nonlocal effects of massless fermions in two space–time dimensions, the discrete symmetry which governs the screening of charges is spontaneously broken even in an effective one-dimensional model, when the volume is infinite. In this limit, the thermal state of the Schwinger model screens an arbitrary external charge; consequently the model is in the deconfined phase, with the charge of the deconfined fermions completely screened. In a finite volume we show that the Schwinger model is always confining.

We evaluate the finite part of the regularized zero-point energy for a massless scalar field confined in the interior of a D-dimensional spherical region. While some insight is offered into the dimensional dependence of the WKB approximations by examining the residues of the spectral-zeta-function poles, a mode-sum technique based on an integral representation of the Bessel spectral zeta function is applied with the help of uniform asymptotic expansions (u.a.e.’s).

We extend the definitions of characters and partition functions to the case of conformal field theories which contain operators with logarithmic correlation functions. As an example we consider the theories with central charge c=c_p,1=13−6(p+p⁻¹), the “border” of the discrete minimal series. We show that there is a slightly generalized form of the property of rationality for such logarithmic theories. In particular, we obtain a classification of theories with c=c_p,1 which is similar to the A-D-E classification of c=1 models.