Microwave assisted organic synthesis-a review

Phases of N = 2 theories in two dimensions

In this paper we shall study a special class of solutions of the self-dual Yang-Mills equations. The original self-duality equations which arose in mathematical physics were defined on Euclidean 4-space. The physically relevant solutions were the ones with finite action-the so-called 'instantons'. The same equations may be dimensionally reduced to Euclidean 3-space by imposing invariance under translation in one direction. These equations also have physical relevance-the solutions which have finite action in three dimensions are the 'magnetic monopoles'. If we take the reduction process one step further and consider solutions which are invariant under two translations, we obtain a set of equations in the plane. Here, however, there is no clear physical meaning and, indeed, attempts to find finite action solutions have failed. Nevertheless, these are the equations we shall consider. Despite the lack of interesting solutions in R2, the equations have the important property-conformal invariance-which allows them to be defined on manifolds modelled on R2 by conformal maps, namely Riemann surfaces. We shall consider here solutions of the self-duality equations defined on a compact Riemann surface. There are in fact solutions, as we shall show, and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study. It brings together in a harmonious way the subjects of Riemannian geometry, topology, algebraic geometry, and symplectic geometry. Illuminating all these facets of the same object accounts for the length of this paper. The self-duality equations are equations from gauge theory; geometrically they are defined in terms of connections on principal bundles. While the group of the principal bundle may be chosen arbitrarily for the equations to make sense, we restrict attention here to the simplest case of SU(2) or SO(3). There are two reasons for this. The first, and most obvious, is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general Lie group of higher rank. The second reason is that solutions for SU(2) have an intimate relationship with the internal structure of the Riemann surface. As a consequence of results we shall prove about solutions to the self-duality equations, we learn something about the moduli space of complex structures on the surface itself, namely Teichmuller space.

The self-duality equations on a riemann surface

Superstring theoryをめぐって(放談室)

Type iib superstrings, bps monopoles, and three-dimensional gauge dynamics

https://cds.cern.ch/record/129466/files/200030314.pdf

The supercurrent in five dimensions

We present a new formulation of the tensionless string ($T= 0$) where the space-time conformal symmetry is manifest. Using a Hamiltonian BRST scheme we quantize this {\em Conformal String} and find that it has critical dimension $D=2$. This is in keeping with our classical result that the model describes massless particles in this dimension. It is also consistent with our previous results which indicate that quantized conformally symmetric tensionless strings describe a topological phase away {}from $D=2$. We reach our result by demanding nilpotency of the BRST charge and consistency with the Jacobi identities. The derivation is presented in two different ways: in operator language and using mode expansions. Careful attention is payed to regularization, a crucial ingredient in our calculations.

Hamiltonian BRST Quantization of the Conformal String

On 3D non-linear vector-vector duality

We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahler geometry. The relation between the gerbe and the generalized Kahler potential is discussed.

Ulf Lindström

Papers

The supercurrent in five dimensions

Hamiltonian BRST Quantization of the Conformal String

On 3D non-linear vector-vector duality

Generalized Kahler geometry and gerbes

Hamiltonian BRST quantization of the conformal string