v 1 9 D ec 1 99 7 Analysis in R 1 , 1 or the Principal Function Theory ∗ Vladimir

ar X iv : m at h / 99 07 08 5 v 2 [ m at h . G R ] 1 7 D ec 1 99 9 LOOPS AND SEMIDIRECT PRODUCTS

D ec 1 99 7 q R – CONFORMAL SYMMETRIES IN 2 D NONLOCAL QUANTUM FIELD THEORY , CATEGORICAL REPRESENTATION THEORY , AND VIRASORO ALGEBRA

Analysis in R 1 , 1 or the Principal Function Theory ∗ Vladimir

We explore a function theory connected with the principal series representation of SL(2, R) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy space, the Cauchy-Riemann equation and the Taylor expansion. ∗Supported by grant 3GP03196 of the FWO-Vlaanderen (Fund of Scientific ResearchFlanders), Scientif...

ar X iv : h ep - t h / 97 12 24 2 v 1 2 9 D ec 1 99 7 Duality and cosmological compactification of superstrings with unbroken supersymmetry

The cosmological compactification of D = 10 , N = 1 supergravity– super–Yang–Mills theory obtained from superstring theory is studied. The constraint of unbroken N = 1 supersymmetry is imposed. A duality transformation is performed on the resulting consistency conditions. The original equations as well as the transformed equations are solved numerically to obtain new configurations with a nontr...

ar X iv : c on d - m at / 9 41 20 39 v 1 7 D ec 1 99 4 Phase diagram of UPt 3 in the E 1 g model

The phase diagram of the unconventional superconductor UPt3 is explained under the long-standing hypothesis that the pair wavefunction belongs to the E1g representation of the point group. The main objection to this theory has been that it disagrees with the experimental phase diagram when a field is applied along the c-axis. By a careful analysis of the free energy this objection is shown to b...