The Moduli Space and M(Atrix) Theory of 9d N=1 Backgrounds of M/String Theory

We discuss the moduli space of nine dimensional N = 1 supersymmetric compactifications of M theory/string theory with reduced rank (rank 10 or rank 2), exhibiting how all the different theories (including M theory compactified on a Klein bottle and on a Moebius strip, the Dabholkar-Park background, CHL strings and asymmetric orbifolds of type II strings on a circle) fit together, and what are the weakly coupled descriptions in different regions of the moduli space. We argue that there are two disconnected components in the moduli space of theories with rank 2. We analyze in detail the limits of the M theory compactifications on a Klein bottle and on a Moebius strip which naively give type IIA string theory with an uncharged orientifold 8-plane carrying discrete RR flux. In order to consistently describe these limits we conjecture that this orientifold non-perturbatively splits into a D8-brane and an orientifold plane of charge (-1) which sits at infinite coupling. We construct the M(atrix) theory for M theory on a Klein bottle (and the theories related to it), which is given by a 2 + 1 dimensional gauge theory with a varying gauge coupling compactified on a cylinder with specific boundary conditions. We also clarify the construction of the M(atrix) theory for backgrounds of rank 18, including the heterotic string on a circle

Comments on worldsheet theories dual to free large N gauge theories

We continue to investigate properties of the worldsheet conformal field theories (CFTs) which are conjectured to be dual to free large N gauge theories, using the mapping of Feynman diagrams to the worldsheet suggested in hep-th/0504229. The modular invariance of these CFTs is shown to be built into the formalism. We show that correlation functions in these CFTs which are localized on subspaces of the moduli space may be interpreted as delta-function distributions, and that this can be consistent with a local worldsheet description given some constraints on the operator product expansion coefficients. We illustrate these features by a detailed analysis of a specific four-point function diagram. To reliably compute this correlator we use a novel perturbation scheme which involves an expansion in the large dimension of some operators.Comment: 43 pages, 16 figures, JHEP format. v2: added reference

The Black Hole in the Throat - Thermodynamics of Strongly Coupled Cascading Gauge Theories

We numerically construct black hole solutions corresponding to the deconfined, chirally symmetric phase of strongly coupled cascading gauge theories at various temperatures. We compute the free energy as a function of the temperature, and we show that it becomes positive below some critical temperature, indicating the possibility of a first order phase transition at which the theory deconfines and restores the chiral symmetry