We propose an effective model of strongly coupled gauge theory at finite temperature on $R^3$ in the presence of an infrared cutoff. It is constructed by considering the theory on $S^3$ with an infrared cutoff and then taking the size of the $S^3$ to
infinity while keeping the cutoff fixed. This model reproduces various qualitative features expected from its gravity dual.
After reviewing the thermodynamics and critical phenomena associated with AdS black holes carrying multiple R-charges in various dimensions, we do a Bragg-Williams like analysis of the systems around its critical points. This leads us to propose an e
ffective potential governing the equilibrium properties of the boundary gauge theory. We also study certain non-equilibrium phenomena associated with these gauge theories. In particular, we compute the conductivities and diffusion coefficients for theories with multiple R-charges in four, three and six dimensions.
In this note we discuss a possible holographic dual of the two dimensional conformal field theory associated with the world-sheet of a macroscopic superstring in a compactification on four-torus. We assume the near horizon geometry of the black strin
g has symmetries of $AdS_3times S^3times T^4$ and construct a sigma model in the bulk. Analyzing the symmetries of the bulk theory and comparing them with those of the CFT in a special light-cone gauge we find agreement between global symmetries. Due to non-standard gauge realization it is not clear how affine symmetries can be realized.
Various topological properties of D-branes in the type--IIA theory are captured by the topologically twisted B-model, treating D-branes as objects in the bounded derived category of coherent sheaves on the compact part of the target space. The set of
basic D-branes wrapped on the homology cycles of the compact space are taken to reside in the heart of t-structures of the derived category of coherent sheaves on the space at any point in the Kahler moduli space. The stability data entails specifying a t-structure along with a grade for sorting the branes. Considering an example of a degenerate Calabi-Yau space, obtained via geometric engineering, that retains but a projective curve as the sole non-compact part, we identify the regions in the Kahler moduli space of the curve that pertain to the different t-structures of the bounded derived category of coherent sheaves on the curve corresponding to the different phases of the topological branes.
Problems of stabilizing moduli of the type--IIB string theory on toroidal orientifolds $T^6/Z_2$, in presence of worldvolume fluxes on various D-branes, are considered. For $Z_2$ actions, introducing either O9 or O3 planes, we rule out the possibilit
y of moduli stabilization in a wide class of models with $mathcal{N}=1$ supersymmetry, characterized by the type of fluxes turned on along D-brane worldvolume. Our results, in particular, imply that Abelian worldvolume fluxes can not by themselves stabilize closed string moduli, in a consistent supersymmtric model, for above orientifold compactifications. We also discuss other $Z_2$ orientifolds of $T^6$ and show that certain other brane wrappings are also ruled out by similar consistency requirements. In specific setups we consider examples with D9-branes wrapping on a complex three-torus with its world-volume fluxes taken to be semi-homogeneous bundles and D7-branes wrapping holomorphic four-cycles of the complex three-torus carrying world-volume fluxes.
This is a continuation of our earlier work where we constructed a phenomenologically motivated effective action of the boundary gauge theory at finite temperature and finite gauge coupling on $S^3 times S^1$. In this paper, we argue that this effecti
ve action qualitatively reproduces the gauge theory representing various bulk phases of R-charged black hole with Gauss-Bonnet correction. We analyze the system both in canonical and grand canonical ensemble.
