Black-holes, topological strings and large N phase transitions

The counting of microstates of BPS black-holes on local Calabi-Yau of the form ${\mathcal O}(p-2)\oplus{\mathcal O}(-p) \longrightarrow S^2$ is explored by computing the partition function of q-deformed Yang-Mills theory on $S^2$. We obtain, at finite $N$, the instanton expansion of the gauge theory. It can be written exactly as the partition function for U(N) Chern-Simons gauge theory on a Lens space, summed over all non-trivial vacua, plus a tower of non-perturbative instanton contributions. In the large $N$ limit we find a peculiar phase structure in the model. At weak string coupling the theory reduces to the trivial sector and the topological string partition function on the resolved conifold is reproduced in this regime. At a certain critical point, instantons are enhanced and the theory undergoes a phase transition into a strong coupling regime. The transition from the strong coupling phase to the weak coupling phase is of third order.Comment: 16 pages, 3 figures; Invited talk given at QG05, Cala Gonone (Italy), September 200

Matrix Models of Noncommutative (2d+1) Lattice Gauge Theories

We investigate the problem of mapping, through the Morita equivalence, odd dimensional noncommutative lattice gauge theories onto suitable matrix models. We specialize our analysis to noncommutative three dimensional QED (NCQED) and scalar QED (NCSQED), for which we explicitly build the corresponding Matrix Model.Comment: 13 pages, LaTeX, no Figure

Instanton Counting and Wall-Crossing for Orbifold Quivers

Noncommutative Donaldson-Thomas invariants for abelian orbifold singularities can be studied via the enumeration of instanton solutions in a six-dimensional noncommutative {Mathematical expression} gauge theory; this construction is based on the generalized McKay correspondence and identifies the instanton counting with the counting of framed representations of a quiver which is naturally associated with the geometry of the singularity. We extend these constructions to compute BPS partition functions for higher-rank refined and motivic noncommutative Donaldson-Thomas invariants in the Coulomb branch in terms of gauge theory variables and orbifold data. We introduce the notion of virtual instanton quiver associated with the natural symplectic charge lattice which governs the quantum wall-crossing behaviour of BPS states in this context. The McKay correspondence naturally connects our formalism with other approaches to wall-crossing based on quantum monodromy operators and cluster algebras

Spacetime Properties of ZZ D-Branes

We study the tachyon and the RR field sourced by the $(m,n)$ ZZ D-branes in type 0 theories using three methods. We first use the mini-superspace approximation of the closed string wave functions of the tachyon and the RR scalar to probe these fields. These wave functions are then extended beyond the mini-superspace approximation using mild assumptions which are motivated by the properties of the corresponding wave functions in the mini-superspace limit. These are then used to probe the tachyon and the RR field sourced. Finally we study the space time fields sourced by the $(m,n)$ ZZ D-branes using the FZZT brane as a probe. In all the three methods we find that the tension of the $(m,n)$ ZZ brane is $mn$ times the tension of the $(1,1)$ ZZ brane. The RR charge of these branes is non-zero only for the case of both $m$ and $n$ odd, in which case it is identical to the charge of the $(1,1)$ brane. As a consistency check we also verify that the space time fields sourced by the branes satisfy the corresponding equations of motion.Comment: 32 pages, 4 figures. Clarifications on the principal characterization of ZZ branes added. Reference adde

Area-preserving diffeomorphisms in gauge theory on a non-commutative plane: a lattice study

We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results are consistent with the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either.Comment: 28 pages, 15 figures, published versio

Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED

We re-examine the perturbative properties of four-dimensional non-commutative QED by extending the pinch techniques to the theta-deformed case. The explicit independence of the pinched gluon self-energy from gauge-fixing parameters, and the absence of unphysical thresholds in the resummed propagators permits a complete check of the optical theorem for the off-shell two-point function. The known anomalous (tachyonic) dispersion relations are recovered within this framework, as well as their improved version in the (softly broken) SUSY case. These applications should be considered as a first step in constructing gauge-invariant truncations of the Schwinger-Dyson equations in the non-commutative case. An interesting result of our formalism appears when considering the theory in two dimensions: we observe a finite gauge-invariant contribution to the photon mass because of a novel incarnation of IR/UV mixing, which survives the commutative limit when matter is present.Comment: 30 pages, 2 eps figure, uses axodraw. Citations adde

Morita Duality and Noncommutative Wilson Loops in Two Dimensions

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the combinatorics of non-planar graphs. Several nonperturbative examples of symmetry breaking under area-preserving diffeomorphisms are thereby presented. Analytic expressions for correlators of Wilson loops with infinite winding number are also derived and shown to agree with results from ordinary Yang-Mills theory.Comment: 32 pages, 9 figures; v2: clarifying comments added; Final version to be published in JHE

Magnetic and transport properties of the new antiferromagnetic Kondo-lattice CeNiBi2

We report results of the first studies on the magnetic and transport properties of a new material CeNiBi_2. The magnetic susceptibility exhibits a sharp peak at T_N = 6K, indicating an antiferromagnetic phase transition. This antiferromagnetic order below T_N is confirmed by magnetization measurement, which displays a metamagnetic-like transition at H_m = 5 T. Both low-temperature susceptibility and high-field magnetization are suggestive of strong crystalline-electric-field effect in CeNiBi_2. The electrical resistivity shows the presence of Kondo and crystal-field effects with a sharp drop below TN due to the antiferromagnetic ordering. This sharp drop below T_N in the electrical resistivity is suppressed slightly to higher temperatures by an applied magnetic field to 18 T. With increasing magnetic field, the slope of magnetoresistance changes from positive to negative, being indicative of the transition to a ferromagnetic state.Comment: 11 pages, including 4 figure

An example of localized D-branes solution on PP-wave backgrounds

In this note we provide an explicit example of type IIB supersymmetric D3-branes solution on a pp-wave like background, consisting in the product of an eight-dimensional pp-wave times a two-dimensional flat space. An interesting property of our solution is the fully localization of the D3-branes (i.e. the solution depends on all the transverse coordinates). Then we show the generalization to other Dp-branes and to the D1/D5 system.Comment: 14 pages, 1 table; v2. references adde