A Monte Carlo study of the three-states antiferromagnetic Potts model in two dimensions

Using Monte Carlo methods the author studies the two-dimensional three-stages Potts model with antiferromagnetic nearest neighbours and ferromagnetic next-nearest neighbours couplings on a square lattice. The author focuses on the case with only antiferromagnetic coupling; from the analysis of the data gathered, there is evidence that this system shows critical behaviour only at T=0

Wilson Loops and Chiral Correlators on Squashed Sphere

We study chiral deformations of ${\cal N}=2$ and ${\cal N}=4$ supersymmetric gauge theories obtained by turning on $\tau_J \,{\rm tr} \, \Phi^J$ interactions with $\Phi$ the ${\cal N}=2$ superfield. Using localization, we compute the deformed gauge theory partition function $Z(\vec\tau|q)$ and the expectation value of circular Wilson loops $W$ on a squashed four-sphere. In the case of the deformed ${\cal N}=4$ theory, exact formulas for $Z$ and $W$ are derived in terms of an underlying $U(N)$ interacting matrix model replacing the free Gaussian model describing the ${\cal N}=4$ theory. Using the AGT correspondence, the $\tau_J$-deformations are related to the insertions of commuting integrals of motion in the four-point CFT correlator and chiral correlators are expressed as $\tau$-derivatives of the gauge theory partition function on a finite $\Omega$-background. In the so called Nekrasov-Shatashvili limit, the entire ring of chiral relations is extracted from the $\epsilon$-deformed Seiberg-Witten curve. As a byproduct of our analysis we show that $SU(2)$ gauge theories on rational $\Omega$-backgrounds are dual to CFT minimal models.Comment: 33 pages, 2 figure, in this version we have added two new references and a detailed comparison with the results obtained in one of these tw

On the Stability of a Stringy Black Hole

We study the stability under perturbations of a charged four dimensional stringy black hole arising from gauging a previously studied WZW model. We find that the black hole is stable only in the extremal case $Q=M$.Comment: 14 pages + 1 figure (not included but available on request

Exotic prepotentials from D(-1)D7 dynamics

We compute the partition functions of D(-1)D7 systems describing the multi-instanton dynamics of SO(N) gauge theories in eight dimensions. This is the simplest instance of the so called exotic instantons. In analogy with the Seiberg-Witten theory in four space-time dimensions, the prepotential and correlators in the chiral ring are derived via localization formulas and found to satisfy relations of the Matone type. Exotic prepotentials of SO(N) gauge theories with N=2 supersymmetries in four-dimensions are also discussed.Comment: 19 page