Antonio González-Arroyo

A bstract: We investigate the universal features of chiral symmetry breaking in large- N QCD by comparing non-perturbative determinations of the low-lying Dirac spectrum with chiral Random Matrix Theory (RMT) predictions. Our numerical Monte Carlo calculations are based on a chiral lattice discretization of the Dirac operator, and exploit twisted volume reduction to reach N as large as 841. Matching lattice data with RMT analytic results, we are able to extract the large- N chiral condensate, which is compared with a recent determination obtained with non-chiral Wilson quarks from twisted volume-reduced models.

A bstract: We study the behaviour of SU(2) Yang-Mills fields on a T ₂ × R ² geometry where the two-torus is equipped with twisted boundary conditions. We monitor the evolution of the dynamics of the system as a function of the torus size l _s . For small sizes the behaviour of the system is well understood in terms of semiclassical predictions. In our case, the long distance structure is that of a two-dimensional gas of vortex-like fractional instantons with size and density growing with l _s . Our lattice Monte Carlo simulations confirm the semiclassical predictions and allow the determination of the relevant scale signalling the transition to the non-dilute situation. At low densities the string tension takes the standard value of a 2D center-vortex gas, growing with the density and approaching the value measured at infinite volume. Our work includes preliminary studies of the extension to SU(N) and to the region of large sizes in which boundary conditions are irrelevant, and all physical scales are determined by the Λ parameter.

We report results obtained for SU(2) Yang-Mills theory on a four dimensional torus with two directions much smaller than the other two. The small 2-torus is equipped with twisted boundary conditions. This construction provides a way to interpolate from a region in which semiclassical methods can be applied (for small 2-torus size) to the standard infinite volume case. Our simulations at small torus sizes show how the topological charge and the string tension result from a gas of vortex-like fractional instantons. As the size becomes larger the density increases and the separation of structures tends to a constant in agreement with the fractional instanton liquid model picture of the Yang-Mills vacuum.

We report results obtained for SU(2) Yang-Mills theory on a 4d torus with two directions much smaller than the other two. The small 2-torus is equipped with twisted boundary conditions. This construction provides a way to interpolate from a region in which semiclassical methods can be applied (for small 2-torus size) to the standard infinite volume case. Our simulations at small torus sizes show how the topological charge and the string tension result from a gas of vortex-like fractional instantons. As the size becomes larger the density increases and the separation of structures tends to a constant in agreement with the fractional instanton liquid model picture of the Yang-Mills vacuum.

We present results for the large-$N$ limit of the chiral condensate computed from twisted reduced models. We followed a two-fold strategy, one constiting in extracting the condensate from the quark-mass dependence of the pion mass, the other consisting in extracting the condensate from the mode number of the Dirac operator.