Claudio Pica

Higher representations on the lattice: Numerical simulations, SU(2) with adjoint fermions

We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group and present in detail the implementation of the hybrid Monte Carlo (HMC)/rational HMC algorithm for simulating dynamical fermions. We discuss the validation of the implementation through an extensive set of tests and the stability of simulations by monitoring the distribution of the lowest eigenvalue of the Wilson-Dirac operator. Working with two flavors of Wilson fermions in the adjoint representation, benchmark results for realistic lattice simulations are presented. Runs are performed on different lattice sizes ranging from 4{sup 3}x8 to 24{sup 3}x64 sites. For the two smallest lattices we also report the measured values of benchmark mesonic observables. These results can be used as a baseline for rapid cross-checks of simulations in higher representations. The results presented here are the first steps toward more extensive investigations with controlled systematic errors, aiming at a detailed understanding of the phase structure of these theories, and of their viability as candidates for strong dynamics beyond the standard model.

Two flavor QCD and confinement

We argue that the order of the chiral transition for N_f=2 is a sensitive nprobe of the QCD vacuum, in particular of the mechanism of color confinement. A nstrategy is developed to investigate the order of the transition by use of nfinite size scaling analysis. An in-depth numerical investigation is performed nwith staggered fermions on lattices with N_t=4 and N_s=12,16,20,24,32 and quark nmasses am_q ranging from 0.01335 to 0.307036. The specific heat and a number of nsusceptibilities are measured and compared with the expectations of an O(4) nsecond order and of a first order phase transition. A second order transition nin the O(4) and O(2) universality classes are excluded. Substantial evidence nemerges for a first order transition. A detailed comparison with previous works nis performed.

Topological susceptibility from the overlap

The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge. Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study the topology of the gauge configurations. The topological charge is obtained from the zero modes of the overlap and using a new algorithm for the spectral flow analysis. A detailed comparison with cooling techniques is presented. Particular care is taken in assessing the systematic errors. Relatively high statistics (500 to 1000 independent configurations) yield an extrapolated continuum limit with errors that are comparable with other methods. Our current value from the overlap is χ1/4 = 188±12±5 MeV.

Correlation functions of the energy-momentum tensor in SU(2) gauge theory at finite temperature

We calculate correlation functions of the energy-momentum tensor in the vicinity of the deconfinement phase transition of (3 + 1)-dimensional SU(2) gauge theory and discuss their critical behavior in the vicinity of the second order deconfinement transition. We show that correlation functions of the trace of the energy-momentum tensor diverge uniformly at the critical point in proportion to the specific heat singularity. Correlation functions of the pressure, on the other hand, stay finite at the critical point. We discuss the consequences of these findings for the analysis of transport coefficients, in particular, the bulk viscosity, in the vicinity of a second order phase transition point.

Quenched mesonic spectrum at large N

We compute the masses of the π and of the ρ mesons in the quenched approximation on a lattice with fixed lattice spacing a ≃ 0.145 fm for SU(N) gauge theory with N = 2,3,4,6. We find that a simple linear expression in 1/N 2 correctly captures the features of the lowest-lying meson states at those values of N. This enables us to extrapolate to N = ∞ the behaviour of mas a function of the quark mass and of mas a function of m�. Our results for the latter agree within 5% with recent predictions obtained in the AdS/CFT framework.

Baryon currents in QCD with compact dimensions

On a compact space with nontrivial cycles, for sufficiently small values of the radii of the compact dimensions, SU(N) gauge theories coupled with fermions in the fundamental representation spontaneously break charge conjugation, time reversal, and parity. We show at one loop in perturbation theory that a physical signature for this phenomenon is a nonzero baryonic current wrapping around the compact directions. The persistence of this current beyond the perturbative regime is checked by lattice simulations.

Lattice study of planar equivalence: The quark condensate

We study quenched SU(N) gauge theories with fermions in the two-index symmetric, antisymmetric and the adjoint representations. Our main motivation is to check whether at large number of colors those theories become nonperturbatively equivalent. We prove the equivalence assuming that the charge-conjugation symmetry is not broken in pure Yang-Mills theory. We then carry out a quenched lattice simulation of the quark condensate in the symmetric, antisymmetric and the adjoint representations for SU(2), SU(3), SU(4), SU(6), and SU(8). We show that the data support the equivalence and discuss the size of subleading corrections.

Monopole condensation in two-flavor adjoint QCD

In QCD with adjoint fermions, the deconfining transition takes place at a lower temperature than the chiral transition. We study the two transitions by use of the Polyakov loop, the monopole order parameter, and the chiral condensate. The deconfining transition is first order, the chiral is a crossover. The order parameters for confinement are not affected by the chiral transition. We conclude that the degrees of freedom relevant to confinement are different from those describing chiral symmetry.

G2 gauge theory at finite temperature

The gauge group being centreless, G2 gauge theory is a good laboratory for studying the role of the centre of the group for colour confinement in Yang-Mills gauge theories. In this paper, we investigate G2 pure gauge theory at finite temperature on the lattice. By studying the finite size scaling of the plaquette, the Polyakov loop and their susceptibilities, we show that a deconfinement phase transition takes place. The analysis of the pseudocritical exponents give strong evidence of the deconfinement transition being first order. Implications of our findings for scenarios of colour confinement are discussed.

Deconfining transition in two-flavor QCD

SUMMARY The order and the nature of the finite-temperature phase transition of QCD nwith two flavors of dynamical quarks is investigated. An analysis of the ncritical exponent of the specific heat is performed through finite-size and nfinite-mass scaling of various susceptibilities. Dual superconductivity of QCD nvacuum is investigated using a disorder parameter, namely the v.e.v. of a nmonopole creation operator. Hybrid R simulations were run at lattice spatial nsizes of