Michele Pepe

Static quark potential and effective string corrections in the (2+1)-d SU(2) Yang-Mills theory

We report on a very accurate measurement of the static quark potential in SU(2) Yang-Mills theory in (2+1) dimensions in order to study the corrections to the linear behaviour. We perform numerical simulations at zero and finite temperature comparing our results with the corrections given by the effective string picture in these two regimes. We also check for universal features discussing our results together with those recently published for the (2+1)-d (2) and SU(3) pure gauge theories.

The deconfinement phase transition of Sp(2) and Sp(3) Yang–Mills theories in 2+1 and 3+1 dimensions

Abstract Some time ago, Svetitsky and Yaffe have argued that—if the deconfinement phase transition of a ( d +1)-dimensional Yang–Mills theory with gauge group G is second order—it should be in the universality class of a d -dimensional spin model symmetric under the center of G . For d =3 these arguments have been confirmed numerically only in the SU (2) case with center Z (2) , simply because all SU ( N ) Yang–Mills theories with N ⩾3 seem to have non-universal first order phase transitions. The symplectic groups Sp ( N ) also have the center Z (2) and provide another extension of SU (2)= Sp (1) to general N . Using lattice simulations, we find that the deconfinement phase transition of Sp (2) Yang–Mills theory is first order in 3+1 dimensions, while in 2+1 dimensions stronger fluctuations induce a second order transition. In agreement with the Svetitsky–Yaffe conjecture, for (2+1)d Sp (2) Yang–Mills theory we find the universal critical behavior of the 2d Ising model. For Sp (3) Yang–Mills theory the transition is first order both in 2+1 and in 3+1 dimensions. This suggests that the size of the gauge group—and not the center symmetry—determines the order of the deconfinement phase transition.

Width of the confining string in Yang-Mills theory.

We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)D SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multilevel algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher-order terms in the effective string action are calculated analytically. They accurately fit the numerical data.

The Width of the Color Flux Tube at 2-Loop Order

The color flux tube connecting a static quark-anti-quark pair in Yang-Mills theory supports massless transverse fluctuations, which are the Goldstone bosons of spontaneously broken translation invariance. Just as in chiral perturbation theory, the dynamics of these Goldstone bosons is described by a systematic low-energy effective field theory. We use the effective theory to calculate the width of the fluctuating string at the 2-loop level, using both cylindrical and toroidal boundary conditions. At zero temperature, the string width diverges logarithmically with the quark-anti-quark distance r. On the other hand, at low but non-zero temperature T = 1/β, for r ≫ β the string width diverges linearly.

Topological lattice actions

We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge Q. Irrespective of this, in the 2-d O(3) model the topological susceptibility

Linear broadening of the confining string in Yang-Mills theory at low temperature

{\chi_t} = {{{\left\langle {{Q^2}} \right\rangle }} \left/ {V} \right.}

Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case

is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some classically important features of an action are irrelevant for reaching the correct quantum continuum limit.

Thedeconfinement phase transition in Yang-Mills theory with general Lie group G☆

The logarithmic broadening predicted by the systematic low-energy effective field theory for the confining string has recently been verified in numerical simulations of (2 + 1)-d SU(2) lattice Yang-Mills theory at zero temperature. The same effective theory predicts linear broadening of the string at low non-zero temperature. In this paper, we verify this prediction by comparison with very precise Monte Carlo data. The comparison involves no additional adjustable parameters, because the low-energy constants of the effective theory have already been fixed at zero temperature. It yields very good agreement between the underlying Yang-Mills theory and the effective string theory.

Equation of state of the SU(3) Yang–Mills theory: A precise determination from a moving frame

Slowly walking technicolor models provide a mechanism for electroweak symmetry breaking whose nonperturbative lattice investigation is rather challenging. Here we demonstrate walking near a conformal fixed point considering the 2-d lattice O(3) model at vacuum angle

Equation of state of a relativistic theory from a moving frame.

\theta \approx \pi