Evidence for a conformal phase in SU(N) gauge theories

We discuss the existence of a conformal phase in SU(N) gauge theories in four dimensions. In this lattice study we explore the model in the bare parameter space, varying the lattice coupling and bare mass. Simulations are carried out with three colors and twelve flavors of dynamical staggered fermions in the fundamental representation. The analysis of the chiral order parameter and the mass spectrum of the theory indicates the restoration of chiral symmetry at zero temperature and the presence of a Coulomb-like phase, depicting a scenario compatible with the existence of an infrared stable fixed point at nonzero coupling. Our analysis supports the conclusion that the onset of the conformal window for QCD-like theories is smaller than Nf=12, before the loss of asymptotic freedom at sixteen and a half flavors. We discuss open questions and future directions.Comment: 11 pages, 11 figures; extended analysis, conclusions unchanged. (version to appear in PRD

Quenched penguin operators and the Delta I=1/2 rule

The transformation properties of strong penguin operators under the action of the flavor group change when they are considered as operators in (partially) quenched QCD instead of the unquenched theory. As a result, additional operators and new low-energy constants appear in the effective theory describing non-leptonic kaon decay matrix elements in the partially quenched setting. These new low-energy constants do not have a counterpart in the unquenched theory, and should thus be considered as an artifact of the quenched approximation. Here we consider strong penguin operators consisting of products of two left-handed flavor currents, and give a complete one-loop analysis in the effective theory for K^0 to vacuum and K^+ to pi^+ matrix elements. We find that the new low-energy constants already appear in these matrix elements at leading order. This implies that (partially) quenched lattice computations of for instance the Delta I=1/2 rule are affected by ambiguities intrinsic to the use of the quenched approximation at leading order. The only exception is the partially quenched case with three light sea quarks, consistent with general expectations. Our results are also relevant when the charm quark is kept in the theory.Comment: 18 pages; footnote added with comment on hep-lat/0603025, appendix and other minor clarifications adde

One,Two,Zero: Scales of Strong Interactions

We discuss our results on QCD with a number of fundamental fermions ranging from zero to sixteen. These theories exhibit a wide array of fascinating phenomena which have been under close scrutiny, especially in recent years, first and foremost is the approach to conformality. To keep this review focused, we have chosen scale generation, or lack thereof as a guiding theme, however the discussion will be set in the general framework of the analysis of the phases and phase transitions of strong interactions at zero and nonzero temperature.Comment: 15 pages, prepared for IJMPA Special Issue 'Recent Nonperturbative Developments in QCD-like Theories

On the particle spectrum and the conformal window

We study the SU(3) gauge theory with twelve flavours of fermions in the fundamental representation as a prototype of non-Abelian gauge theories inside the conformal window. Guided by the pattern of underlying symmetries, chiral and conformal, we analyze the two-point functions theoretically and on the lattice, and determine the finite size scaling and the infinite volume fermion mass dependence of the would-be hadron masses. We show that the spectrum in the Coulomb phase of the system can be described in the context of a universal scaling analysis and we provide the nonperturbative determination of the fermion mass anomalous dimension gamma*=0.235(46) at the infrared fixed point. We comment on the agreement with the four-loop perturbative prediction for this quantity and we provide a unified description of all existing lattice results for the spectrum of this system, them being in the Coulomb phase or the asymptotically free phase. Our results corroborate the view that the fixed point we are studying is not associated to a physical singularity along the bare coupling line and estimates of physical observables can be attempted on either side of the fixed point. Finally, we observe the restoration of the U(1) axial symmetry in the two-point functions.Comment: 40 pages, 22 figure

Chiral symmetry restoration in QCD with many flavours

We discuss the phases of QCD in the parameter space spanned by the number of light flavours and the temperature with respect to the realisation of chiral and conformal symmetries. The intriguing interplay of these symmetries is best studied by means of lattice simulations, and some selected results from our recent work are presented here.Comment: 10 pages, proceedings of the 9th International Workshop on Critical Point and Onset of Deconfinement, 17-21 November, 2014, ZiF, Bielefeld, German

Chiral symmetry of QCD with twelve light flavors

We study QCD with twelve light flavors at intermediate values of the bare lattice coupling. We contrast the results for the order parameter with different theoretical models motivated by the physics of the Goldstone phase and of the symmetric phase, and we perform a model independent analysis of the meson spectrum inspired by universal properties of chiral symmetry. Our analysis favors chiral symmetry restoration.Comment: 7 pages, 3 figures. To appear in the proceedings of the XXVIII International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Ital