[Paper Review] The strong coupling regime of twelve flavors QCD

Tiago Nunes da Silva, Elisabetta Pallante|arXiv (Cornell University)|Nov 15, 2012

Quantum Chromodynamics and Particle Interactions4 references4 citations

TL;DR

This paper investigates the strong coupling phase transition in SU(3) lattice QCD with twelve fundamental flavors, comparing non-improved and improved Wilson actions. It confirms a first-order bulk transition at strong coupling using both actions, while showing that improvement induces a second rapid crossover and an exotic chirally symmetric phase due to non-hermiticity from non-nearest-neighbor interactions, with implications for strongly coupled systems near the conformal window.

ABSTRACT

da Silva and E. Pallante,“The bulk transition of QCD with twelve flavors and the role of im-provement”] for the SU(3) gauge theory with N f = 12 fundamental flavors, and we add some numerical evidence and theoretical discussion. In particular, we study the nature of the bulk tran-sition that separates a chirally broken phase at strong coupling from a chirally restored phase at weak coupling. When a non-improved action is used, a rapid crossover is observed at small bare quark masses. Our results confirm a first order nature for this transition, in agreement with pre-vious results we obtained using an improved action. As shown in Ref. [1], when improvement of the action is used, the transition is preceded by a second rapid crossover at weaker coupling and an exotic phase emerges, where chiral symmetry is not yet broken. This can be explained [1] by the non hermiticity of the improved lattice Transfer matrix, arising from the competition of nearest-neighbor and non-nearest neighbor interactions, the latter introduced by improvement and becoming increasingly relevant at strong coupling and coarse lattices. We further comment on how improvement may generally affect any lattice system at strong coupling, be it graphene or non abelian gauge theories inside or slightly below the conformal window.

Motivation & Objective

• To investigate the nature of the bulk phase transition in SU(3) QCD with twelve fundamental flavors at strong coupling.
• To examine how improvement of the lattice action affects the phase structure and chiral symmetry realization.
• To understand the origin of an exotic chirally symmetric phase observed with improved actions.
• To analyze the role of non-hermiticity in the lattice transfer matrix arising from non-nearest-neighbor interactions in the improved action.
• To generalize insights on improvement effects in strongly coupled systems, including non-Abelian gauge theories and materials like graphene.

Proposed method

• Numerical simulations of SU(3) gauge theory with Nf = 12 fundamental fermions on the lattice.
• Use of both non-improved and improved Wilson fermion actions to compare phase structure.
• Analysis of the bulk transition via the behavior of the chiral condensate and Polyakov loop as functions of bare quark mass and gauge coupling.
• Investigation of the non-hermiticity of the improved lattice transfer matrix due to additional non-nearest-neighbor interactions introduced by improvement.
• Study of the emergence of a second rapid crossover at weaker coupling in the improved action case.
• Theoretical discussion of how strong coupling and coarse lattices amplify the impact of non-nearest-neighbor terms in improved actions.

Experimental results

Research questions

• RQ1 What is the nature of the bulk phase transition in 12-flavor QCD at strong coupling when using a non-improved action?
• RQ2 How does the use of an improved lattice action alter the phase diagram and chiral symmetry realization?
• RQ3 What causes the emergence of an exotic chirally symmetric phase in the improved action scenario?
• RQ4 Why does the improved action lead to non-hermiticity in the lattice transfer matrix, and how does this affect the phase structure?
• RQ5 To what extent do these effects generalize to other strongly coupled systems, such as those near the conformal window or in condensed matter systems like graphene?

Key findings

• The bulk transition in 12-flavor QCD is confirmed to be first order when using a non-improved action, consistent with previous results.
• With the improved action, a second rapid crossover appears at weaker coupling, preceding the main transition.
• An exotic phase emerges where chiral symmetry is not yet broken, even at strong coupling, due to the influence of non-nearest-neighbor interactions.
• The non-hermiticity of the improved lattice transfer matrix arises from the competition between nearest-neighbor and longer-range interactions introduced by improvement.
• The effects of improvement become increasingly significant at strong coupling and coarse lattice spacing, altering the phase structure substantially.
• These findings suggest that improvement can induce qualitatively new phases and non-trivial dynamics in strongly coupled lattice systems, including those near the conformal window or in systems like graphene.