θ -dependence and center symmetry in Yang-Mills theories

Abstract

We investigate the relation between the realization of center symmetry and the dependence on the topological parameter θ in SU (N ) Yang-Mills theories, exploiting trace deformations as a tool to regulate center symmetry breaking in a theory with a small compactified direction. We consider, in particular, SU (4) gauge theory, which admits two possible independent deformations, and study, as a first step, its phase diagram in the deformation plane for two values of the inverse compactified radius going up to L −1 ∼ 500 MeV, comparing the predictions of the effective 1-loop potential of the Polyakov loop with lattice results. The θ-dependence of the various phases is then addressed, up to the fourth order in θ, by numerical simulations: results are found to coincide, within statistical errors, with those of the standard confined phase iff center symmetry is completely restored and independently of the particular way this happens, i.e. either by local suppression of the Polyakov loop traces or by long range disorder.

The large $$N_{c}$$ limit of QCD on the lattice

“…[174]. A number of results at varying N c at finite-temperature exist 19 [64,82,84,[175][176][177][178][179][180][181][182][183][184]. Recent lattice results with different gauge groups and fermion content can be found in [114,[185][186][187].…”

Large-N SU(N) Yang-Mills theories with milder topological freezing

“…Analytic estimates ofχ and of theb 2n coefficients are available only for two dimensional models [9][10][11][12][13]. Given the non-perturbative nature of θ-dependence, the numerical lattice approach is the natural tool to investigate such topics quantitatively, and in particular to test large-N predictions [11,[13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. There are however some non-trivial computational challenges that have to be faced, especially in the large N regime.…”

“…The method was exploited for the determination of the b 2n coefficients first in ref. [22] and later developed and applied in several works to both SU(N ) Yang-Mills theory [13,[25][26][27] and two dimensional CP N −1 models [37,38].…”

Prospects for large N gauge theories on the lattice

“…Unquestionably, as the parameter h is switched on, both quantities approach the zero-temperature values. Furthermore, a study in SU(4) has shown that the θ -dependence of the deformed theory coincides with that at zero temperature whenever there is full center symmetry restoration [35,36].…”