Light adjoint quarks in the instanton-dyon liquid model. IV.

Abstract

We discuss the instanton-dyon liquid model with N f Majorana quark flavors in the adjoint representation of color SUc(2) at finite temperature. We briefly recall the index theorem on S 1 × R 3 for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with N f light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective theory with adjoint quarks with manifest SU (N f ) × Z4N f symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for N f = 1. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry throughAs the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.

Instanton-dyon liquid model. V. Twisted light quarks

“…This work is a continuation of our earlier studies [3][4][5][6] of the gauge topology using the instanton-dyon liquid model. The starting point of the model are the KvBLL instantons threaded by finite holonomies and their splitting into instanton-dyon constituents [7], with strong semi-classical interactions [8][9][10].…”

“…For ν 1 → 1/3 the holonomy induced mass-like contribution in (64) becomes arbitrarily small. As we noted earlier, we use it to regulate the infrared sensitivity of the ds-contributions in (67) through a suitable redefinition of the fugacities f 2,3 as in [6]. With this in mind, the extrema of (67) with respect to Σ, Λ yield the respective gap equations…”

“…We will follow our original discussion with light quarks in [4], with the determinantal interactions in (1) providing for an effective core repulsion on average. We omit the explicit repulsion between the cores as in [6], for simplicity. The fugacities f i are related to the overall instanton-dyon density, and can be estimated using lattice simulations [2].…”

“…We note that for the flavor twisted boundary condition (4), f = d, s corresponds toφ = ∓π/3 (mod 2π) in (13) which are not normalizable BPS zero modes at exactly ν = 1/3. Following our analysis in [6], we choose to regulate the zero modes by approaching the holonomies in the center symmetric phase as follows ( 1,2 → +0)…”

Recent progress in understanding deconfinement and chiral restoration phase transitions

“…The lattice simulation indeed show weakening of chiral symmetry violation effects with increasing N f , but specific results about on the end of chiral symmetry breaking are so far rather incomplete: for N c = 3 we know that in the N f = 4 case the chiral in the conformal window. Another important generalization -for quarks in the adjoint representation -is made in a separate paper [19]. The number of fermionic zero modes increases, and they are more comlicated.…”