Instanton-dyon liquid model. III. Finite chemical potential

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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.

Section: Introductionmentioning

confidence: 67%

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

Liu¹,

Shuryak²,

Zahed³

2016

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“…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].…”

Section: Introductionmentioning

confidence: 89%

Instanton-dyon liquid model. V. Twisted light quarks

Liu¹,

Shuryak²,

Zahed³

2016

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We discuss an extension of the instanton-dyon liquid model that includes twisted light quarks in the fundamental representation with explicit ZN c symmetry for the case with equal number of colors Nc and flavors N f . We map the model on a 3-dimensional quantum effective theory, and analyze it in the mean-field approximation. The effective potential and the vacuum chiral condensates are made explicit for N f = Nc = 2, 3. The low temperature phase is center symmetric but breaks spontaneously flavor symmetry with N f − 1 massless pions. The high temperature phase breaks center symmetry but supports finite and unequal quark condensates.

“…Recent progress to be discussed below is related to studies of the instanton-dyon ensembles. One series of papers were devoted to high-density phase and mean field approximation [11][12][13][14][15]. Our efforts were so far focused on the direct numerical simulation of the dyon ensembles [16][17][18][19] .…”

Section: Introductionmentioning

confidence: 99%

Hadronic correlation functions in the random instanton-dyon ensemble

Larsen

Shuryak

2017

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It is known since 1980's that the instanton-induced 't Hooft effective Lagrangian not only can solve the so called U (1)a problem, by making the η meson heavy etc, but it can also lead to chiral symmetry breaking. In 1990's it was demonstrated that, taken to higher orders, this Lagrangian correctly reproduces effective forces in a large set of hadronic channels, mesonic and baryonic ones. Recent progress in understanding gauge topology at finite temperatures is related with the so called instanton-dyons, the constituents of the instantons. Some of them, called L-dyons, possess the antiperiodic fermionic zero modes, and thus form a new version of the 't Hooft effective Lagrangian. This paper is our first study of a wide set of hadronic correlation function. We found that, at the lowest temperatures at which this approach is expected to be applicable, those may be well compatible with what is known about them based on phenomenological and lattice studies, provided L and M type dyons are strongly correlated.