The semiclassical theory of deconfinement, chiral and Roberge-Weiss-like phase transitions Edward Shuryak Stony Brook University “Probing the phase structure of strongly interacting matter: theory and experiment” GSI, March 2019
outline • VEV of Polyakov line and the instanton-dyons • Deconfinement transition • Chiral symmetry breaking • Generalized quark periodicity phases • New set of phase transitions • Instanton-dyons on the lattice Instanton-dyons <=> Monopoles relation: examples of the Poisson duality Semiclassics at finite T and pre-clustering at freeze out
the semiclassical theory Of gauge field solitons at finite T
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s)
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s)
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s) Chiral symmetry breaking
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s) Chiral symmetry breaking => collectivization of instanton zero modes (1980’s)
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s) Chiral symmetry breaking => collectivization of instanton zero modes (1980’s)
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s) Chiral symmetry breaking => collectivization of instanton zero modes (1980’s) Lattice in 2000’s
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s) Chiral symmetry breaking => collectivization of instanton zero modes (1980’s) Lattice in 2000’s => topological objects observed but
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s) Chiral symmetry breaking => collectivization of instanton zero modes (1980’s) Lattice in 2000’s => topological objects observed but They are not quite instantons (?)
the semiclassical theory Of gauge field solitons at finite T Confinement => BEC of monopoles, flux tubes (1970’s) Chiral symmetry breaking => collectivization of instanton zero modes (1980’s) Lattice in 2000’s => topological objects observed but They are not quite instantons (?)
� “action cooling” is known to eliminate gluons and lead to instantons Negele et al perhaps dyons were first observed in “constrained cooling” preserving local L while the total top.charge of the box is always integer, local bumps are not! They are all (anti)selfdual But top charge and actions Were not integers! Langfeld and Ilgenfritz, 2011 a lot of work on finding instanton-dyons was done by C.Gatringer et al, Ilgenfritz et al
<latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> Instantons have top.charges Q = ± 1 and thus are elementary quanta of topology: How can they have a substructure? What about topological classification of fields? Like a nucleon is made of 3 quarks, an instanton is made of Nc instanton-dyons
<latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> Instantons have top.charges Q = ± 1 and thus are elementary quanta of topology: How can they have a substructure? What about topological classification of fields? Like a nucleon is made of 3 quarks, an instanton is made of Nc instanton-dyons Because they have magnetic charges They are connected by (invisible!) Dirac strings Thus they avoid topological charge quantization
The Polyakov line is used as order parameter for deconfinement I P = Pexp ( i µ T a dx µ ) A a L = τ = x 4 P L = diag ( e iµ 1 , e iµ 2 , ...e iµ Nc ) ∈ [0 , ~ /T ] 1 ∼ e − F q /T Tr ( L ) ~ x N c 1.2 0.35 L ren (T) 0.3 1 HISQ: N τ =6 N τ =8 0.25 0.8 N τ =10 pure gauge N τ =12 0.2 L ren (T) SU(3) cont. 0.6 stout, cont. 0.15 0.4 0.1 QCD N τ =4 0.05 0.2 N τ =8 T [MeV] 0 0 120 140 160 180 200 1 2 3 4 5 6 T/T c Kaczmarek et al 2002 Bazavov et al 2016 L jumps to zero Pisarski ``semi-QGP" paradigm, the first order transition PNJL model
Non-zero Polyakov line splits instantons BPST into Nc instanton-dyons (Kraan,van Baal, Lee,Lu 1998) Explained mismatch of quark condensate in SUSY QCD V.Khoze (jr) et al 2001 Explained confinement by back reaction to free energy D.Diakonov 2012, Larsen+ES,Liu,Zahed+ES 2016 Explain chiral symmetry breaking in QCD and in setting with modified fermion periodicities R.Larsen+ES 2017, Unsal et al 2017 Pierre van Baal
<latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> <latexit sha1_base64="(nul)">(nul)</latexit> general SU ( N c ) the SU(2) case is simpler A 4 = 2 π Tdiag ( µ 1 , µ 2 , ...µ N c ) µ ν m = µ m +1 − µ m ν = 1 − ν ¯ L type ν X M type ν i = 1 i 8 π 2 = ν i (11 N c − 2 N f 3 ) log ( T/ Λ ) − µ S i = ν i 3 g 2 A a 4 = ⌥ n a v Φ ( vr ) 1 � R ( vr ) together they make one instanton A a i = ✏ aij n j instanton-dyons r =selfdual BPS mono E = ~ ~ B In SU(2) there are 4 types of dyons, Electric and magnetic charges = +1,-1 M, ¯ M, L, ¯ L all one needs to do is to study their ensemble
(with Rasmus Larsen) confined free energy vs holonomy 0.0 ● ● ● ● ● ● ● ● ● ● ● ● - 0.2 = v τ 3 2 = 2 π T ν τ 3 ○ A 3 ● ○ ⌦ ↵ - 0.4 ● 4 2 ▲ ● ▲ < P > = cos ( πν ) → 0 ○ ○ ○ - 0.6 ○ ○ ■ ○ ○ ■ f ◆ if ν = 1 / 2 ○ ▼ ○ ○ ▼ ○ ▼ ▼ - 0.8 ▼ ◆ ▼ ▼ ▼ ▼ ▼ ▼ ▲ ▲ ▲ - 1.0 ▲ ▲ ■ ▲ ■ ▲ holonomy ▲ ▲ ◆ ◆ ■ ■ ◆ ◆ ◆ ◆ ◆ - 1.2 ■ - 1.4 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ν ν = 0 is the trivial case So, as a function of the dyon density the potential changes its shape ν = 1 / 2 confining and confinement takes place
the Debye mass, we will find it from the pot n show only the “selfconsistent” input set. hat we actually need to describe at the T/T c T/T c 0.87 1. 1.15 1.31 1.51 1.73 1.98 2.27 2.6 0.87 1. 1.15 1.31 1.51 1.73 1.98 2.27 2.6 0.5 0.4 0.4 M 0.3 0.3 ν 0.2 n 0.2 0.1 L 0.0 6 8 10 12 0.1 S T/T c 0.87 1. 1.15 1.31 1.51 1.73 1.98 2.27 2.6 0.0 0.7 6 8 10 12 S 0.6 <P> 0.5 FIG. 8: (Color online). Density n (of an individual kind of 0.4 dyons) as a function of action S (lower scale) which is related P to T/T c (upper scale) for M dyons(higher line) and L dyons 0.3 (lower line). The error bars are estimates based on the density 0.2 of points and the fluctuations of the numerical data. 0.1 0.0 6 8 10 12 S confining phase is symmetric FIG. 6: Self-consistent value of the holonomy ν (upper plot) n L =n M and Polyakov line (lower plot) as a function of action S (lower scales), which is related to T/T c (upper scales). The error bars are estimates based on the fluctuations of the numerical data. S = (11 N c − 2 N f 3 ) log ( T ) . 3 Λ T
Instanton-dyon Ensemble with two Dynamical Quarks: the Chiral Symmetry Breaking Rasmus Larsen and Edward Shuryak Department of Physics and Astronomy, Stony Brook University, Stony Brook NY 11794-3800, USA arXiv:1511.02237v1 [hep-ph] 6 Nov 2015 This is the second paper of the series aimed at understanding of the ensemble of the instanton- dyons, now with two flavors of light dynamical quarks. The partition function is appended by the fermionic factor, ( detT ) N f and Dirac eigenvalue spectra at small values are derived from the numerical simulation of 64 dyons. Those spectra show clear chiral symmetry breaking pattern at high dyon density. Within current accuracy, the confinement and chiral transitions occur at very similar densities. high density 70 60 broken chiral sym | < ¯ ψψ > | = πρ ( λ ) λ ! 0 ,m ! 0 ,V !1 50 40 N Bin collectivized 30 zero mode zone 20 10 dip near zero is 0 a finite size effect 0.0 0.1 0.2 0.3 0.4 λ FIG. 1: Eigenvalue distribution for n M = n L = 0 . 47, N F = 2 massless fermions. 50 low density 40 unbroken chiral sum 30 N Bin extracting condensate 20 is far from trivial… 10 0 0.0 0.1 0.2 0.3 0.4 λ FIG. 2: Eigenvalue distribution for n M = n L = 0 . 08, N F = 2 massless fermions.
QCD with quarks having arbitrary periodicity phases (over the Matsubara time) ψ ( τ + ~ /T ) = e 2 π iz f ψ ( τ ) z f = 0 bosons z f = − 1 / 2 fermions
Ordinary Nc=Nf=5 QCD P without a trace is a diagonal unitary matrix => Nc phases (red dots) quark periodicity phases => Nf blue dots are in this case all =pi quarks are fermions as a consequence, out of 5 types of instanton-dyons only one L has zero modes
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