Anomaly matching in QCD thermal phase transition Kazuya Yonekura - PowerPoint PPT Presentation

1 Anomaly matching in QCD thermal phase transition Kazuya Yonekura Tohoku U. Based on •[1706.06104] with Hiroyuki Shimizu •[1901.08188]

2 Introduction QCD phase transition is important for cosmology: Axiom abundance etc. Most radical scenario: [Witten,1984] If the phase transition is first order, the dark matter might be produced purely by QCD phase transition. (Several other conditions need to be satisfied.) The dark matter might be explained by the standard model! / 41

3 Introduction Some lattice simulations say that QCD phase transition is cross-over (i.e. no definite phase transition). But it is not completely settled yet, especially in the limit of small quark masses. Therefore, it is desirable to study it by methods which do not rely on numerical simulations. / 41

4 Introduction A rough version of my claim (I will explain more precise technical result later.) If • Small quark mass approximation is good, • Large N expansion is good, then • QCD phase transition may be naturally first order. / 41

5 Introduction Both small quark mass approximation and large N expansion are qualitatively very good in QCD at zero temperature. • Chiral perturbation theory,… • Most mesons as q ¯ q qq ¯ q ¯ q (rather than ), OZI rule, • Simulation for pure Yang-Mills, AdS/CFT,… N c = 3 ≃ ∞ ( ) Crossover phase transition may be in tension with those good concepts of QCD and the argument I discuss later. / 41

6 Contents 1. Introduction 2. ’t Hooft Anomaly matching 3. Confinement in finite temperature QCD 4. Results and implications 5. Derivation of Anomaly 6. Summary / 41

7 ’t Hooft anomaly What method do we have to study strong dynamics such as QCD? ’t Hooft anomaly matching gauge fields + fermions with UV: global symmetry F confinement IR: ??? Anomaly of F in UV = Anomaly of F in IR / 41

8 ’t Hooft anomaly in QCD ’t Hooft anomaly matching in QCD at zero temperature In QCD, there exist approximate chiral symmetry SU ( N f ) L × SU ( N f ) R SU ( N f ) L : rotate left handed quarks SU ( N f ) R : rotate right handed quarks Chiral symmetry has the well-known ’t Hooft anomaly at zero temperature. / 41

9 ’t Hooft anomaly in QCD UV: The quarks have the ’t Hooft anomaly confinement If there is no chiral fermion, IR: the chiral symmetry must be spontaneously broken. / 41

10 ’t Hooft anomaly in QCD ’t Hooft anomaly matching gives an important relation between the two most important concepts in QCD: Chiral symmetry Confinement breaking How about finite temperature? The usual anomaly associated to triangle diagrams vanishes at finite temperature. / 41

11 Anomaly at finite temperature I will argue the existence of a subtler anomaly at finite temperature if we include a small imaginary chemical potential. Chiral symmetry Confinement breaking Anomaly at finite temperature / 41

12 Contents 1. Introduction 2. ’t Hooft Anomaly matching 3. Confinement in finite temperature QCD 4. Results and implications 5. Derivation of Anomaly 6. Summary / 41

13 A problem in QCD Chiral symmetry Confinement breaking We want to study this relation at finite temperature. However, a well-known problem is that “confinement” is not well-defined in finite temperature QCD because dynamical quarks can screen color fluxes. / 41

14 Pure Yang-Mills Let us recall how to define confinement in pure Yang-Mills. R 3 × S 1 Z = tr e − β H Finite temperature: β = T − 1 : inverse temperature I S 1 A µ dx µ ) Polyakov loop: W = tr P exp( i S 1 Wilson loop wrapping on the / 41

15 Pure Yang-Mills Intuitively, the Polyakov loop behaves as W ∼ exp( − β E q ) : energy of a single probe quark E q Confinement : E q → ∞ W = 0 Deconfinement : E q < ∞ W 6 = 0 / 41

16 Order parameter So the Polyakov loop can be regarded as an order parameter of confinement in pure-Yang-Mills. How about QCD with dynamical quarks? / 41

17 QCD In QCD, the probe quark energy is always finite. E q Q ¯ q Bound state E q < ∞ W probe dynamical quark anti-quark Q ¯ q The Polyakov loop cannot be used to define W confinement phase. Always W 6 = 0 / 41

18 Imaginary chemical potential To define confinement rigorously, I slightly change the problem. tr exp( − β H ) → tr exp( − β H + iµ B B ) : baryon number charge B : baryon imaginary chemical potential µ B This changes the thermodynamics, but I will argue that the effect of the imaginary chemical potential is subleading in the large expansion. N c / 41

19 Imaginary chemical potential I take µ B = π [Roberge-Weiss,1986] What is special about this value? All gauge invariant composites have integer B ∈ Z Mesons: B = 0 Baryons: B = 1 However, quarks have fractional baryon numbers. Quarks: B = 1 /N c real for gauge invariant composites { exp( i π B ) = imaginary for colored quarks / 41

20 Criterion for confinement W ∼ exp( − β E q + i π B ) Q ¯ q Q W probe probe dynamical quark quark anti-quark Q Q ¯ q Im( W ) = 0 Im( W ) 6 = 0 deconfinement confinement / 41

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22 Definition of confinement We can summarize the above discussion as follows. • There exists a symmetry (flipping the direction) S 1 Z 2 • The imaginary part of the Polyakov loop Im( W ) is charged under the Z 2 • Confinement and deconfinement are distinguished by Deconfinement : Im( W ) 6 = 0 broken Z 2 Confinement : unbroken Im( W ) = 0 Z 2 / 41

23 Remark on imaginary chemical The effect of imaginary chemical potential is very suppressed in the large N expansion: total free energy ∼ N f e ff ect of µ B N 3 c This follows from the fact that the baryon charge of quarks is 1/ N c μ B = π Therefore, the situation at should be similar μ B = 0 N to as far as large expansion is qualitatively good. / 41

24 Contents 1. Introduction 2. ’t Hooft Anomaly matching 3. Confinement in finite temperature QCD 4. Results and implications 5. Derivation of Anomaly 6. Summary / 41

25 Symmetry and Anomaly Massless QCD at finite temperature with imaginary chemical potential has (at least) two symmetries: µ B = π • Chiral symmetry SU ( N f ) L × SU ( N f ) R • symmetry Z 2 Result : (derivation later) [KY, 2019] There exists a mixed ’t Hooft anomaly between chiral symmetry and symmetry. Z 2 This is a parity anomaly in 3-dimensions. / 41

26 Symmetry and Anomaly Anomaly Confinement Chiral symmetry ( symmetry) ℤ 2 breaking Result : (derivation later) [KY, 2019] There exists a mixed ’t Hooft anomaly between chiral symmetry and symmetry. Z 2 This is a parity anomaly in 3-dimensions. / 41