Confinement/Deconfinement Transitions 1 MOHAMED ANBER INSTITUTE OF - PowerPoint PPT Presentation

QCD(adj) on : R  3 1 S Confinement/Deconfinement Transitions 1 MOHAMED ANBER INSTITUTE OF THEORETICAL PHYSICS R E C E N T D E V E L O P M E N T S I N S E M I C L A S S I C A L P R O B E S O F Q U A N T U M F I E L D T H E O R I E S A C F I , U M A S S A M H E R S T M A R C H 1 9 , 2 0 1 6 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 2  Deconfinement transitions Link? Weak coupling Strong coupling compare Study analytically Lattice simulations 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 3  Confinement is the mechanism for holding quarks inside nucleons: no isolated color charges Not confined 1 Charges in QED  V R Confined + -   Quark-Antiquark V R  This picture has been confirmed through extended lattice simulations 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 4  As we increase the temperature deconfinement phase transition T  T c + - + -  Quark-gluon plasma: a new state of matter  We need an order parameter 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 5 Watch out! Many circles! 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 6  Order parameter in pure YM: Polyakov loop     S    A x , t A x , t        i A dx    0 0 P tr tr pe s   F F F   Thermal circle: 1  1  T is gauge invariant compact time  P  circumfere nce F transforms under the center P  F       P z P , Z I , I  F F SU ( 2 ) 2 2 2 2 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 7    Confined phase: the center is preserved 0, T T P F c    Deconfined phase: the center is broken P 0, T T F c Free energy of quarks  The physics is that  / F T P ~ e F P F T 0 c 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 8  Pure YM is very difficult since the transition happens  at QCD              P tr [ ] tr exp i A dx 0 tr F [ ] 0   F F F  0 0    s Eigenvalue distribution Nonabelian confinement Deconfinement T  T Increase T  T ~ c c QCD 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 9  Pure YM is strongly coupled , we can not do semi- classical analysis  Brute force calculations gives      1 2  2     n 2 V tr 1 O ( g ) Deconfinement   per 2 4 4 n   n 1 T ~ c QCD    This potential is minimized when , so center tr N symmetry is broken    True for T QCD 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 10  This potential can not capture the phase transition  The hope is that a non-perturbative part can help: a       2 2 g V g V e V  per non per  But pure YM is strongly coupled at the transition and no reliable semi-classics can help 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 11  Analytic understanding: separation of scale  This is QCD(adj) on    2 , 1 1 3 1 R S R S 1 L S A 3   A ( x , y , t , z ) A ( x , y , t , z L )   SU ( 4 )     ( x , y , t , z ) ( x , y , t , z L ) Periodic boundary Adjoint fermions conditions   tr [ ] 0 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 12 Motivation:  Hosotani Mechanism (unification)  Egushi-Kawai reduction (Large-N volume independence, dream!)  Laboratory for gauge theories 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 13 Progress: (see M. Unsal and T. Sulejmanpasic talks)  Confinement in QCD(adj) (microscopic picture) M. Unsal 2009; M. Unsal, E Poppitz 2010, M.A, E. Poppitz 2011; T Misumi, M. Nitta, N. Sakai 2014; T Misumi, T. Kanazawa 2014  Deconfinement transition in hot QCD(adj) M. A, E. Poppitz, M. Unsal 2012; M. A, S. Collier, E. Poppitz 2013; M. A, S. Collier, S. Strimas-Mackey, E. Poppitz, B, Teeple 2013  Deconfinement in pure YM through a continuity conjecture YM QCD(adj) E. Poppitz, T. Schafer, M. Unsal 2012; E. Poppitz, T.Schafer, M. Unsal 2013; E. Poppitz, T Sulejmanpasic 2013; M.A. 2013; M.A.; M.A., B. Teeple, E. Poppitz 2014 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 14  Resurgence and the renormalon problem in QCD(adj) M. Unsal, P. Argyres 2012; M. A., T. Sulejmanpasic 2014  Strings in QCD(adj) M.A., E. Poppitz, T. Sulejmanpasic 2015  Global structure in QCD(adj) M.A., E. Poppitz 2015  Lattice QCD(susy) G. Bergner, S. Piemonte 2014, G. Bergner, G. Giudice, G. Munster, S. Piemonte 2015 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Preliminaries 15 Goals of studying the theory on a circle  Analytic understanding of the physics  Compare the results on the circle with lattice results on 4 R  The ultimate goal is to decompactify the theory (Clay Mathematics Institute $1000,000 question!!) 03/19/2016 M. Anber, ACFI, UMASS AMHERST

Outline 16 R   Part I: Confinement in QCD(adj) on 3 1 S  Part II: Deconfinement in pure YM on 4 R R   Part III: Deconfinement in hot QCD(adj) on 3 1 S 03/19/2016 M. Anber, ACFI, UMASS AMHERST

17 Part I: Formulation and confinement 03/19/2016 M. Anber, ACFI, UMASS AMHERST

QCD(adj) on : Formulation R  3 1 S 18 SU ( 2 ) :   1 1  m      mn tr - 2i S F F D   mn I m I   2 g 2  3 1 R S Adjoint fermions with periodic boundary   1 5 . 5 n conditions along the circle 1 f S    small L 2 1   L g      2   tr - F F D A V ( A )  i 3 per 3 2   g 2 2 3                    Compact scalar One-loop effect R Georgi - Glashow model 03/19/2016 M. Anber, ACFI, UMASS AMHERST

QCD(adj) on : Formulation R  3 1 S 19  One-loop calculation     SU(2)   1 n  2  2 n 1    f n V tr f  per 2 4 4 L n  n 1  3 i A dx   3 e     For center symmetry is preserved; n 1 tr 0 f      At we find . This is SUSY .   N 1 n 1 V 0 f per The center is stabilized by non-perturbative effects 03/19/2016 M. Anber, ACFI, UMASS AMHERST

QCD(adj) on : Formulation R  3 1 S 20   Higsing: the theory abelianizes SU ( 2 ) U ( 1 )  /   At small the gauge coupling freezes at L 1 QCD a small value g ( E ) 1 M W ~ L U ( 1 ) SU ( 2 )  1 / L QCD E  In 3D the photon has one degree of freedom       2 F F   03/19/2016 M. Anber, ACFI, UMASS AMHERST

QCD(adj) on : Formulation R  3 1 S 21  For  n 1 f            2  i ,  I  eff I   For (SUSY), the field is massless (modulus) A n 1 3 f                 2 2    i , A L   I  eff I 3 03/19/2016 M. Anber, ACFI, UMASS AMHERST

QCD(adj) on : Formulation R  3 1 S 22  More interesting story to tell: non-perturbative effects  Feynman path integral    S Z e E Euclidean paths Perturbative +non-perturbative (instantons) Instantons 03/19/2016 M. Anber, ACFI, UMASS AMHERST

QCD(adj) on : Formulation R  3 1 S 23  Magnetic bion Neutral bion    2  8 2 8     2 g e   2 2 g i 2 e e e    2 M. Unsal 2009 03/19/2016 M. Anber, ACFI, UMASS AMHERST

QCD(adj) on : Formulation R  3 1 S 24 Summing up all contributions:   For n 1 f  2     8        2 e S  cos 2 , S 0       eff bosonic 0 2 g photon mass  For SUSY                     2 2 S S  e cos 2 e cosh 2 0 0       eff bosonic photon m ass Notice the relative sign, from analytic continuation 03/19/2016 M. Anber, ACFI, UMASS AMHERST

QCD(adj) on : Confinement R  3 1 S 25  Magnetic bions proliferate in the vacuum: 3D Coulomb gas   2  2  2 2  2 1   2 2  g 2 2 r   2  2  2 2 S / 3  Le  0 2 2  2 + - Electric charge Electric charge 03/19/2016 M. Anber, ACFI, UMASS AMHERST