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

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

QCD(adj) on : Confinement/Deconfinement Transitions

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• M. Anber, ACFI, UMASS AMHERST

1 1 3

S R 

Preliminaries

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2

 Deconfinement transitions

Weak coupling Strong coupling Study analytically Lattice simulations

Link? compare

Preliminaries

 Confinement is the mechanism for holding quarks inside

nucleons: no isolated color charges

 This picture has been confirmed through extended lattice

simulations

R V  

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R V 1 

Not confined Confined

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3

Quark-Antiquark +

• Charges in QED

Preliminaries

 As we increase the temperature deconfinement

phase transition

 Quark-gluon plasma: a new state of matter  We need an order parameter

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c

T T 

+

• +

Preliminaries

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Watch out! Many circles!

Preliminaries

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 Order parameter in pure YM: Polyakov loop 

is gauge invariant



transforms under the center

 

        



s

dx A i F F F

pe tr tr P

Thermal circle: compact time

nce circumfere 1 1    T

F

P

   



 

  t x A t x A , ,

 

2 2 2 2 ) 2 ( F F

, Z , P P

  

  I I z

SU

F

P

S

Preliminaries

 Confined phase: the center is preserved  Deconfined phase: the center is broken  The physics is that

c

T T 0,  

F

P

c

T T 0,  

F

P

T F F

e P

/

~



F

P

c

T

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Free energy of quarks

Preliminaries

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 Pure YM is very difficult since the transition happens

at

QCD



Nonabelian confinement Deconfinement

exp tr ] [ tr

F F F

                

s

dx A i P

Increase T

] [ trF  

QCD c

T  ~

c

T T 

Eigenvalue distribution

Preliminaries

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 Pure YM is strongly coupled, we can not do semi-

classical analysis

 Brute force calculations gives  This potential is minimized when , so center

symmetry is broken

 True for

 

 

) ( 1 tr 2 1

2 1 2 4 4 2

g O n V

n n per

    





 

N   tr

QCD

T  

Deconfinement

QCD c

T  ~

Preliminaries

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 This potential can not capture the phase transition  The hope is that a non-perturbative part can help:  But pure YM is strongly coupled at the transition and

no reliable semi-classics can help

 

per non g a per

V e V g V

 

  

2

2

Preliminaries

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 Analytic understanding: separation of scale  This is QCD(adj) on

3

A

] [ tr  

1 3 1 1 , 2

S R S R   

) , , , ( ) , , , ( ) , , , ( ) , , , ( L z t y x z t y x L z t y x A z t y x A      

 

Periodic boundary conditions Adjoint fermions

) 4 ( SU

1

S

L

Preliminaries

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Motivation:

 Hosotani Mechanism (unification)  Egushi-Kawai reduction (Large-N volume

independence, dream!)

 Laboratory for gauge theories

Preliminaries

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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

Preliminaries

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 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

Preliminaries

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Goals of studying the theory on a circle

 Analytic understanding of the physics  Compare the results on the circle with lattice results

• n

 The ultimate goal is to decompactify the theory (Clay

Mathematics Institute $1000,000 question!!)

4

R

Outline

 Part I: Confinement in QCD(adj) on  Part II: Deconfinement in pure YM on  Part III: Deconfinement in hot QCD(adj) on

1 3

S R 

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S R 

4

R

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Part I: Formulation and confinement

QCD(adj) on : Formulation



 

                  

model Glashow

• Georgi

3 2 2 3 2 small 2

) ( 2 2 1

• tr

2i 2 1

• tr

1

3 1 3

                

 



A V g A D F F g L D F F g S

per i R L I m m I mn mn S R  

  

Compact scalar One-loop effect Adjoint fermions with periodic boundary conditions along the circle

5 . 5 1  

f

n

1

S

1 3

S R 

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: ) 2 ( SU

QCD(adj) on : Formulation

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 One-loop calculation  For center symmetry is preserved;  At we find . This is SUSY.

The center is stabilized by non-perturbative effects

1 3

S R 

  



       





3 3

1 2 4 4 2

tr 2 1

dx A i n n f per

e n L n V 

1 

f

n

 

 

per

V

SU(2)

1 

f

n 1 

f

n

1  N tr  

QCD(adj) on : Formulation

 Higsing: the theory abelianizes  At small the gauge coupling freezes at

a small value

 In 3D the photon has one degree of freedom

QCD

L   / 1

) 1 ( ) 2 ( U SU 

 

2



  

  F F

1 3

S R 

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L MW 1 ~

) 2 ( SU

QCD



) 1 ( U ) (E g E

L / 1

QCD(adj) on : Formulation

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 For  For (SUSY), the field is massless (modulus)

1 3

S R 

1 

f

n 1 

f

n

3

A

   

,

2 2 I I eff

i    

   

       

L A

3

 

 

,

2 I I eff

i    

  

    

QCD(adj) on : Formulation

 More interesting story to tell: non-perturbative

effects

 Feynman path integral







paths Euclidean

E

S

e Z

Perturbative +non-perturbative (instantons) Instantons

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1 3

S R 

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QCD(adj) on : Formulation

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 Magnetic bion

Neutral bion

1 3

S R 

  2 

• M. Unsal 2009

     2 8

2 2

e e

g    2 8

2 2

i g e

e

 

QCD(adj) on : Formulation

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Summing up all contributions:

 For  For SUSY

       

       

  

2 cosh 2 cos

m ass photon 2 2 bosonic eff S S

e e        

1 3

S R 

Notice the relative sign, from analytic continuation

1 

f

n

   

2 2 mass photon 2 bosonic eff

8 , 2 cos g S e S       

 

     

QCD(adj) on : Confinement

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 Magnetic bions proliferate in the vacuum: 3D

Coulomb gas

1 3

S R 

3 / S

Le

2  2  2  2  2  2  2  2  2  2  2  2  2  2  2 

r g 2 1

Electric charge Electric charge +

SUSY on : Confinement

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 One can use chiral dualities to dualize the photon  Perturbatively:  Next we add the nonperturbative part:

       i X X X K xd d S ) , (

4 3

 

) (

2 3 pert

• non

X W X W xd d S    

2 2

8

~

g X X

e e W

  



1 3

S R 

SUSY on : Confinement

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 Then one obtains:

1 3

S R 

   

 

       

 

               

  

2 cosh 2 cos 2 cosh 2 cos ~

2 2 4

  

S S

e A e X W X W V 

Magnetic and neutral bions are the physical manifestation

QCD(adj) on : Confinement

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Take home messages

 QCD(adj) preserves the center separation of

scales

 QCD(adj) trivial perturbatively  Confinement is due to magnetic bions  SUSY is curse and blessing!

1 3

S R 

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Part II: Phase Transition in pure YM on via mass deformed SUSY

• n

1 3

S R 

4

R

Mass deformed SUSY on

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 Adding mass deformation (MD) to Super-Yang-Mills

(QCD(adj) with ), we can study phase transition in pure Yang-Mills

1 3

S R 

1 

f

n

Mass deformed SUSY on

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S R 

• T. Schafer, E. Poppitz, M. Unsal 2012

?

Mass Deformed SUSY on

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 Now, we add a massive fermion (gaugino)  The mass lifts the fermions zero mode  Monopoles contribute to the potential

1 3

S R 





cosh cos ~

2 2 /

 L me V

S m

         

                  

       

2 cosh 2 cos c.c.

0 2

/ 2 2 S S m i m i S eff

e e e e e    

 



Mass deformed SUSY on

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 Total potential 

stabilizes the center



destabilizes the center

 The competition between and determines

the nature of the quantum phase transition

1 3

S R 

   

 

                     

m bion

V g V g t

e L m e L V      

 

cosh cos 2 cosh 2 cos 1

2 2 2 2

4 2 8 3

 

 

bion

V

m

V

bion

V

m

V

Phase transitions in pure YM

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 Behavior of the Polyakov loop

] [ tr   ] [ tr  





 

  .

] [ tr

i

e

Phase transitions in pure YM

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 The phase transition is first order in all groups:

SU(N), spin(2N+1), Sp(2N), Spin(2N), E6, E7,E8,F4,G2. M.A, B. Teeple, E. Poppitz 2014

 SU(2) and are exception:

second order transition

 Lattice simulations for SU(2), SU(N>2) and Sp(4)

indicated second order for SU(2), first order for

SU(N>2) and Sp(4) (Holland, Pepe, and Wiese 2003) SU(2) SU(2) Spin(4)  

Phase transitions in pure YM

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 String tension

rL

e 

 

   (0) (x)tr tr

Compare lattice Simulations: Bicudo 2010 done for SU(3) Discontinuous transition Same behavior for SU(3)

S

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Phase transitions in pure YM

 Topological angle:



Compare lattice studies for SU(3): Bonati, D’Elia, Panagopoulos, Vicari 2013 SU(3)

c

T T

] tr[



  

• M. A. 2013

mn mnF

F ~ 

Phase transitions in pure YM

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Take home messages

 Mass deformed SUSY is a great tool to study pure

YM

 No single test has failed!  Continuity? (see the resurgence talks)

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Part III: Deconfinement transition in QCD(adj) on

1 3

S R 

Thermal QCD(adj) on

 At finite temperature we compactify the time

direction

L 1/T

1  LT

2

R

2 

T / 1

identified

03/19/2016

2 

r g log 1

2

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M.A., E. Poppitz, M. Unsal, 2011

1 3

S R 

Thermal QCD(adj) on

 The story has one more twist!  At finite temperature, the W’s and charged fermions

are important

T mW

e

/

density





 

r

W W

r g log

2

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Electric charge

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1 3

S R 

Thermal QCD(adj) on

 2-D Coulomb gas

2  2  2  2  2  2  2  2  2  2  2  2  2  2  2                

03/19/2016

r log r log



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1 3

S R 

Thermal QCD(adj) on

 The partition function for SU(2)                            

    

       

      B A b ja i j A i a A a j B i A B A j b i a b a i a Ai A i a i N N q q W W N N bion bion N N

R R q iq R R LT q q g R R g q LTq R d R d N N N N Z

W N W N bion bion A a W i W i W bion i bion i bion

, , , , susy 2 2 , 2 2 , ,

part scalar 4 log 2 log 32 exp ! ! ! !

, , ,

      

 

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Non-SUSY e-m duality Weakly coupled self-dual point

1 3

S R 

Mapping QCD(adj) to spin models

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 This 2D Coulomb gas is EXACTLY equivalent to

XY-spin models:

           

susy

part scalar ) 4 cos( ) cos(    

 

   i i S S ij j i

B A H

j i

  

Nearest neighbor interaction External field

Results for thermal QCD(adj) on

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 Analytic results for non-SUSY SU(2) indicate a

second transition deconfinement

 Numerical results for SUSY SU(2) indicate a second

• rder transition

1 3

S R 

Results for thermal QCD(adj) on

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 XY-model simulations SUSY SU(2)

1 3

S R 

• M. Anber, S. Collier, S. Strimas-Mackey, E. Poppitz, B, Teeple, 2013

Results for thermal QCD(adj) on

 Results for nonsusy SU(3): phase coexistence at the

critical temperature:

03/19/2016

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• M. Anber, ACFI, UMASS AMHERST

1 3

S R 

• M. Anber, S. Collier, E. Poppitz, 2013

Summary of the deconfinement picture

         

+

• +
• +
• +
• +
• +
• +
• +
• +
• +
• c

T T 

+

• +
• +
• +
• +
• +
• +
• +
• +
• +
• +
• +
• 

          

c

T T 

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Results for thermal QCD(adj) on

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The transition in QCD(adj) on

 Second order for SU(2)  First order for SU(3)

Compare with lattice results of QCD(adj) on

 Second order for SU(2) SUSY, G. Bergner, P. Giudice, G. Munster,

• S. Peimont, S. Sandbrink 2014

 First order for SU(3), Karsch and Lutgemeir 1998

1 3

S R 

4

R

1 3

S R 

Results for thermal QCD(adj) on

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Take home messages

 The order of the transition is the same for

and

 Is there a deep reason? Continuity?

1 3

S R 

1 3

S R 

4

R

Conclusion

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 New insights from studying this class of theories  Continuity? More tests are needed  More lattice studies are needed, can we see the

composite strings?

 Plenty of other works regarding compact theories on

a circle (need for more future workshops)

Appendix

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 To study phase transitions order parameter  E.g. to study magntization in 2D 

is invariant under



• rder parameter

 

 

 

  

   

 

, ,

cos .

x x x x x x S

S H

 

c SO    : 2

H





x i

x

e M



Appendix

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53

 Demagnetized phase and is unbroken  Magnetized phase and is broken  M

 

2 SO

 M

 

2 SO

Appendix

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54

 Order parameter for pure YM: Polyakov loop 

is gauge invariant:

 

        



s

dx A i F F F

pe tr tr P

Thermal circle: compact time

nce circumfere 1 1    T

F

P

       

, , , , , x U x U x U e x U e

A dx i A dx i

 

  

 

 

Gauge transformations are periodic

 

   U U U UA A

  

   



 

  t x A t x A , ,

Appendix

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• M. Anber, ACFI, UMASS AMHERST

55

 We can also consider Center transformations:  The center of a group are the elements that commute

with all the elements in the group:

   

, , x zU x U  

Element of the center

 

gz zg G z Z    ,

Appendix

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• M. Anber, ACFI, UMASS AMHERST

56

 For SU(N)  The Lagrangian

invariant under the center

 In the fundamental rep

1 ,..., 1 , , 1 . . 1 1

2

                  



N k e z

N N N k i k 

F F

zP P 

a a F

F

 

 