QCD on : from confinement/deconfinement to the effect of ...

M O H A M E D A N B E R

I N S T I T U T E O F T H E O R E T I C A L P H Y S I C S

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 LP 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

03/19/2016M. Anber, ACFI, UMASS AMHERST

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Preliminaries


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

RV

03/19/2016

RV

1

Not confined

Confined

M. Anber, ACFI, UMASS AMHERST

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Quark-Antiquark + -

Charges in QED

Preliminaries

As we increase the temperature deconfinementphase transition

Quark-gluon plasma: a new state of matter

We need an order parameter


4

cTT + - + -

Preliminaries


5

Watch out! Many circles!

Preliminaries


6

Order parameter in pure YM: Polyakov loop

is gauge invariant

transforms under the center

s

dxAi

FFF pe00

trtrP

Thermal circle: compact time ncecircumfere

11

T

FP

txAtxA ,,

2222)2(FF , Z,PP IIz SU

FP

S

Preliminaries

Confined phase: the center is preserved

Deconfined phase: the center is broken

The physics is that

cTT 0, FP

cTT 0, FP

TF

F eP /~

FP

cT 0


7

Free energy of quarks

Preliminaries


8

Pure YM is very difficult since the transition happens at QCD

Nonabelianconfinement

Deconfinement

0exptr][tr 00FFF

s

dxAiP

Increase T

0][trF

QCDcT ~cTT

Eigenvaluedistribution

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

)(1tr21 2

1

2

442gO

nV

n

n

per

Ntr

QCDT

Deconfinement

QCDcT ~

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

pernon

g

a

per VeVgV

22

Preliminaries


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Analytic understanding: separation of scale

This is QCD(adj) on

3A

0][tr

1311,2 SRSR

),,,(),,,(

),,,(),,,(

Lztyxztyx

LztyxAztyxA

Periodic boundary conditions

Adjoint fermions

)4(SU

1S 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 on

The ultimate goal is to decompactify the theory (Clay Mathematics Institute $1000,000 question!!)

4R

Outline

Part I: Confinement in QCD(adj) on

Part II: Deconfinement in pure YM on

Part III: Deconfinement in hot QCD(adj) on

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4R


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Part I:

Formulation and confinement

QCD(adj) on : Formulation

model Glashow-Georgi

3

22

32

small

2

)(22

1-tr

2i2

1-tr

1

3

13

AVg

ADFFg

L

DFFg

S

peri

R

L

Im

m

I

mn

mn

SR

Compact scalar One-loop effect

Adjoint fermions with periodic boundary conditions along the circle5.51 fn 1S

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:)2(SU



19

One-loop calculation

For center symmetry is preserved;

At we find . This is SUSY. The center is stabilized by non-perturbative effects

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1

2

442tr

21

dxAi

n

nf

per

e

nL

nV

1fn 0perV

SU(2)

1fn

1fn

1N

0tr


Higsing: the theory abelianizes

At small the gauge coupling freezes at a small value

In 3D the photon has one degree of freedom

QCDL /1

)1()2( USU

2

FF

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LMW

1~

)2(SU

QCD

)1(U

)(Eg

EL/1



21

For

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

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1fn

1fn 3A

,22

IIeff i LA3

,2

IIeff i


More interesting story to tell: non-perturbativeeffects

Feynman path integral

paths

EuclideanES

eZ

Perturbative +non-perturbative (instantons)

Instantons

03/19/2016

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22



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Magnetic bion Neutral bion

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2 M. Unsal 2009

2

82

2

ee g

2

82

2

ig ee



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Summing up all contributions:

For

For SUSY

2cosh 2cos 00

massphoton

22

bosoniceff

SSee

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Notice the relative sign, from analytic continuation

1fn

2

2

0

massphoton

2

bosoniceff

8 , 2cos0

gSe

S

QCD(adj) on : Confinement


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Magnetic bions proliferate in the vacuum: 3D Coulomb gas

13 SR

3/0SLe

2

2

2

2

2

2

2

2

2

2

22

22

2rg 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:

iX

XXKxddS ),(43

)( 23

pert-non XWXWxddS

2

28

~ gX

X eeW

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SUSY on : Confinement


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Then one obtains:

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2cosh2cos

2cosh2cos~

0

0

22

4

S

S

e

AeX

W

X

WV

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!

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

on 13 SR

4R

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

13 SR

1fn



31

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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

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coshcos~2

2/0

L

meV

S

m

2cosh2cos

c.c.

00

0 2/22

SS

m

i

m

iS

eff

ee

eee



33

Total potential

stabilizes the center

destabilizes the center

The competition between and determines the nature of the quantum phase transition

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mbion V

g

V

g

t eL

me

LV

coshcos2cosh2cos1 2

2

2

2 4

2

8

3

bionV

mV

bionV mV

Phase transitions in pure YM


34

Behavior of the Polyakov loop

0][tr 0][tr

.

][tri

e



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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)



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String tension

rLe (0)(x)trtr

Compare latticeSimulations: Bicudo 2010done for SU(3)

Discontinuous transition

Same behavior for SU(3)

S


37


Topological angle:

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

SU(3)

cTT]tr[

M. A. 2013

mn

mnFF~



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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: Deconfinementtransition in QCD(adj) on

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Thermal QCD(adj) on

At finite temperature we compactify the time direction

L1/T

1LT

2R

2T/1

identified

03/19/2016

2 rg

log1

2


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

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Thermal QCD(adj) on

The story has one more twist!

At finite temperature, the W’s and charged fermions are important

TmWe/

density

r

W W

rg log2

03/19/2016

Electric charge


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13 SR

Thermal QCD(adj) on

2-D Coulomb gas

22

2

2

2

2

2

2

2

22

2

2

2

2

03/19/2016

rlog

rlog


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Thermal QCD(adj) on

The partition function for SU(2)

BAbjaij

A

i

aAa

j

B

i

ABA

j

b

i

aba

ia Ai

Ai

ai

NNqqWW

NN

bionbion

NN

RRqiq

RRLT

qqgRR

g

qLTq

RdRdNNNNZ

WNWNbionbionAa

Wi

Wi

W

bioni

bioni

bion

,,,,

susy

2

2

,

22

,,

partscalar 4

log2

log32

exp

!!!!,,,


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

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Mapping QCD(adj) to spin models


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This 2D Coulomb gas is EXACTLY equivalent to XY-spin models:

susy

partscalar )4cos()cos(

i

i

SS

ij

ji BAH

ji

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 order transition

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XY-model simulations SUSY SU(2)

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


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

03/19/2016

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13 SR

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

Summary of the deconfinement picture

+-

+-

+-

+-

+-

+-

+-

+-

+-

+-

cTT

+-

+-

+-

+-

+-

+-

+-+-

+-

+-

+-

+-

cTT

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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

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4R

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Take home messages

The order of the transition is the same for and

Is there a deep reason? Continuity?

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13 SR

4R

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

order parameter

,,

cos.x

xx

x

xx SSH

cSO :2H

x

i xeM

Appendix


53

Demagnetized phase and is unbroken

Magnetized phase and is broken

0M 2SO

0M 2SO

Appendix


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Order parameter for pure YM: Polyakov loop

is gauge invariant:

s

dxAi

FFF pe00

trtrP

Thermal circle: compact time ncecircumfere

11

T

FP

0,, , , 0, 00

0

00

0

xUxUxUexUeAdxiAdxi

Gauge transformationsare periodic

UUUUAA

txAtxA ,,

Appendix


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We can also consider Center transformations:

The center of a group are the elements that commute with all the elements in the group:

0,, xzUxU

Element of the center

gzzgGzZ ,

Appendix


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For SU(N)

The Lagrangian invariant under the center

In the fundamental rep

1,...,1,0,

1

.

.

1

1

2

Nkez

NN

N

ki

k

FF zPP

aa FF

QCD on : from confinement/deconfinement to the effect of ...

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