Complex Path Integrals and Saddles in Two-Dimensional Gauge Theory

Buividovich, P.V.; Dunne, Gerald V.; Valgushev, S.N.

doi:10.1103/PhysRevLett.116.132001

Complex Path Integrals and Saddles in Two-Dimensional Gauge Theory

Dec 30, 2015

5 pages

Published in:

Phys.Rev.Lett. 116 (2016) 13, 132001

Published: Mar 30, 2016

e-Print:

1512.09021 [hep-th]

DOI:

10.1103/PhysRevLett.116.132001

View in:

pdf

reference search46 citations

Citations per year

Abstract: (APS)

We study numerically the saddle point structure of two-dimensional lattice gauge theory, represented by the Gross-Witten-Wadia unitary matrix model. The saddle points are, in general, complex valued, even though the original integration variables and action are real. We confirm the trans-series and instanton gas structure in the weak-coupling phase, and we identify a new complex-saddle interpretation of nonperturbative effects in the strong-coupling phase. In both phases, eigenvalue tunneling refers to eigenvalues moving off the real interval, into the complex plane, and the weak-to-strong coupling phase transition is driven by saddle condensation.

Note:

4+4 pages RevTeX, 9 figures; v2: version published in PRL

12.38.Aw
02.10.Yn
matrix model: unitarity
effect: nonperturbative
instanton: gas
lattice field theory
critical phenomena
gauge field theory
strong coupling
weak coupling

References(34)

Figures(0)

[1]

Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings

Marcos Marino
(
- CERN
)
,
Ricardo Schiappa
(
- CERN
)
,
Marlene Weiss
(
- CERN and
- Zurich, ETH
)

- Commun.Num.Theor.Phys. 2 (2008) 349-419
•
e-Print:
- 0711.1954
•
DOI:
- 10.4310/CNTP.2008.v2.n2.a3

[2]

Nonperturbative effects and nonperturbative definitions in matrix models and topological strings

Marcos Marino
(
- Geneva U.
)

- JHEP 12 (2008) 114
•
e-Print:
- 0805.3033
•
DOI:
- 10.1088/1126-6708/2008/12/114

[3]

Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models

Sara Pasquetti
(
- CERN
)
,
Ricardo Schiappa
(
- Lisbon, IST
)

- Annales Henri Poincare 11 (2010) 351-431
•
e-Print:
- 0907.4082
•
DOI:
- 10.1007/s00023-010-0044-5

[4]

Asymptotics of the instantons of Painlevé I

- Int.Math.Res.Not. 2012 (2012) 3, 561-606
•
e-Print:
- 1002.3634
•
DOI:
- 10.1093/imrn/rnr029

[5]

The Resurgence of Instantons in String Theory

- Commun.Num.Theor.Phys. 6 (2012) 339-496
•
e-Print:
- 1106.5922
•
DOI:
- 10.4310/CNTP.2012.v6.n2.a3

[6]

Finite N from Resurgent Large N

- Annals Phys. 356 (2015) 1-28
•
e-Print:
- 1501.01007
•
DOI:
- 10.1016/j.aop.2015.02.019

[7]

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

Philip C. Argyres
(
- Cincinnati U.
)
,
Mithat Unsal
(
- SLAC and
- San Francisco State U.
)

- JHEP 08 (2012) 063
•
e-Print:
- 1206.1890
•
DOI:
- 10.1007/JHEP08(2012)063

[8]

Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model

- JHEP 11 (2012) 170
•
e-Print:
- 1210.2423
•
DOI:
- 10.1007/JHEP11(2012)170

[9]

Resurgence in Quantum Field Theory: Nonperturbative Effects in the Principal Chiral Model

- Phys.Rev.Lett. 112 (2014) 021601
•
e-Print:
- 1308.0127
•
DOI:
- 10.1103/PhysRevLett.112.021601

[10]

Resurgence and Dynamics of O(N) and Grassmannian Sigma Models

Gerald V. Dunne
(
- Connecticut U.
)
,
Mithat Unsal
(
- NCSU, Raleigh
)

- JHEP 09 (2015) 199
•
e-Print:
- 1505.07803
•
DOI:
- 10.1007/JHEP09(2015)199

[11]

Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories

Inês Aniceto
(
- Lisbon, IST
)
,
Jorge G. Russo
(
- ICREA, Barcelona and
- Barcelona U., ECM and
- ICC, Barcelona U.
)
,
Ricardo Schiappa
(
- CERN and
- Lisbon, IST
)

- JHEP 03 (2015) 172
•
e-Print:
- 1410.5834
•
DOI:
- 10.1007/JHEP03(2015)172

[12]

New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble

AuroraScience

Collaboration

•

Marco Cristoforetti
(
- ECT, Trento
)

et al.

- Phys.Rev.D 86 (2012) 074506
•
e-Print:
- 1205.3996
•
DOI:
- 10.1103/PhysRevD.86.074506

[13]

Hybrid Monte Carlo on Lefschetz thimbles - A study of the residual sign problem

et al.

- JHEP 10 (2013) 147
•
e-Print:
- 1309.4371
•
DOI:
- 10.1007/JHEP10(2013)147

[14]

Nonperturbative effects in matrix models and vacua of two-dimensional gravity

Francois David
(
- Saclay
)

- Phys.Lett.B 302 (1993) 403-410
•
e-Print:
- hep-th/9212106
•
DOI:
- 10.1016/0370-2693(93)90417-G

[15]

Analytic Continuation Of Chern-Simons Theory

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- AMS/IP Stud.Adv.Math. 50 (2011) 347-446
•
e-Print:
- 1001.2933

[16]

Analytic Continuation of Liouville Theory

Daniel Harlow
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Jonathan Maltz
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Edward Witten
(
)

- JHEP 12 (2011) 071
•
e-Print:
- 1108.4417
•
DOI:
- 10.1007/JHEP12(2011)071

[17]

Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production

Cesim K. Dumlu
(
- Connecticut U.
)
,
Gerald V. Dunne
(
- Connecticut U.
)

- Phys.Rev.D 84 (2011) 125023
•
e-Print:
- 1110.1657
•
DOI:
- 10.1103/PhysRevD.84.125023

[18]

Instantons and Large N : An Introduction to Non-Perturbative Methods in Quantum Field Theory

Marcos Mariño
(
- U. Geneva (main)
)

•
DOI:
- 10.1017/CBO9781107705968

[19]

Resurgence and the Nekrasov-Shatashvili limit: connecting weak and strong coupling in the Mathieu and Lamé systems

- JHEP 02 (2015) 160
•
e-Print:
- 1501.05671
•
DOI:
- 10.1007/JHEP02(2015)160

[20]

Lattice QCD Phase Diagram In and Away from the Strong Coupling Limit

Philippe de Forcrand
(
- CERN and
- Zurich, ETH
)
,
Jens Langelage
(
- Zurich, ETH
)
,
Owe Philipsen
(
- Frankfurt U.
)
,
Wolfgang Unger
(
- Frankfurt U.
)

- Phys.Rev.Lett. 113 (2014) 15, 152002
•
e-Print:
- 1406.4397
•
DOI:
- 10.1103/PhysRevLett.113.152002

[21]

Possible Third Order Phase Transition in the Large N Lattice Gauge Theory

D.J. Gross
(
- Princeton U.
)
,
Edward Witten
(
- Harvard U.
)

- Phys.Rev.D 21 (1980) 446-453,
- In *Brezin, E. (ed.), Wadia, S.R. (ed.): The large N expansion in quantum field theory and statistical physics* 584-591,
- Preprint - GROSS, D. J. (REC.AUG 79) 25p
•
DOI:
- 10.1103/PhysRevD.21.446

[22]

A Study of U(N) Lattice Gauge Theory in 2-dimensions

Spenta R. Wadia
(
- Tata Inst.
)

e-Print:
- 1212.2906

[23]

$N$ = Infinity Phase Transition in a Class of Exactly Soluble Model Lattice Gauge Theories

Spenta R. Wadia
(
- Chicago U., EFI
)

- Phys.Lett.B 93 (1980) 403-410
•
DOI:
- 10.1016/0370-2693(80)90353-6

[24]

Nonperturbative Contributions in Models With a Nonanalytic Behavior at Infinite $N$

H. Neuberger
(
- UC, Berkeley
)

- Nucl.Phys.B 179 (1981) 253-282
•
DOI:
- 10.1016/0550-3213(81)90238-8

[25]

Large N phase transition in continuum QCD in two-dimensions

- Phys.Lett.B 319 (1993) 219-230
•
e-Print:
- hep-th/9305047
•
DOI:
- 10.1016/0370-2693(93)90806-S

1-25 of 34
1
2
25 / page