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

DataBETA

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

Aug 1, 2013

5 pages

Published in:

Phys.Rev.Lett. 112 (2014) 021601

Published: Jan 15, 2014

e-Print:

1308.0127 [hep-th]

DOI:

10.1103/PhysRevLett.112.021601

Report number:

FTPI-MINN-13-28,
UMN-TH-3218-23,
DAMTP-2013-40

View in:

ADS Abstract Service

reference search132 citations

Citations per year

Abstract: (APS)

We explain the physical role of nonperturbative saddle points of path integrals in theories without instantons, using the example of the asymptotically free two-dimensional principal chiral model (PCM). Standard topological arguments based on homotopy considerations suggest no role for nonperturbative saddles in such theories. However, the resurgence theory, which unifies perturbative and nonperturbative physics, predicts the existence of several types of nonperturbative saddles associated with features of the large-order structure of the perturbation theory. These points are illustrated in the PCM, where we find new nonperturbative “fracton” saddle point field configurations, and suggest a quantum interpretation of previously discovered “uniton” unstable classical solutions. The fractons lead to a semiclassical realization of IR renormalons in the circle-compactified theory and yield the microscopic mechanism of the mass gap of the PCM.

Note:

v2: references added

11.15.Kc
11.10.Kk
12.38.Cy
12.38.Lg
model: chiral
mass: gap
dimension: 2
nonperturbative
renormalon
perturbation theory

References(49)

Figures(4)

[1]

Integrability of the Principal Chiral Field Model in (1+1)-dimension

- Annals Phys. 167 (1986) 227
•
DOI:
- 10.1016/0003-4916(86)90201-0

[2]

Principal chiral field at large N

V.A. Fateev
(
- Montpellier U.
)
,
V.A. Kazakov
(
- Ecole Normale Superieure
)
,
P.B. Wiegmann
(
- Chicago U., EFI and
- Chicago U. and
- Landau Inst.
)

- Nucl.Phys.B 424 (1994) 505-520
•
e-Print:
- hep-th/9403099
•
DOI:
- 10.1016/0550-3213(94)90405-7

[2]

Large N chiral field in two-dimensions

V.A. Fateev
(
- Montpellier U. and
- Chicago U., EFI and
- Moscow, ITEP
)
,
P.B. Wiegmann
(
- Montpellier U. and
- Chicago U., EFI and
- Moscow, ITEP
)
,
V.A. Kazakov
(
- Ecole Normale Superieure
)

- Phys.Rev.Lett. 73 (1994) 1750-1753
•
DOI:
- 10.1103/PhysRevLett.73.1750

[3]

Summing Planar Diagrams by an Integrable Bootstrap

Peter Orland
(
- Baruch Coll. and
- CUNY, Graduate School - U. Ctr. and
- Bohr Inst.
)

- Phys.Rev.D 84 (2011) 105005
•
e-Print:
- 1108.0058
•
DOI:
- 10.1103/PhysRevD.84.105005

[3]

Multiparticle Form Factors of the Principal Chiral Model At Large N

Axel Cortes Cubero
(
- Baruch Coll. and
- CUNY, Graduate School - U. Ctr.
)

- Phys.Rev.D 86 (2012) 025025
•
e-Print:
- 1205.2069
•
DOI:
- 10.1103/PhysRevD.86.025025

[3]

Correlation functions of the SU(∞) principal chiral model

Axel Cortes Cubero
(
- Baruch Coll. and
- CUNY, Graduate School - U. Ctr.
)
,
Peter Orland
(
- Baruch Coll. and
- CUNY, Graduate School - U. Ctr. and
- Bohr Inst.
)

- Phys.Rev.D 88 (2013) 2, 025044
•
e-Print:
- 1306.1930
•
DOI:
- 10.1103/PhysRevD.88.025044

[5]

Gauge Fields and Strings

A.M. Polyakov

[6]

Quantum Field Theory in Condensed Matter Physics

A. Tsvelik

[7]

G. 't Hooft

- Subnuclear series 15 (1979) 943

[8]

Lectures on non-perturbative effects in large $N$ gauge theories, matrix models and strings

Marcos Mariño
(
- Geneva U.
)

- Fortsch.Phys. 62 (2014) 455-540
•
e-Print:
- 1206.6272
•
DOI:
- 10.1002/prop.201400005

[9]

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

[9]

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

[9]

Multi-Instantons and Multi-Cuts

Marcos Marino
(
- Geneva U.
)
,
Ricardo Schiappa
(
- Lisbon, IST
)
,
Marlene Weiss
(
- CERN and
- Zurich, ETH
)

- J.Math.Phys. 50 (2009) 052301
•
e-Print:
- 0809.2619
•
DOI:
- 10.1063/1.3097755

[9]

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

[9]

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

[9]

The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation

Ricardo Schiappa
(
- Lisbon, IST
)
,
Ricardo Vaz
(
- YITP, Stony Brook
)

- Commun.Math.Phys. 330 (2014) 655-721
•
e-Print:
- 1302.5138
•
DOI:
- 10.1007/s00220-014-2028-7

[10]

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

[10]

A semiclassical realization of infrared renormalons

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

- Phys.Rev.Lett. 109 (2012) 121601
•
e-Print:
- 1204.1661
•
DOI:
- 10.1103/PhysRevLett.109.121601

[11]

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

[11]

Continuity and Resurgence: towards a continuum definition of the $\mathbb{CP}$ (N-1) model

- Phys.Rev.D 87 (2013) 025015
•
e-Print:
- 1210.3646
•
DOI:
- 10.1103/PhysRevD.87.025015

[12]

Monopoles and instantons on partially compactified D-branes

Ki-Myeong Lee
(
- Columbia U.
)
,
Piljin Yi
(
- Columbia U.
)

- Phys.Rev.D 56 (1997) 3711-3717
•
e-Print:
- hep-th/9702107
•
DOI:
- 10.1103/PhysRevD.56.3711

[13]

Periodic instantons with nontrivial holonomy

Thomas C. Kraan
(
- Leiden U.
)
,
Pierre van Baal
(
- Leiden U.
)

- Nucl.Phys.B 533 (1998) 627-659
•
e-Print:
- hep-th/9805168
•
DOI:
- 10.1016/S0550-3213(98)00590-2

[14]

Instanton constituents in the O(3) model at finite temperature

Falk Bruckmann
(
- Regensburg U.
)

- Phys.Rev.Lett. 100 (2008) 051602
•
e-Print:
- 0707.0775
•
DOI:
- 10.1103/PhysRevLett.100.051602

[14]

Instanton constituents and fermionic zero modes in twisted CP**n models

Wieland Brendel
(
- Erlangen - Nuremberg U.
)
,
Falk Bruckmann
(
- Erlangen - Nuremberg U. and
- Regensburg U.
)
,
Lukas Janssen
(
- Jena U.
)
,
Andreas Wipf
(
- Jena U.
)
,
Christian Wozar
(
- Jena U.
)

- Phys.Lett.B 676 (2009) 116-125
•
e-Print:
- 0902.2328
•
DOI:
- 10.1016/j.physletb.2009.04.055

[14]

Kinks, chains, and loop groups in the CP**n sigma models

Derek Harland
(
- Hannover U.
)

- J.Math.Phys. 50 (2009) 122902
•
e-Print:
- 0902.2303
•
DOI:
- 10.1063/1.3266172

1-25 of 49
1
2
25 / page