Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz

Meneghelli, Carlo; Yang, Gang

doi:10.1007/JHEP05(2014)112

Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz

Carlo Meneghelli
(
- DESY and
- Hamburg U., Dept. Math.
)
,
Gang Yang
(
- Humboldt U., Berlin
)

Dec 16, 2013

42 pages

Published in:

JHEP 05 (2014) 112

Published: 2014

e-Print:

1312.4537 [hep-th]

DOI:

10.1007/JHEP05(2014)112

Report number:

HU-EP-13-77,
HAMBURGER-BEITRAGE-ZUR-MATHEMATIK-497,
DESY-13-251

View in:

ADS Abstract Service

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Abstract: (arXiv)

In arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations. In this work we present an explicit derivation of this fact as well as generalizations to quiver gauge theories. To do so we combine various techniques like the iterated Mayer expansion, the method of expansion by regions, and the path integral tricks for non-perturbative summation. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. We hope that the derivation presented in this paper elucidates further this completely new point of view on the origin, as well as on the structure, of TBA equations in integrable models.

Note:

v2: typos corrected and references added. 27+15 pages, 4 figures; v3: preprint number added

Supersymmetry and Duality
Supersymmetric gauge theory
Lattice Integrable Models
Statistical Methods
Bethe ansatz: thermodynamical
instanton: partition function
instanton: expansion
gauge field theory: quiver
model: integrability
path integral

References(88)

Figures(5)

[1]

Review of AdS/CFT Integrability: An Overview

Niklas Beisert
(
- Potsdam, Max Planck Inst.
)
,
Changrim Ahn
(
- Ewha Women's U., Seoul
)
,
Luis F. Alday
(
- Oxford U. and
- Princeton, Inst. Advanced Study
)
,
Zoltan Bajnok
(
- Hungarian Acad. Sci., Budapest
)
,
James M. Drummond
(
- CERN and
- Annecy, LAPTH
)

et al.

- Lett.Math.Phys. 99 (2012) 3-32
•
e-Print:
- 1012.3982
•
DOI:
- 10.1007/s11005-011-0529-2

[2]

Electric - magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory

- Nucl.Phys.B 426 (1994) 19-52,
- Nucl.Phys.B 430 (1994) 485-486 (erratum)
•
e-Print:
- hep-th/9407087
•
DOI:
- 10.1016/0550-3213(94)90124-4

[3]

Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD

- Nucl.Phys.B 431 (1994) 484-550
•
e-Print:
- hep-th/9408099
•
DOI:
- 10.1016/0550-3213(94)90214-3

[4]

Integrability and Seiberg-Witten exact solution

- Phys.Lett.B 355 (1995) 466-474
•
e-Print:
- hep-th/9505035
•
DOI:
- 10.1016/0370-2693(95)00723-X

[5]

Supersymmetric Yang-Mills theory and integrable systems

- Nucl.Phys.B 460 (1996) 299-334
•
e-Print:
- hep-th/9510101
•
DOI:
- 10.1016/0550-3213(95)00609-5

[6]

Prepotential and the Seiberg-Witten theory

H. Itoyama
(
- Osaka U.
)
,
A. Morozov
(
- Moscow, ITEP
)

- Nucl.Phys.B 491 (1997) 529-573
•
e-Print:
- hep-th/9512161
•
DOI:
- 10.1016/S0550-3213(96)00679-7

[6]

Integrability and Seiberg-Witten theory: Curves and periods

H. Itoyama
(
- Osaka U.
)
,
A. Morozov
(
- Moscow, ITEP
)

- Nucl.Phys.B 477 (1996) 855-877
•
e-Print:
- hep-th/9511126
•
DOI:
- 10.1016/0550-3213(96)00358-6

[7]

Lectures on supersymmetric Yang-Mills theory and integrable systems

Eric D'Hoker
(
- UCLA
)
,
D.H. Phong
(
- Columbia U.
)

•
e-Print:
- hep-th/9912271

[8]

Integrating over Higgs branches

- Commun.Math.Phys. 209 (2000) 97-121
•
e-Print:
- hep-th/9712241
•
DOI:
- 10.1007/PL00005525

[9]

Testing Seiberg-Witten solution

A. Lossev
(
- Moscow, ITEP
)
,
N. Nekrasov
(
- Moscow, ITEP and
- Harvard U.
)
,
Samson L. Shatashvili
(
- Yale U.
)

- NATO Sci.Ser.C 520 (1999) 359-372
•
e-Print:
- hep-th/9801061

[10]

D particle bound states and generalized instantons

Gregory W. Moore
(
- Yale U.
)
,
Nikita Nekrasov
(
- Moscow, ITEP and
- Harvard U.
)
,
Samson Shatashvili
(
- Yale U. and
- CERN
)

- Commun.Math.Phys. 209 (2000) 77-95
•
e-Print:
- hep-th/9803265
•
DOI:
- 10.1007/s002200050016

[11]

Seiberg-Witten prepotential from instanton counting

Nikita A. Nekrasov
(
- IHES, Bures-sur-Yvette
)

- Adv.Theor.Math.Phys. 7 (2003) 5, 831-864
•
e-Print:
- hep-th/0206161
•
DOI:
- 10.4310/ATMP.2003.v7.n5.a4

[12]

Five dimensional gauge theories and relativistic integrable systems

Nikita Nekrasov
(
- Harvard U.
)

- Nucl.Phys.B 531 (1998) 323-344
•
e-Print:
- hep-th/9609219
•
DOI:
- 10.1016/S0550-3213(98)00436-2

[13]

Instanton counting and Chern-Simons theory

Amer Iqbal
(
- Harvard U., Phys. Dept.
)
,
Amir-Kian Kashani-Poor
(
- Stanford U., Phys. Dept. and
- SLAC
)

- Adv.Theor.Math.Phys. 7 (2003) 3, 457-497
•
e-Print:
- hep-th/0212279
•
DOI:
- 10.4310/ATMP.2003.v7.n3.a4

[14]

SU(N) geometries and topological string amplitudes

Amer Iqbal
(
- Harvard U., Phys. Dept.
)
,
Amir-Kian Kashani-Poor
(
- Stanford U., Phys. Dept. and
- SLAC
)

- Adv.Theor.Math.Phys. 10 (2006) 1, 1-32
•
e-Print:
- hep-th/0306032
•
DOI:
- 10.4310/ATMP.2006.v10.n1.a1

[15]

Matrix models, geometric engineering and elliptic genera

Timothy J. Hollowood
(
- Swansea U.
)
,
Amer Iqbal
(
- Harvard U., Phys. Dept.
)
,
Cumrun Vafa
(
- Harvard U., Phys. Dept.
)

- JHEP 03 (2008) 069
•
e-Print:
- hep-th/0310272
•
DOI:
- 10.1088/1126-6708/2008/03/069

[16]

The Refined topological vertex

Amer Iqbal
(
- Washington U., Seattle
)
,
Can Kozcaz
(
- Washington U., Seattle
)
,
Cumrun Vafa
(
- Harvard U., Phys. Dept. and
- MIT, LNS
)

- JHEP 10 (2009) 069
•
e-Print:
- hep-th/0701156
•
DOI:
- 10.1088/1126-6708/2009/10/069

[17]

Liouville Correlation Functions from Four-dimensional Gauge Theories

- Lett.Math.Phys. 91 (2010) 167-197
•
e-Print:
- 0906.3219
•
DOI:
- 10.1007/s11005-010-0369-5

[18]

Quantization of Integrable Systems and Four Dimensional Gauge Theories

- Published in 16th International Congress on Mathematical Physics, Prague, August 2009, P. Exner, Editor, pp.265-289, World Scientific 2010
•
e-Print:
- 0908.4052
•
DOI:
- 10.1142/9789814304634_0015