Seiberg-Witten theory, matrix model and AGT relation

Eguchi, Tohru; Maruyoshi, Kazunobu

doi:10.1007/JHEP07(2010)081

Seiberg-Witten theory, matrix model and AGT relation

Jun, 2010

20 pages

Published in:

JHEP 07 (2010) 081

e-Print:

1006.0828 [hep-th]

DOI:

10.1007/JHEP07(2010)081

Report number:

YITP-10-40

View in:

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Abstract: (arXiv)

We discuss the Penner-type matrix model which has been proposed to explain the AGT relation between the 2-dimensional Liouville theory and 4-dimensional N=2 superconformal gauge theories. In our previous communication we have obtained the spectral curve of the matrix model and showed that it agrees with that derived from M-theory. We have also discussed the decoupling limit of massive flavors and proposed new matrix models which describe Seiberg-Witten theory with flavors N_f=2,3. In this article we explicitly evaluate the free energy of these matrix models and show that they in fact reproduce the amplitudes of Seiberg-Witten theory.

Note:

19 pages, 1 figure

Matrix Models
Extended Supersymmetry
Nonperturbative Effects
Super-symmetric gauge theory
gauge field theory: conformal
supersymmetry: 2
field theory: Liouville
dimension: 2
dimension: 4
matrix model

References(32)

Figures(1)

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

Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions

A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)
,
Sh. Shakirov
(
- Moscow, ITEP and
- Moscow, MIPT
)

- JHEP 02 (2010) 030
•
e-Print:
- 0911.5721
•
DOI:
- 10.1007/JHEP02(2010)030

Conformal blocks as Dotsenko-Fateev Integral Discriminants

A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)
,
Sh. Shakirov
(
- Moscow, ITEP and
- Moscow, MIPT
)

- Int.J.Mod.Phys.A 25 (2010) 3173-3207
•
e-Print:
- 1001.0563
•
DOI:
- 10.1142/S0217751X10049141

Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model

H. Itoyama
(
- Osaka City U. and
- OCAMI, Osaka
)
,
T. Oota
(
- OCAMI, Osaka
)

- Nucl.Phys.B 838 (2010) 298-330
•
e-Print:
- 1003.2929
•
DOI:
- 10.1016/j.nuclphysb.2010.05.002

Conformal blocks and generalized Selberg integrals

A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
Alexei Morozov
(
- Moscow, ITEP
)
,
Andrey Morozov
(
- Moscow, ITEP and
- Moscow State U.
)

- Nucl.Phys.B 843 (2011) 534-557
•
e-Print:
- 1003.5752
•
DOI:
- 10.1016/j.nuclphysb.2010.10.016

The matrix model version of AGT conjecture and CIV-DV prepotential

A. Morozov
(
- Moscow, ITEP
)
,
S. Shakirov
(
- Moscow, ITEP and
- Moscow, MIPT
)

- JHEP 08 (2010) 066
•
e-Print:
- 1004.2917
•
DOI:
- 10.1007/JHEP08(2010)066

Recursion relations in CFT and N=2 SYM theory

Rubik Poghossian
(
- INFN, Rome2 and
- Yerevan Phys. Inst.
)

- JHEP 12 (2009) 038
•
e-Print:
- 0909.3412
•
DOI:
- 10.1088/1126-6708/2009/12/038

Recursive representation of the torus 1-point conformal block

- JHEP 01 (2010) 063
•
e-Print:
- 0911.2353
•
DOI:
- 10.1007/JHEP01(2010)063

On AGT conjecture

V.A. Fateev
(
- Landau Inst. and
- Montpellier U.
)
,
A.V. Litvinov
(
- Landau Inst. and
- Rutgers U., Piscataway
)

- JHEP 02 (2010) 014
•
e-Print:
- 0912.0504
•
DOI:
- 10.1007/JHEP02(2010)014

Proving the AGT relation for $N_{f}$ = 0,1,2 antifundamentals

- JHEP 06 (2010) 046
•
e-Print:
- 1004.1841
•
DOI:
- 10.1007/JHEP06(2010)046

Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems

e-Print:
- 0909.2453

Penner Type Matrix Model and Seiberg-Witten Theory

- JHEP 02 (2010) 022
•
e-Print:
- 0911.4797
•
DOI:
- 10.1007/JHEP02(2010)022

The Quiver Matrix Model and 2d-4d Conformal Connection

Hiroshi Itoyama
(
- Osaka City U. and
- OCAMI, Osaka
)
,
Kazunobu Maruyoshi
(
- Kyoto U., Yukawa Inst., Kyoto
)
,
Takeshi Oota
(
- OCAMI, Osaka
)

- Prog.Theor.Phys. 123 (2010) 957-987
•
e-Print:
- 0911.4244
•
DOI:
- 10.1143/PTP.123.957

An A(r) threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories

Ricardo Schiappa
(
- Lisbon, IST
)
,
Niclas Wyllard
(
- Chalmers U. Tech.
)

- J.Math.Phys. 51 (2010) 082304
•
e-Print:
- 0911.5337
•
DOI:
- 10.1063/1.3449328

Conformal Algebra and Multipoint Correlation Functions in Two-Dimensional Statistical Models

V.S. Dotsenko
(
- Nordita
)
,
V.A. Fateev
(
- Landau Inst.
)

- Nucl.Phys.B 240 (1984) 312,
- IN *ITZYKSON, C. (ED.) ET AL.: CONFORMAL INVARIANCE AND APPLICATIONS TO STATISTICAL MECHANICS* 214-250. (NUCL. PHYS. B240 |FS12| (1984) 312-348) AND NORDITA COPENHAGEN - NORDITA-84-08 (84,REC.MAY) 75 P. (SEE BOOK INDEX),
•
DOI:
- 10.1016/0550-3213(84)90269-4

Four Point Correlation Functions and the Operator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c < 1

V.S. Dotsenko
(
- Nordita
)
,
V.A. Fateev
(
- Landau Inst.
)

- Nucl.Phys.B 251 (1985) 691-734
•
DOI:
- 10.1016/S0550-3213(85)80004-3

Generalized matrix models as conformal field theories: Discrete case

- Phys.Lett.B 265 (1991) 99-107
•
DOI:
- 10.1016/0370-2693(91)90021-H

Conformal matrix models as an alternative to conventional multimatrix models

- Nucl.Phys.B 404 (1993) 717-750
•
e-Print:
- hep-th/9208044
•
DOI:
- 10.1016/0550-3213(93)90595-G

Instantons and recursion relations in N=2 SUSY gauge theory

Marco Matone
(
- Padua U. and
- INFN, Padua
)

- Phys.Lett.B 357 (1995) 342-348
•
e-Print:
- hep-th/9506102
•
DOI:
- 10.1016/0370-2693(95)00920-G

On the relation between the holomorphic prepotential and the quantum moduli in SUSY gauge theories

- Phys.Lett.B 367 (1996) 145-150
•
e-Print:
- hep-th/9510129
•
DOI:
- 10.1016/0370-2693(95)01399-7

Prepotentials of N=2 supersymmetric gauge theories and soliton equations

Tohru Eguchi
(
- Tokyo U.
)
,
Sung-Kil Yang
(
- Tsukuba U.
)

- Mod.Phys.Lett.A 11 (1996) 131-138,
- Mod. Phys. Lett. A11 (1996) 131-138, and Tokyo U. - UT-728 (95/10,rec.Nov.) 10 p
•
e-Print:
- hep-th/9510183
•
DOI:
- 10.1142/S0217732396000151

Nonperturbative effective actions of N=2 supersymmetric gauge theories

- Int.J.Mod.Phys.A 11 (1996) 1929-1974
•
e-Print:
- hep-th/9505150
•
DOI:
- 10.1142/S0217751X96001000

Prepotentials in N=2 SU(2) supersymmetric Yang-Mills theory with massless hypermultiplets

Katsushi Ito
(
- Tsukuba U.
)
,
Sung-Kil Yang
(
- Tsukuba U.
)

- Phys.Lett.B 366 (1996) 165-173
•
e-Print:
- hep-th/9507144
•
DOI:
- 10.1016/0370-2693(95)01310-5

Wall-crossing, Hitchin systems, and the WKB approximation

- Adv.Math. 234 (2013) 239-403
•
e-Print:
- 0907.3987
•
DOI:
- 10.1016/j.aim.2012.09.027

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

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