Gauge/Liouville Triality - INSPIRE

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Gauge/Liouville Triality

Mina Aganagic
(
- UC, Berkeley, Math. Dept. and
- UC, Berkeley
)
,
Nathan Haouzi
(
- UC, Berkeley
)
,
Can Kozcaz
(
- SISSA, Trieste and
- INFN, Trieste
)
,
Shamil Shakirov
(
- UC, Berkeley and
- UC, Berkeley, Math. Dept. and
- Moscow, ITEP
)

Sep 6, 2013

50 pages

Published in:

Commun.Math.Phys. 405 (2024) 12, 285

Published: Nov 13, 2024

e-Print:

1309.1687 [hep-th]

DOI:

10.1007/s00220-024-05163-8

Report number:

ITEP-TH-30-13,
SISSA-42-2013-FISI

View in:

ADS Abstract Service

reference search90 citations

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Abstract: (Springer)

Conformal blocks of the Virasoro algebra have a Coulomb-gas representation as Dotsenko-Fateev integrals over the positions of screening charges. In q-deformed Virasoro, the conformal blocks on a sphere with an arbitrary number of punctures are manifestly the same, when written in Dotsenko-Fateev representation, as the partition functions of a class of 3d U(N) gauge theories with

{{\mathcal {N}}}=2

supersymmetry, in the

\Omega

-background. Coupling the 3d gauge theory to a flavor in fundamental representation corresponds to inserting a Virasoro vertex operator; the two real mass parameters determine the momentum and position of the puncture. The Dotsenko-Fateev integrals can be computed by residues. The result is the instanton sum of a five dimensional

{{\mathcal {N}}}=1

gauge theory. The positions of the poles are labeled by tuples of partitions, the residues of the integrand are the Nekrasov summands.

Note:

50 pages, 3 figures. v2: Typos corrected, aspects of 3d gauge theory clarified, references added

gauge field theory: U(N)
field theory: Liouville
mass: deformation
supersymmetry: 4
operator: vertex
dimension: 5
conformal block
partition function
instanton
triality

References(71)

Figures(3)

[1]

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

[2]

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

e-Print:
- 0909.2453

[3]

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

[4]

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

[5]

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

[6]

On 'Dotsenko-Fateev' representation of the toric conformal blocks

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

- J.Phys.A 44 (2011) 085401
•
e-Print:
- 1010.1734
•
DOI:
- 10.1088/1751-8113/44/8/085401

[7]

A direct proof of AGT conjecture at beta = 1

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

- JHEP 02 (2011) 067
•
e-Print:
- 1012.3137
•
DOI:
- 10.1007/JHEP02(2011)067

[8]

Five-dimensional AGT Relation and the Deformed beta-ensemble

Hidetoshi Awata
(
- Nagoya U.
)
,
Yasuhiko Yamada
(
- Kobe U.
)

- Prog.Theor.Phys. 124 (2010) 227-262
•
e-Print:
- 1004.5122
•
DOI:
- 10.1143/PTP.124.227

[9]

Selberg Integral and SU(N) AGT Conjecture

Hong Zhang
(
- Tokyo U.
)
,
Yutaka Matsuo
(
- Tokyo U.
)

- JHEP 12 (2011) 106
•
e-Print:
- 1110.5255
•
DOI:
- 10.1007/JHEP12(2011)106

[10]

A Quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

Jun'ichi Shiraishi
(
- Tokyo U., ISSP
)
,
Harunobu Kubo
(
- Tokyo U.
)
,
Hidetoshi Awata
(
- Kyoto U., Yukawa Inst., Kyoto
)
,
Satoru Odake
(
- Shinshu U.
)

- Lett.Math.Phys. 38 (1996) 33-51
•
e-Print:
- q-alg/9507034
•
DOI:
- 10.1007/BF00398297

[11]

Vertex operators of the q Virasoro algebra: Defining relations, adjoint actions and four point functions

- Lett.Math.Phys. 41 (1997) 65-78
•
e-Print:
- q-alg/9604023
•
DOI:
- 10.1023/A:1007321109584

[12]

Vortices, instantons and branes

Amihay Hanany
(
- MIT, LNS
)
,
David Tong
(
- MIT, LNS
)

- JHEP 07 (2003) 037
•
e-Print:
- hep-th/0306150
•
DOI:
- 10.1088/1126-6708/2003/07/037

[13]

Vortex strings and four-dimensional gauge dynamics

Amihay Hanany
(
- MIT, LNS
)
,
David Tong
(
- MIT, LNS
)

- JHEP 04 (2004) 066
•
e-Print:
- hep-th/0403158
•
DOI:
- 10.1088/1126-6708/2004/04/066

[14]

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

[15]

Spectral Duality in Integrable Systems from AGT Conjecture

A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)
,
Y. Zenkevich
(
- Moscow State U. and
- Moscow, ITEP
)
,
A. Zotov
(
- Moscow, ITEP
)

- JETP Lett. 97 (2013) 45-51,
- Pisma Zh.Eksp.Teor.Fiz. 97 (2013) 49-56
•
e-Print:
- 1204.0913
•
DOI:
- 10.1134/S0021364013010062

[16]

Spectral dualities in XXZ spin chains and five dimensional gauge theories

A. Mironov
(
- Moscow, ITEP and
- Lebedev Inst.
)
,
A. Morozov
(
- Moscow, ITEP
)
,
B. Runov
(
- Moscow, ITEP and
- Moscow, MIPT
)
,
Y. Zenkevich
(
- Moscow, ITEP and
- Moscow, INR
)
,
A. Zotov
(
- Moscow, ITEP and
- Moscow, MIPT and
- Steklov Math. Inst., Moscow
)

- JHEP 12 (2013) 034
•
e-Print:
- 1307.1502
•
DOI:
- 10.1007/JHEP12(2013)034

[17]

Knot invariants and topological strings

Hirosi Ooguri
(
- Caltech
)
,
Cumrun Vafa
(
- Harvard U.
)

- Nucl.Phys.B 577 (2000) 419-438
•
e-Print:
- hep-th/9912123
•
DOI:
- 10.1016/S0550-3213(00)00118-8

[18]

Mirror symmetry, D-branes and counting holomorphic discs

Mina Aganagic
(
- Harvard U.
)
,
Cumrun Vafa
(
- Harvard U.
)

e-Print:
- hep-th/0012041

[19]

String theory of the Omega deformation

- JHEP 01 (2012) 148
•
e-Print:
- 1106.0279
•
DOI:
- 10.1007/JHEP01(2012)148

[20]

On Three Dimensional Quiver Gauge Theories and Integrability

- JHEP 05 (2013) 126
•
e-Print:
- 1304.0779
•
DOI:
- 10.1007/JHEP05(2013)126

[21]

Knot Homology and Refined Chern-Simons Index

Mina Aganagic
(
- UC, Berkeley, Math. Dept. and
- UC, Berkeley
)
,
Shamil Shakirov
(
- UC, Berkeley, Math. Dept. and
- Moscow, ITEP
)

- Commun.Math.Phys. 333 (2015) 1, 187-228
•
e-Print:
- 1105.5117
•
DOI:
- 10.1007/s00220-014-2197-4

[22]

Refined Chern-Simons Theory and Knot Homology

Mina Aganagic
(
- UC, Berkeley and
- UC, Berkeley, Math. Dept.
)
,
Shamil Shakirov
(
- UC, Berkeley, Math. Dept. and
- Moscow, ITEP
)

- Proc.Symp.Pure Math. 85 (2012) 3-32
•
e-Print:
- 1202.2489
•
DOI:
- 10.1090/pspum/085/1372

[23]

Orientifolds and the Refined Topological String

Mina Aganagic
(
- UC, Berkeley
)
,
Kevin Schaeffer
(
- UC, Berkeley
)

- JHEP 09 (2012) 084
•
e-Print:
- 1202.4456
•
DOI:
- 10.1007/JHEP09(2012)084

[24]

Super-A-polynomial for knots and BPS states

Hiroyuki Fuji
(
- Caltech and
- Nagoya U.
)
,
Sergei Gukov
(
- Caltech and
- Bonn, Max Planck Inst., Math.
)
,
Piotr Sulkowski
(
- Caltech and
- Amsterdam U. and
- Warsaw U.
)

- Nucl.Phys.B 867 (2013) 506-546
•
e-Print:
- 1205.1515
•
DOI:
- 10.1016/j.nuclphysb.2012.10.005

[25]

Notes on SUSY Gauge Theories on Three-Sphere

- JHEP 03 (2011) 127
•
e-Print:
- 1012.3512
•
DOI:
- 10.1007/JHEP03(2011)127

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