Modular and duality properties of surface operators in N=2* gauge theories - INSPIRE

DataBETA

Modular and duality properties of surface operators in N=2* gauge theories

S.K. Ashok
(
- HBNI, Mumbai and
- IMSc, Chennai
)
,
M. Billo
(
- INFN, Turin and
- Turin U.
)
,
E. Dell'Aquila
(
- HBNI, Mumbai and
- IMSc, Chennai
)
,
M. Frau
(
- INFN, Turin and
- Turin U.
)
,
R.R. John
(
- HBNI, Mumbai and
- IMSc, Chennai
)

Feb 9, 2017

54 pages

Published in:

JHEP 07 (2017) 068

Published: Jul 14, 2017

e-Print:

1702.02833 [hep-th]

DOI:

10.1007/JHEP07(2017)068

View in:

reference search24 citations

Citations per year

Abstract: (Springer)

We calculate the instanton partition function of the four-dimensional

\mathcal{N}={2}^{\star }

SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the surface operator, satisfies a modular anomaly equation. Exploiting the localization results, we solve this equation in terms of elliptic and quasi-modular forms which resum all non-perturbative corrections. We also show that our results, derived for monodromy defects in the four-dimensional theory, match the effective twisted superpotential describing the infrared properties of certain two-dimensional sigma models coupled either to pure

\mathcal{N}=2

or to

\mathcal{N}={2}^{\star }

gauge theories.

Note:

51 pages, v3: references added, typos fixed, footnote added, some small changes in the text, appendix B streamlined. Matches the published version

Duality in Gauge Field Theories
Extended Supersymmetry
Supersymmetry and Duality
D-branes
operator: surface
superpotential: twist
gauge field theory: SU(N)
instanton: partition function
localization
infrared

References(78)

Figures(0)

[1]

Surface operators.

Sergei Gukov
(
- Caltech
)

- ,
•
e-Print:
- 1412.7127
•
DOI:
- 10.1007/978-3-319-18769-3_8

[2]

Gauge Theory, Ramification, And The Geometric Langlands Program

e-Print:
- hep-th/0612073

[3]

Rigid Surface Operators

- Adv.Theor.Math.Phys. 14 (2010) 1, 87-178
•
e-Print:
- 0804.1561
•
DOI:
- 10.4310/ATMP.2010.v14.n1.a3

[4]

Surface Operators in N = 2 4d Gauge Theories

Davide Gaiotto
(
- Princeton, Inst. Advanced Study
)

- JHEP 11 (2012) 090
•
e-Print:
- 0911.1316
•
DOI:
- 10.1007/JHEP11(2012)090

[5]

Surface Defects and Resolvents

- JHEP 09 (2013) 070
•
e-Print:
- 1307.2578
•
DOI:
- 10.1007/JHEP09(2013)070

[6]

Solutions of four-dimensional field theories via M-theory

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- ,
- Nucl.Phys.B 500 (1997) 3-42,
•
e-Print:
- hep-th/9703166
•
DOI:
- 10.1201/9781482268737-38

[7]

N=2 dualities

Davide Gaiotto
(
- Princeton, Inst. Advanced Study
)

- JHEP 08 (2012) 034
•
e-Print:
- 0904.2715
•
DOI:
- 10.1007/JHEP08(2012)034

[8]

Affine SL(2) conformal blocks from 4d gauge theories

- Lett.Math.Phys. 94 (2010) 87-114
•
e-Print:
- 1005.4469
•
DOI:
- 10.1007/s11005-010-0422-4

[9]

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

[10]

Affine sl(N) conformal blocks from N=2 SU(N) gauge theories

Can Kozcaz
(
- CERN
)
,
Sara Pasquetti
(
- CERN
)
,
Filippo Passerini
(
- Humboldt U., Berlin
)
,
Niclas Wyllard
(
- Unlisted
)

- JHEP 01 (2011) 045
•
e-Print:
- 1008.1412
•
DOI:
- 10.1007/JHEP01(2011)045

[11]

Loop and surface operators in N=2 gauge theory and Liouville modular geometry

Luis F. Alday
(
- Princeton, Inst. Advanced Study
)
,
Davide Gaiotto
(
- Princeton, Inst. Advanced Study
)
,
Sergei Gukov
(
- Caltech and
- UC, Santa Barbara
)
,
Yuji Tachikawa
(
- Princeton, Inst. Advanced Study
)
,
Herman Verlinde
(
- Princeton U.
)

- JHEP 01 (2010) 113
•
e-Print:
- 0909.0945
•
DOI:
- 10.1007/JHEP01(2010)113

[12]

On AGT Conjecture for Pure Super Yang-Mills and W-algebra

Masato Taki
(
- Kyoto U., Yukawa Inst., Kyoto
)

- JHEP 05 (2011) 038
•
e-Print:
- 0912.4789
•
DOI:
- 10.1007/JHEP05(2011)038

[13]

On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles

A. Marshakov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)

- J.Geom.Phys. 61 (2011) 1203-1222
•
e-Print:
- 1011.4491
•
DOI:
- 10.1016/j.geomphys.2011.01.012

[14]

A & B model approaches to surface operators and Toda theories

- JHEP 08 (2010) 042
•
e-Print:
- 1004.2025
•
DOI:
- 10.1007/JHEP08(2010)042

[15]

Vortex Counting and Lagrangian 3-manifolds

Tudor Dimofte
(
- Caltech
)
,
Sergei Gukov
(
- Caltech and
- UC, Santa Barbara
)
,
Lotte Hollands
(
- Caltech and
- UC, Santa Barbara
)

- Lett.Math.Phys. 98 (2011) 225-287
•
e-Print:
- 1006.0977
•
DOI:
- 10.1007/s11005-011-0531-8

[16]

Deformed Prepotential, Quantum Integrable System and Liouville Field Theory

- Nucl.Phys.B 841 (2010) 388-425
•
e-Print:
- 1006.4505
•
DOI:
- 10.1016/j.nuclphysb.2010.08.008

[17]

Surface Operator, Bubbling Calabi-Yau and AGT Relation

Masato Taki
(
- Kyoto U., Yukawa Inst., Kyoto
)

- JHEP 07 (2011) 047
•
e-Print:
- 1007.2524
•
DOI:
- 10.1007/JHEP07(2011)047

[18]

Defects and Quantum Seiberg-Witten Geometry

- JHEP 05 (2015) 095
•
e-Print:
- 1412.6081
•
DOI:
- 10.1007/JHEP05(2015)095

[19]

Six-dimensional origin of $\mathcal{N} = 4$ SYM with duality defects

- JHEP 12 (2016) 058
•
e-Print:
- 1610.03663
•
DOI:
- 10.1007/JHEP12(2016)058

[20]

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

[21]

Deformed N=2 theories, generalized recursion relations and S-duality

M. Billo
(
- INFN, Turin and
- Turin U.
)
,
M. Frau
(
- INFN, Turin and
- Turin U.
)
,
L. Gallot
(
- Annecy, LAPTH
)
,
A. Lerda
(
- Piemonte Orientale U., Alessandria and
- INFN, Turin
)
,
I. Pesando
(
- INFN, Turin and
- Turin U.
)

- JHEP 04 (2013) 039
•
e-Print:
- 1302.0686
•
DOI:
- 10.1007/JHEP04(2013)039

[22]

Modular anomaly equation, heat kernel and S-duality in $N=2$ theories

M. Billo
(
- INFN, Turin and
- Turin U.
)
,
M. Frau
(
- INFN, Turin and
- Turin U.
)
,
L. Gallot
(
- Annecy, LAPTH
)
,
A. Lerda
(
- Piemonte Orientale U., Alessandria and
- INFN, Turin
)
,
I. Pesando
(
- INFN, Turin and
- Turin U.
)

- JHEP 11 (2013) 123
•
e-Print:
- 1307.6648
•
DOI:
- 10.1007/JHEP11(2013)123

[23]

Instanton expansions for mass deformed N=4 superYang-Mills theories

- Nucl.Phys.B 528 (1998) 109-132
•
e-Print:
- hep-th/9710146
•
DOI:
- 10.1016/S0550-3213(98)00314-9

[24]

Holomorphic anomalies in topological field theories

- Nucl.Phys.B 405 (1993) 279-304,
- ,
- AMS/IP Stud.Adv.Math. 1 (1996) 655-682
•
e-Print:
- hep-th/9302103
•
DOI:
- 10.1016/0550-3213(93)90548-4

[25]

Quantum background independence in string theory

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Salamfest 1993:0257-275
•
e-Print:
- hep-th/9306122

1-25 of 78
1
2
3
4
25 / page