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Seiberg-Witten prepotential for E-string theory and global symmetries

Kazuhiro Sakai
(
- Kyoto U., Yukawa Inst., Kyoto
)

Jul, 2012

22 pages

Published in:

JHEP 09 (2012) 077

e-Print:

1207.5739 [hep-th]

DOI:

10.1007/JHEP09(2012)077

Report number:

YITP-12-59

View in:

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Abstract: (arXiv)

We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2 with nontrivial Wilson lines. We consider compactification with four general Wilson line parameters, which partially break the E_8 global symmetry. In particular, we investigate in detail the cases where the Lie algebra of the unbroken global symmetry is E_n + A_{8-n} with n=8,7,6,5 or D_8. All our Nekrasov-type expressions can be viewed as special cases of the elliptic analogue of the Nekrasov partition function for the SU(N) gauge theory with N_f=2N flavors. We also present a new expression for the Seiberg-Witten curve for the E-string theory with four Wilson line parameters, clarifying the connection between the E-string theory and the SU(2) Seiberg-Witten theory with N_f=4 flavors.

Note:

22 pages. v2: comments and a reference added, version to appear in JHEP

flavor: 4
algebra: Lie
dimension: 4
Wilson loop
prepotential
Seiberg-Witten model
partition function
surface: del Pezzo
BPS
Calabi-Yau

References(23)

Figures(0)

[1]

Small E(8) instantons and tensionless noncritical strings

- Nucl.Phys.B 474 (1996) 122-140
•
e-Print:
- hep-th/9602120
•
DOI:
- 10.1016/0550-3213(96)00243-X

[2]

Comments on string dynamics in six-dimensions

- Nucl.Phys.B 471 (1996) 121-134
•
e-Print:
- hep-th/9603003
•
DOI:
- 10.1016/0550-3213(96)00189-7

[3]

BPS states of exceptional noncritical strings

- Nucl.Phys.B Proc.Suppl. 58 (1997) 177,
•
e-Print:
- hep-th/9607139
•
DOI:
- 10.1016/S0920-5632(97)00422-2

[4]

Branes, Calabi-Yau spaces, and toroidal compactification of the N=1 six-dimensional E(8) theory

- Nucl.Phys.B 487 (1997) 93-127
•
e-Print:
- hep-th/9610251
•
DOI:
- 10.1016/S0550-3213(96)00690-6

[5]

E strings and N=4 topological Yang-Mills theories

J.A. Minahan
(
- Southern California U.
)
,
D. Nemeschansky
(
- Southern California U.
)
,
C. Vafa
(
- Harvard U.
)
,
N.P. Warner
(
- Southern California U.
)

- Nucl.Phys.B 527 (1998) 581-623
•
e-Print:
- hep-th/9802168
•
DOI:
- 10.1016/S0550-3213(98)00426-X

[6]

Toroidal compactification of heterotic 6-d noncritical strings down to four-dimensions

Ori J. Ganor
(
- Princeton U.
)

- Nucl.Phys.B 488 (1997) 223-235
•
e-Print:
- hep-th/9608109
•
DOI:
- 10.1016/S0550-3213(96)00687-6

[7]

Extremal transitions and five-dimensional supersymmetric field theories

David R. Morrison
(
- Duke U.
)
,
Nathan Seiberg
(
- Rutgers U., Piscataway
)

- Nucl.Phys.B 483 (1997) 229-247
•
e-Print:
- hep-th/9609070
•
DOI:
- 10.1016/S0550-3213(96)00592-5

[8]

Small instantons, Del Pezzo surfaces and type I-prime theory

Michael R. Douglas
(
- Rutgers U., Piscataway
)
,
Sheldon H. Katz
(
- Oklahoma State U.
)
,
Cumrun Vafa
(
- Rutgers U., Piscataway and
- Harvard U.
)

- Nucl.Phys.B 497 (1997) 155-172
•
e-Print:
- hep-th/9609071
•
DOI:
- 10.1016/S0550-3213(97)00281-2

[9]

Noncritical strings, Del Pezzo singularities and Seiberg-Witten curves

W. Lerche
(
- CERN
)
,
P. Mayr
(
- CERN
)
,
N.P. Warner
(
- Southern California U.
)

- Nucl.Phys.B 499 (1997) 125-148
•
e-Print:
- hep-th/9612085
•
DOI:
- 10.1016/S0550-3213(97)00312-X

[10]

Investigating the BPS spectrum of noncritical E(n) strings

J.A. Minahan
(
- Southern California U.
)
,
D. Nemeschansky
(
- Southern California U.
)
,
N.P. Warner
(
- Santa Barbara, KITP
)

- Nucl.Phys.B 508 (1997) 64-106
•
e-Print:
- hep-th/9705237
•
DOI:
- 10.1016/S0550-3213(97)00527-0

[11]

Partition functions for BPS states of the noncritical E(8) string

J.A. Minahan
(
- Southern California U.
)
,
D. Nemeschansky
(
- Southern California U.
)
,
N.P. Warner
(
- Santa Barbara, KITP
)

- Adv.Theor.Math.Phys. 1 (1998) 167-183
•
e-Print:
- hep-th/9707149
•
DOI:
- 10.4310/ATMP.1997.v1.n1.a7

[12]

Exceptional string: Instanton expansions and Seiberg-Witten curve

Kenji Mohri
(
- Tsukuba U.
)

- Rev.Math.Phys. 14 (2002) 913-975
•
e-Print:
- hep-th/0110121
•
DOI:
- 10.1142/S0129055X02001466

[13]

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

[14]

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

[15]

Seiberg-Witten curve for the E string theory

Tohru Eguchi
(
- Tokyo U.
)
,
Kazuhiro Sakai
(
- Tokyo U.
)

- JHEP 05 (2002) 058
•
e-Print:
- hep-th/0203025
•
DOI:
- 10.1088/1126-6708/2002/05/058

[16]

Seiberg-Witten prepotential for E-string theory and random partitions

Kazuhiro Sakai
(
- Kyoto U., Yukawa Inst., Kyoto
)

- JHEP 06 (2012) 027
•
e-Print:
- 1203.2921
•
DOI:
- 10.1007/JHEP06(2012)027

[17]

Local mirror symmetry: Calculations and interpretations

T.M. Chiang
(
- Harvard U.
)
,
A. Klemm
(
- Princeton, Inst. Advanced Study
)
,
Shing-Tung Yau
(
- Harvard U.
)
,
E. Zaslow
(
- Northwestern U.
)

- Adv.Theor.Math.Phys. 3 (1999) 495-565
•
e-Print:
- hep-th/9903053
•
DOI:
- 10.4310/ATMP.1999.v3.n3.a3

[18]

M theory, topological strings and spinning black holes

Sheldon H. Katz
(
- Oklahoma State U.
)
,
Albrecht Klemm
(
- Princeton, Inst. Advanced Study
)
,
Cumrun Vafa
(
- Harvard U.
)

- Adv.Theor.Math.Phys. 3 (1999) 1445-1537
•
e-Print:
- hep-th/9910181
•
DOI:
- 10.4310/ATMP.1999.v3.n5.a6

[19]

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

[20]

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

[21]

Topological string amplitudes for the local $\frac{1}{2}$ K3 surface

Kazuhiro Sakai
(
- Kyoto U., Yukawa Inst., Kyoto
)

- PTEP 2017 (2017) 3, 033B09
•
e-Print:
- 1111.3967
•
DOI:
- 10.1093/ptep/ptx027

[22]

Seiberg-Witten curve for E string theory revisited

Tohru Eguchi
(
- Tokyo U.
)
,
Kazuhiro Sakai
(
- Tokyo U.
)

- Adv.Theor.Math.Phys. 7 (2003) 3, 419-455
•
e-Print:
- hep-th/0211213
•
DOI:
- 10.4310/ATMP.2003.v7.n3.a3

[23]

Counting BPS states via holomorphic anomaly equations

Shinobu Hosono
(
- Tokyo U., Math. Sci.
)

- Fields Inst.Commun. 38 (2013) 57-86
•
e-Print:
- hep-th/0206206