Multi instanton calculus on ALE spaces

Fucito, Francesco; Morales, Jose F.; Poghossian, Rubik

doi:10.1016/j.nuclphysb.2004.09.014

Multi instanton calculus on ALE spaces

Francesco Fucito
(
- Rome U., Tor Vergata and
- INFN, Rome2
)
,
Jose F. Morales
(
- Frascati
)
,
Rubik Poghossian
(
- Yerevan Phys. Inst.
)

Jun, 2004

27 pages

Published in:

Nucl.Phys.B 703 (2004) 518-536

e-Print:

hep-th/0406243 [hep-th]

DOI:

10.1016/j.nuclphysb.2004.09.014

Report number:

ROM2F-2004-06

View in:

pdf

reference search82 citations

Citations per year

Abstract:

We study SYM gauge theories living on ALE spaces. Using localization formulae we compute the prepotential (and its gravitational corrections) for SU(N) supersymmetric

{\cal N}=2, 2^*

gauge theories on ALE spaces of the

A_n

type. Furthermore we derive the Poincar\'{e} polynomial describing the homologies of the corresponding moduli spaces of self-dual gauge connections. From these results we extract the

{\cal N}=4

partition function which is a modular form in agreement with the expectations of

SL(2,\Z)

duality.

11.15.-q
11.30.Pb
11.15.Kc
gauge field theory: SU(N)
supersymmetry
space-time
instanton
potential: prepotential
duality
partition function

References(25)

Figures(0)

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

An Algorithm for the microscopic evaluation of the coefficients of the Seiberg-Witten prepotential

R. Flume
(
- Bonn U.
)
,
R. Poghossian
(
- Yerevan Phys. Inst.
)

- Int.J.Mod.Phys.A 18 (2003) 2541
•
e-Print:
- hep-th/0208176
•
DOI:
- 10.1142/S0217751X03013685

Multiinstanton calculus and equivariant cohomology

Ugo Bruzzo
(
- SISSA, Trieste and
- INFN, Trieste
)
,
Francesco Fucito
(
- Rome U., Tor Vergata and
- INFN, Rome2
)
,
Jose F. Morales
(
- Utrecht U. and
- Frascati
)
,
Alessandro Tanzini
(
- Paris, LPTHE
)

- JHEP 05 (2003) 054
•
e-Print:
- hep-th/0211108
•
DOI:
- 10.1088/1126-6708/2003/05/054

Small instantons, little strings and free fermions

Andrei S. Losev
(
- Moscow, ITEP
)
,
Andrei Marshakov
(
- Bonn, Max Planck Inst., Math. and
- Lebedev Inst. and
- Moscow, ITEP
)
,
Nikita A. Nekrasov
(
- IHES, Bures-sur-Yvette
)

- In *Shifman, M. (ed.) et al.: From fields to strings, vol. 1* 581-621
•
e-Print:
- hep-th/0302191

Seiberg-Witten theory and random partitions

- Prog.Math. 244 (2006) 525-596
•
e-Print:
- hep-th/0306238
•
DOI:
- 10.1007/0-8176-4467-9_15

Matone's relation in the presence of gravitational couplings

Rainald Flume
(
- Bonn U.
)
,
Francesco Fucito
(
- Rome U., Tor Vergata and
- INFN, Rome2
)
,
Jose F. Morales
(
- Frascati
)
,
Rubik Poghossian
(
- Yerevan Phys. Inst.
)

- JHEP 04 (2004) 008
•
e-Print:
- hep-th/0403057
•
DOI:
- 10.1088/1126-6708/2004/04/008

A Note on instanton counting for N=2 gauge theories with classical gauge groups

Marcos Marino
(
- CERN and
- Lisbon, IST
)
,
Niclas Wyllard
(
- CERN
)

- JHEP 05 (2004) 021
•
e-Print:
- hep-th/0404125
•
DOI:
- 10.1088/1126-6708/2004/05/021

ABCD of instantons

- Commun.Math.Phys. 252 (2004) 359-391
•
e-Print:
- hep-th/0404225
•
DOI:
- 10.1007/s00220-004-1189-1

Small instantons in string theory

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Nucl.Phys.B 460 (1996) 541-559
•
e-Print:
- hep-th/9511030
•
DOI:
- 10.1016/0550-3213(95)00625-7

Branes within branes

Michael R. Douglas
(
- Rutgers U., Piscataway
)

- NATO Sci.Ser.C 520 (1999) 267-275
•
e-Print:
- hep-th/9512077

Gauge fields and D-branes

Michael R. Douglas
(
- Rutgers U., Piscataway
)

- J.Geom.Phys. 28 (1998) 255-262
•
e-Print:
- hep-th/9604198
•
DOI:
- 10.1016/S0393-0440(97)00024-7

Multi-instanton calculus and the AdS / CFT correspondence in N=4 superconformal field theory

Nicholas Dorey
(
- Washington U., Seattle and
- Swansea U.
)
,
Timothy J. Hollowood
(
- Los Alamos and
- Swansea U.
)
,
Valentin V. Khoze
(
- Durham U.
)
,
Michael P. Mattis
(
- Los Alamos
)
,
Stefan Vandoren
(
- Swansea U.
)

- Nucl.Phys.B 552 (1999) 88-168
•
e-Print:
- hep-th/9901128
•
DOI:
- 10.1016/S0550-3213(99)00193-5

D-branes, quivers, and ALE instantons

e-Print:
- hep-th/9603167

Aspects of type IIB theory on ALE spaces

Clifford V. Johnson
(
- Santa Barbara, KITP
)
,
Robert C. Myers
(
- McGill U.
)

- Phys.Rev.D 55 (1997) 6382-6393
•
e-Print:
- hep-th/9610140
•
DOI:
- 10.1103/PhysRevD.55.6382

Instantons in N=2 Sp(N) superconformal gauge theories and the AdS / CFT correspondence

E. Gava
(
- INFN, Trieste and
- ICTP, Trieste and
- SISSA, Trieste
)
,
K.S. Narain
(
- ICTP, Trieste
)
,
M.H. Sarmadi
(
- IPM, Tehran
)

- Nucl.Phys.B 569 (2000) 183-208
•
e-Print:
- hep-th/9908125
•
DOI:
- 10.1016/S0550-3213(99)00751-8

Summing the instanton series in N=2 superconformal large N QCD

Timothy J. Hollowood
(
- Los Alamos and
- Swansea U.
)
,
Valentin V. Khoze
(
- Durham U.
)
,
Michael P. Mattis
(
- Los Alamos
)

- JHEP 10 (1999) 019
•
e-Print:
- hep-th/9905209
•
DOI:
- 10.1088/1126-6708/1999/10/019

ADHM and D instantons in orbifold AdS / CFT duality

Timothy J. Hollowood
(
- Los Alamos and
- Swansea U.
)
,
Valentin V. Khoze
(
- Durham U.
)

- Nucl.Phys.B 575 (2000) 78-106
•
e-Print:
- hep-th/9908035
•
DOI:
- 10.1016/S0550-3213(00)00086-9

D instanton probes of non conformal geometries

Francesco Fucito
(
- INFN, Rome2
)
,
Jose F. Morales
(
- Utrecht U.
)
,
Alessandro Tanzini
(
- Paris U., VI-VII and
- INFN, Rome
)

- JHEP 07 (2001) 012
•
e-Print:
- hep-th/0106061
•
DOI:
- 10.1088/1126-6708/2001/07/012

Explicit construction of Yang-Mills instantons on ALE spaces

Massimo Bianchi
(
- Rome U., Tor Vergata and
- INFN, Rome
)
,
Francesco Fucito
(
- Rome U., Tor Vergata and
- INFN, Rome
)
,
Giancarlo Rossi
(
- Rome U., Tor Vergata and
- INFN, Rome
)
,
Maurizio Martellini
(
- Bohr Inst. and
- INFN, Milan
)

- Nucl.Phys.B 473 (1996) 367-404
•
e-Print:
- hep-th/9601162
•
DOI:
- 10.1016/0550-3213(96)00240-4

Yang-Mills instantons on ALE gravitational instantons

- Math.Ann. 288 (1990) 1, 263-307
•
DOI:
- 10.1007/BF01444534

A Strong coupling test of S duality

- Nucl.Phys.B 431 (1994) 3-77
•
e-Print:
- hep-th/9408074
•
DOI:
- 10.1016/0550-3213(94)90097-3

Instantons on noncommutative R**4 and (2,0) superconformal six-dimensional theory

Nikita Nekrasov
(
- Moscow, ITEP and
- Harvard U.
)
,
Albert S. Schwarz
(
- UC, Davis
)

- Commun.Math.Phys. 198 (1998) 689-703,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 468-483
•
e-Print:
- hep-th/9802068
•
DOI:
- 10.1007/s002200050490

Gravitation, Gauge Theories and Differential Geometry

Tohru Eguchi
(
- SLAC and
- Chicago U., EFI and
- Chicago U.
)
,
Peter B. Gilkey
(
- Princeton U., Math. Dept.
)
,
Andrew J. Hanson
(
- LBL, Berkeley and
- NASA, Ames
)

- Phys.Rept. 66 (1980) 213
•
DOI:
- 10.1016/0370-1573(80)90130-1

Elliptic genera of symmetric products and second quantized strings

Robbert Dijkgraaf
(
- Amsterdam U.
)
,
Gregory W. Moore
(
- Yale U.
)
,
Erik P. Verlinde
(
- CERN and
- Utrecht U.
)
,
Herman L. Verlinde
(
- Amsterdam U.
)

- Commun.Math.Phys. 185 (1997) 197-209
•
e-Print:
- hep-th/9608096
•
DOI:
- 10.1007/s002200050087

Instanton calculus and SUSY gauge theories on ALE manifolds

Diego Bellisai
(
- Rome U., Tor Vergata
)
,
Gabriele Travaglini
(
- Rome U., Tor Vergata and
- INFN, Rome
)

- Phys.Rev.D 58 (1998) 025008
•
e-Print:
- hep-th/9712218
•
DOI:
- 10.1103/PhysRevD.58.025008