Space-time foam from noncommutative instantons

Braden, Harry W.; Nekrasov, Nikita A.

doi:10.1007/s00220-004-1127-2

Space-time foam from noncommutative instantons

Harry W. Braden
(
- Edinburgh U. and
- Moscow, ITEP
)
,
Nikita A. Nekrasov
(
- Princeton U. and
- Moscow, ITEP
)

Dec, 1999

22 pages

Published in:

Commun.Math.Phys. 249 (2004) 431-448

e-Print:

hep-th/9912019 [hep-th]

DOI:

10.1007/s00220-004-1127-2

Report number:

PUPT-1900,
ITEP-TH-51-99,
NSF-ITP-99-144

View in:

pdf

reference search54 citations

Citations per year

Abstract:

We show that a U(1) instanton on non-commutative R^4 corresponds to a supersymmetric non-singular U(1) gauge field on a commutative Kahler manifold X which is a blowup of C^2 at a finite number of points. For instanton charge k the manifold X can be viewed as a space-time foam. A direct connection with integrable systems of Calogero-Moser type is established. We also make some comments on the non-abelian case.

Note:

harvmac, 22 pp; v.2, refs added, a section added Report-no: PUPT-1900, ITEP-TH-51/99, NSF-ITP-99-144

space-time: foam
instanton: U(1)
field equations: deformation
field theory: Kaehler
analytic properties

References(24)

Figures(0)

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

- Invent.Math. 133 1

Integrability and Seiberg-Witten exact solution

- Phys.Lett.B 355 (1995) 466-474
•
e-Print:
- hep-th/9505035
•
DOI:
- 10.1016/0370-2693(95)00723-X

Integrable systems and supersymmetric gauge theory

Emil J. Martinec
(
- Chicago U., EFI and
- Chicago U.
)
,
Nicholas P. Warner
(
- Southern California U.
)

- Nucl.Phys.B 459 (1996) 97-112
•
e-Print:
- hep-th/9509161
•
DOI:
- 10.1016/0550-3213(95)00588-9

Supersymmetric Yang-Mills theory and integrable systems

- Nucl.Phys.B 460 (1996) 299-334
•
e-Print:
- hep-th/9510101
•
DOI:
- 10.1016/0550-3213(95)00609-5

Multiscale N=2 SUSY field theories, integrable systems and their stringy / brane origin. 1.

- Nucl.Phys.B 517 (1998) 409-461
•
e-Print:
- hep-th/9707120
•
DOI:
- 10.1016/S0550-3213(98)00055-8

The Ruijsenaars-Schneider model in the context of Seiberg-Witten theory

H.W. Braden
(
- Edinburgh U.
)
,
A. Marshakov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)

- Nucl.Phys.B 558 (1999) 371-390
•
e-Print:
- hep-th/9902205
•
DOI:
- 10.1016/S0550-3213(99)00414-9

Hilbert schemes, separated variables, and D-branes

A. Gorsky
(
- Moscow, ITEP and
- Mittag-Leffler Inst.
)
,
N. Nekrasov
(
- Moscow, ITEP and
- Harvard U. and
- Mittag-Leffler Inst.
)
,
V. Rubtsov
(
- Moscow, ITEP and
- Angers U. and
- Mittag-Leffler Inst.
)

- Commun.Math.Phys. 222 (2001) 299-318
•
e-Print:
- hep-th/9901089
•
DOI:
- 10.1007/s002200100503

Matrix description of interacting theories in six-dimensions

Ofer Aharony
(
- Rutgers U., Piscataway
)
,
M. Berkooz
(
- Rutgers U., Piscataway
)
,
S. Kachru
(
- UC, Berkeley
)
,
N. Seiberg
(
- Princeton, Inst. Advanced Study
)
,
Eva Silverstein
(
- Rutgers U., Piscataway
)

- Adv.Theor.Math.Phys. 1 (1998) 148-157
•
e-Print:
- hep-th/9707079
•
DOI:
- 10.4310/ATMP.1997.v1.n1.a5

Light cone description of (2,0) superconformal theories in six-dimensions

- Adv.Theor.Math.Phys. 2 (1998) 119-153
•
e-Print:
- hep-th/9712117
•
DOI:
- 10.4310/ATMP.1998.v2.n1.a5

String theory and noncommutative geometry

- JHEP 09 (1999) 032,
- In *Li, M. (ed.) et al.: Physics in non-commutative world* 327-401
•
e-Print:
- hep-th/9908142
•
DOI:
- 10.1088/1126-6708/1999/09/032