Note
Seules les adresses mails institutionnelles sont acceptées lors de la création d'un compte. La création de compte est modérée, merci d'attendre leur validation. Only institutional email addresses will be accepted when asking for an account. Account creation is moderated, please wait until then.
de 11 avril 2016 à 15 juillet 2016
Institut Henri Poincaré
Europe/Paris timezone

Pestun

Vasily Pestun, IHES

Localization in gauge theory

1.    Equivariant cohomology. Atiyah-Bott localization formula theorem.
2.    Supersymmetric, cohomological and topological field theories.
3.    Gauge theory partition function on a sphere.

References:

[1] H. Cartan, “Notions d’alg`ebre diff ́erentielle; application aux
groupes de Lie et aux vari ́et ́es ou` op`ere un groupe de Lie,”
Colloque de topologie (espaces fibr ́es), Bruxelles, 1950 (1951)
15–27.

[2] H. Cartan, “La transgression dans un groupe de Lie et dans un
espace fibr ́e principal,” Colloque de topologie (espaces fibr ́es),
Bruxelles, 1950 (1951) 57–71.

[3] V. W. Guillemin and S. Sternberg, Supersymmetry and equivariant de
Rham theory. Mathematics Past and Present. Springer-Verlag, Berlin,
1999. http://dx.doi.org/10.1007/978-3-662-03992-2. With an appendix
containing two reprints by Henri Cartan [ MR0042426 (13,107e);
MR0042427 (13,107f)].

[4] N. Berline, E. Getzler, and M. Vergne, Heat kernels and Dirac
operators. Grundlehren Text Editions. Springer-Verlag, Berlin, 2004.
Corrected reprint of the 1992 original.

[5] R. J. Szabo, “Equivariant localization of path integrals,”
arXiv:hep-th/9608068 [hep-th].

[6] S. Cordes, G. W. Moore, and S. Ramgoolam, “Large N 2-D Yang-Mills
theory and topological string theory,” Commun. Math. Phys. 185 (1997) 543–619, hep-th/9402107.

[7] M. Vergne, “Applications of Equivariant Cohomology,” math/0607389.

[8] J. Milnor, “Construction of universal bundles. I,” Ann. of Math.
(2) 63 (1956) 272–284.

[9] J. Milnor, “Construction of universal bundles. II,” Ann. of Math.
(2) 63 (1956) 430–436.

[10] H. Kanno, “Weyl Algebra Structure and Geometrical Meaning of BRST
Transformation in Topological Quantum Field Theory,” Z. Phys. C43
(1989) 477.

[11] J. M. F. Labastida and M. Pernici, “A Gauge Invariant Action in
Topological Quantum Field Theory,” Phys. Lett. B212 (1988) 56.

[12] R. Bott and L. W. Tu, Equivariant characteristic classes in the
Cartan model. World Sci. Publ., River Edge, NJ, 2001.

[13] N. Berline and M. Vergne, “The equivariant Chern character and
index of G-invariant operators. Lectures at CIME, Venise 1992,”.

[14] R. Bott and L. W. Tu, Differential forms in algebraic topology,
vol. 82 of Graduate Texts in Mathematics. Springer-Verlag, New
York-Berlin, 1982.

[15] V. Mathai and D. Quillen, “Superconnections, Thom classes, and
equivariant differential forms,” Topology 25 (1986) no. 1, 85–110.
http://dx.doi.org/10.1016/0040-9383(86)90007-8.

[16] M. F. Atiyah and L. Jeffrey, “Topological Lagrangians and
cohomology,” J. Geom. Phys. 7 (1990) no. 1, 119–136.

[17] S. Wu, “Mathai-Quillen formalism,” arXiv:hep-th/0505003 [hep-th].

[18] M. F. Atiyah and R. Bott, “The moment map and equivariant
cohomology,” Topology 23 (1984) no. 1,1–28.

[19] A. A. Kirillov, Lectures on the orbit method, vol. 64 of Graduate
Studies in Mathematics. American Mathematical Society, Providence, RI, 2004. http://dx.doi.org/10.1090/gsm/064.

[20] B. Kostant, “Quantization and unitary representations. I.
Prequantization,”.

[21] A. A. Kirillov, “Merits and demerits of the orbit method,” Bull.
Amer. Math. Soc. (N.S.) 36 (1999) no. 4, 433–488. http://dx.doi.org/10.1090/S0273-0979-99-00849-6.

[22] A. Alekseev and S. L. Shatashvili, “Path Integral Quantization of
the Coadjoint Orbits of the Virasoro Group and 2D Gravity,” Nucl. Phys. B323 (1989) 719.

[23] M. F. Atiyah, Elliptic operators and compact groups.
Springer-Verlag, Berlin, 1974. Lecture Notes in Mathematics, Vol. 401.

[24] E. Witten, “Introduction to cohomological field theories,”
Int.J.Mod.Phys. A6 (1991) 2775–2792.

[25] E. Witten, “Topological Quantum Field Theory,” Commun.Math.Phys.
117 (1988) 353.

[26] N. A. Nekrasov, “Seiberg-Witten prepotential from instanton
counting,” Adv.Theor.Math.Phys. 7

(2004) 831–864, arXiv:hep-th/0206161 [hep-th]. To Arkady Vainshtein on
his 60th anniversary.

[27] V. Pestun, “Localization of gauge theory on a four-sphere and
supersymmetric Wilson loops,” Commun.Math.Phys. 313 (2012) 71–129, arXiv:0712.2824 [hep-th].

Your browser is out of date!

Update your browser to view this website correctly. Update my browser now

×