11 April 2016 to 15 July 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].

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