Geodesic
Angular momentum and gravimagnetization of the $\mathcal{N}{=}2$ supersymmetric vacuum
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 2, pp. 225-240 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the gravimagnetization of the $\mathcal N=2$ supersymmetric vacuum in the presence of the $\Omega$-deformation. We argue that the Seiberg–Witten prepotential is related to the vacuum density of the angular momentum in the Euclidean space $\mathbb R^4$. We conjecture the possible role of the dyonic instantons as the microscopic angular momentum carriers that could yield a spontaneous vacuum gravimagnetization. We interpret the dyonic instanton as an analogue of the Euclidean bounce in $\mathbb R^4$. Such a bounce is related to the Schwinger pair production. We also briefly discuss the induced angular momentum in $\mathbb R^4$ in the dual Liouville formulation of the $SU(2)$ theory in terms of the hypothesis of the Alday–Gaiotto–Tachikawa correspondence.
Keywords: supersymmetry, gauge theory, instanton. 
@article{TMF_2012_171_2_a3,
     author = {A. S. Gorsky},
     title = {Angular momentum and gravimagnetization of the~$\mathcal{N}{=}2$ supersymmetric vacuum},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {225--240},
     year = {2012},
     volume = {171},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_2_a3/}
}
TY  - JOUR
AU  - A. S. Gorsky
TI  - Angular momentum and gravimagnetization of the $\mathcal{N}{=}2$ supersymmetric vacuum
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2012
SP  - 225
EP  - 240
VL  - 171
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2012_171_2_a3/
LA  - ru
ID  - TMF_2012_171_2_a3
ER  - 
%0 Journal Article
%A A. S. Gorsky
%T Angular momentum and gravimagnetization of the $\mathcal{N}{=}2$ supersymmetric vacuum
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2012
%P 225-240
%V 171
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2012_171_2_a3/
%G ru
%F TMF_2012_171_2_a3
A. S. Gorsky. Angular momentum and gravimagnetization of the $\mathcal{N}{=}2$ supersymmetric vacuum. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 2, pp. 225-240. http://geodesic.mathdoc.fr/item/TMF_2012_171_2_a3/

[1] N. A. Nekrasov, Adv. Theor. Math. Phys., 7:5 (2004), 831–864, arXiv: hep-th/0206161 | DOI | MR

[2] B. Collie, D. Tong, JHEP, 08 (2009), 006, 26 pp., arXiv: 0905.2267 | DOI | MR

[3] N. Seiberg, E. Witten, Nucl. Phys. B, 426:1 (1994), 19–52 | DOI | MR | Zbl

[4] A. E. Lawrence, N. Nekrasov, Nucl. Phys. B, 513:1–2 (1998), 239–265, arXiv: hep-th/9706025 | DOI | MR | Zbl

[5] N. D. Lambert, D. Tong, Phys. Lett. B, 462:1–2 (1999), 89–04, arXiv: hep-th/9907014 | DOI

[6] D. Mateos, P. K. Townsend, Phys. Rev. Lett., 87:1 (2001), 011602, 4 pp., arXiv: ; E. Eyras, P. K. Townsend, M. Zamaklar, JHEP, 05 (2001), 046, 19 pp., arXiv: ; D. Mateos, S. Ng, P. K. Townsend, JHEP, 03 (2002), 016, 27 pp., arXiv: ; P. K. Townsend, Ann. Henri Poincaré, 4:Suppl. 1 (2003), S183–S195, arXiv: hep-th/0103030hep-th/0012016hep-th/0112054hep-th/0211008 | DOI | MR | DOI | MR | DOI | MR | MR | Zbl

[7] D. S. Bak, K. M. Lee, Phys. Lett. B, 544:3–4 (2002), 329–336, arXiv: ; H. Y. Chen, M. Eto, K. Hashimoto, JHEP, 01 (2007), 017, 26 pp., arXiv: hep-th/0206185hep-th/0609142 | DOI | MR | Zbl | DOI | MR

[8] R. Emparan, D. Mateos, P. K. Townsend, JHEP, 07 (2001), 011, 24 pp., arXiv: hep-th/0106012 | DOI | MR

[9] L. F. Alday, D. Gaiotto, Y. Tachikawa, Lett. Math. Phys., 91:2 (2010), 167–197, arXiv: 0906.3219 | DOI | MR | Zbl

[10] N. Nekrasov, E. Witten, JHEP, 09 (2010), 092, 82 pp., arXiv: 1002.0888 | DOI | MR

[11] R. Gopakumar, C. Vafa, M-theory and topological strings. I, arXiv: hep-th/9809187

[12] I. K. Affleck, O. Alvarez, N. S. Manton, Nucl. Phys. B, 197:3 (1982), 509–519 | DOI | MR

[13] A. S. Gorsky, K. A. Saraikin, K. G. Selivanov, Nucl. Phys. B, 628:1–2 (2002), 270–294 ; arXiv: hep-th/0110178 | DOI | MR | Zbl

[14] H. Ooguri, C. Vafa, E. Verlinde, Lett. Math. Phys., 74:3 (2005), 311–342, arXiv: hep-th/0502211 | DOI | MR | Zbl

[15] A. Gorsky, A. Marshakov, A. Mironov, A. Morozov, Nucl. Phys. B, 527:3 (1998), 690–716, arXiv: hep-th/9802007 | DOI | MR | Zbl

[16] A. Losev, N. Nekrasov, S. L. Shatashvili, Nucl. Phys. B, 534:3 (1998), 549–611, arXiv: hep-th/9711108 | DOI | MR | Zbl

[17] S. Matsuura, JHEP, 09 (2008), 083, 23 pp., arXiv: 0808.3493 | DOI | MR

[18] N. Drukker, J. Gomis, T. Okuda, J. Teschner, JHEP, 02 (2010), 057, 61 pp., arXiv: 0909.1105 | DOI | MR

[19] L. Cantini, P. Menotti, D. Seminara, Nucl. Phys. B, 638:3 (2002), 351–377, arXiv: hep-th/0203103 | DOI | MR | Zbl

[20] N. A. Nekrasov, S. L. Shatashvili, “Quantization of integrable systems and four dimensional gauge theories”, Proceedings of the XVIth International Congress on Mathematical Physics (Prague, August 3–8, 2009), ed. P. Exner, World Sci. Publ., Hackensack, NJ, 2010, 265–289, arXiv: 0908.4052 | DOI | MR | Zbl

[21] L. F. Alday, D. Gaiotto, S. Gukov, Y. Tachikawa, H. Verlinde, JHEP, 01 (2010), 113, 50 pp., arXiv: 0909.0945 | DOI | MR

[22] A. Zamolodchikov, Internat. J. Modern Phys. A, 19:Suppl. 2 (2004), 510–523, arXiv: hep-th/0312279 | DOI | MR | Zbl

[23] A. Zamolodchikov, Al. Zamolodchikov, Liouville field theory on a pseudosphere, arXiv: hep-th/0101152 | MR

[24] N. Seiberg, D. Shih, Compt. Rend. Phys., 6:2 (2005), 165–174, arXiv: hep-th/0409306 | DOI | MR

[25] A. Gerasimov, D. Lebedev, S. Oblezin, Commun. Number Theory Phys., 5:1 (2011), 135–201, arXiv: 1002.2622 | DOI | MR

[26] R. Gopakumar, Phys. Rev. D, 70:2 (2004), 025009, 15 pp., arXiv: hep-th/0308184 | DOI | MR

[27] A. Gorsky, V. Lysov, Nucl. Phys. B, 718:1–2 (2005), 293–318, arXiv: hep-th/0411063 | DOI | MR | Zbl

[28] A. M. Polyakov, Nucl. Phys. Proc. Suppl., 68:1–3 (1998), 1–8, arXiv: hep-th/9711002 | DOI | MR | Zbl

[29] J. Teschner, “From Liouville theory to the quantum geometry of Riemann surfaces”, Prospects in Mathematical Physics, Contemporary Mathematics, 437, AMS, Providence, RI, 2007, 231–246, arXiv: ; Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I, arXiv: ; R. M. Kashaev, Discrete Liouville equation and Teichüller theory, arXiv: hep-th/03080311005.28460810.4352 | DOI | MR | MR

[30] N. Drukker, B. Fiol, J. Simón, JCAP, 10 (2004), 012, 20 pp., arXiv: hep-th/0309199 | DOI | MR

[31] Y. Hikida, S.-J. Rey, Nucl. Phys. B, 669:1–2 (2003), 57–77, arXiv: hep-th/0306148 | DOI | MR | Zbl

[32] A. Gorsky, Phys. Rev. D, 80:12 (2009), 125002, 18 pp., arXiv: 0905.2058 | DOI | MR