superalgebra and (synthetic ) supergeometry
Seiberg-Witten theory studies the moduli space of vacua in N=2 D=4 super Yang-Mills theory, in particular the electric-magnetic duality (Montonen-Olive duality) of the theory.
For more and for general references see at N=2 D=4 super Yang-Mills theory.
The original articles:
Nathan Seiberg, Edward Witten, Monopole condensation, and confinement in supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19-52;
Erratum-ibid. B 430 (1994) 485-486, (arXiv:hep-th/9407087)
Nathan Seiberg, Edward Witten, Monopoles, duality and chiral symmetry breaking in
supersymmetric QCD, Nucl. Phys. B431 (1994) 484-550 [hep-th/9408099]
Review:
Taro Kimura, Seiberg–Witten Geometry, Chapter 4 in: Instanton Counting, Quantum Geometry and Algebra, Mathematical Physics Studies, Springer (2021) [doi:10.1007/978-3-030-76190-5_4]
Jürgen Einhorn, Thomas Friedrich, Seiberg-Witten theory (pdf)
Simon Donaldson, The Seiberg-Witten equations and 4-manifold topology (pdf)
Matilde Marcolli, Seiberg-Witten gauge theory, pdf
piljin yi, Seiberg-Witten theory – with a view toward MQCD (pdf)
Wikipedia, Seiberg-Witten invariants
A useful discussion of the physical origins of the Seiberg-Witten equations for mathematicians:
In relation to integrable systems:
Discussion of lifts of SW-invariants to M-theory:
A lift of Seiberg-Witten invariants to classes in circle group-equivariant stable cohomotopy:
M. Furuta, (2001), Monopole Equation and the 11/8-Conjecture , Mathematical Research Letters 8: 279–291 [doi]
Stefan Bauer, Mikio Furuta, A stable cohomotopy refinement of Seiberg-Witten invariants: I [arXiv:math/0204340]
Stefan Bauer, A stable cohomotopy refinement of Seiberg-Witten invariants: II [arXiv:math/0204267]
See also:
The notion of the Seiberg-Witten curve in Seiberg-Witten theory originates in:
supersymmetric QCD, Nucl. Phys. B431 (1994) 484-550 [hep-th/9408099]
Review:
and in relation to integrable systems:
Observation that under geometric engineering of D=4 N=2 SYM on D4/NS5 intersections and further lift to a single M5-brane, the SW-curve is identified with the M5-worldvolume transverse to the SYM-spacetime:
Albrecht Klemm, Wolfgang Lerche, Peter Mayr, Cumrun Vafa, Nicholas Warner, Self-Dual Strings and Supersymmetric Field Theory, Nucl. Phys. B 477 (1996) 746-766 [arXiv:hep-th/9604034, doi:10.1016/0550-3213(96)00353-7]
Edward Witten, Solutions Of Four-Dimensional Field Theories Via M Theory, Nucl. Phys. B 500 (1997) 3-42 [arXiv:hep-th/9703166, doi:10.1016/S0550-3213(97)00416-1]
Further early discussion:
Karl Landsteiner, Esperanza Lopez, David A. Lowe, =2 Supersymmetric Gauge Theories, Branes and Orientifolds, Nucl. Phys. B 507 (1997) 197-226 [arXiv:hep-th/9705199, doi:10.1016/S0550-3213(97)00559-2]
A. Brandhuber, Jacob Sonnenschein, Stefan Theisen, Shimon Yankielowicz, M Theory And Seiberg-Witten Curves: Orthogonal and Symplectic Groups, Nucl. Phys. B 504 (1997) 175-188 [arXiv:hep-th/9705232, doi:10.1016/S0550-3213(97)00531-2]
Review in:
Csaba Csaki, Joshua Erlich, John Terning, pp. 4 of; Seiberg-Witten Description of the Deconstructed 6D Theory, Phys. Rev. D 67 025019 (2003) [arXiv:hep-th/0208095, doi:10.1103/PhysRevD.67.025019]
Francesco Benini, Sergio Benvenuti, Yuji Tachikawa, p. 2 of: Webs of five-branes and superconformal field theories, JHEP 0909:052 (2009) [arXiv:0906.0359]
Ling Bao, Elli Pomoni, Masato Taki, Futoshi Yagi, p. 5 of: M5-branes, toric diagrams and gauge theory duality, J. High Energ. Phys. 2012 105 (2012) [arXiv:1112.5228, doi:10.1007/JHEP04(2012)105]
Taro Kimura, §4.5.2 in: Seiberg–Witten Geometry, Chapter 4 in: Instanton Counting, Quantum Geometry and Algebra, Mathematical Physics Studies, Springer (2021) [doi:10.1007/978-3-030-76190-5_4]
On the “quantum SW curve”, a kind of quantized SW curve:
In relation to class S-theories and “M3-brane”-defect branes inside M5-branes:
In relation to E-strings and D6-D8-brane bound states:
On why the SW-curve should be quantized this way, as seen from topological string theory:
Mina Aganagic, Robbert Dijkgraaf, Albrecht Klemm, Marcos Mariño, Cumrun Vafa, pp. 7 of: Topological Strings and Integrable Hierarchies, Commun. Math. Phys. 261 (2006) 451-516 [arXiv:hep-th/0312085, doi:10.1007/s00220-005-1448-9]
Mina Aganagic, Miranda Cheng, Robbert Dijkgraaf, Daniel Krefl, Cumrun Vafa, §2 in: Quantum Geometry of Refined Topological Strings, J. High Energ. Phys. 2012 19 (2012) [arXiv:1105.0630, doi:10.1007/JHEP11(2012)019]
On relation between Rozansky-Witten invariants and Seiberg-Witten invariants of 3-manifolds:
Last revised on July 8, 2024 at 06:29:54. See the history of this page for a list of all contributions to it.