Seiberg-Witten theory and random partitions. (English) Zbl 1233.14029
Etingof, Pavel (ed.) et al., The unity of mathematics. In honor of the ninetieth birthday of I. M. Gelfand. Papers from the conference held in Cambridge, MA, USA, August 31–September 4, 2003. Boston, MA: Birkhäuser (ISBN 0-8176-4076-2/hbk). Progress in Mathematics 244, 525-596 (2006).
The authors study \(\mathcal{N}=2\) supersymmetric four dimensional gauge theories in \(\Omega-\) background. They provide various representations for the partition function. By the help of these representations, the authors derive Seiberg-Witten geometry, the curves, the differentials and the prepotential.
The paper contains the study of pure \(\mathcal{N}=2\) theory as well as the theory with matter hypermultiplets in the fundamental or adjoint representations, and the five dimensional theory compactified on a circle.
For the entire collection see [Zbl 1083.00015].
The paper contains the study of pure \(\mathcal{N}=2\) theory as well as the theory with matter hypermultiplets in the fundamental or adjoint representations, and the five dimensional theory compactified on a circle.
For the entire collection see [Zbl 1083.00015].
Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale)
MSC:
| 14J81 | Relationships between surfaces, higher-dimensional varieties, and physics |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 05E10 | Combinatorial aspects of representation theory |
| 11Z05 | Miscellaneous applications of number theory |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 60C05 | Combinatorial probability |
| 81T45 | Topological field theories in quantum mechanics |
