TY - GEN

T1 - On nonabelian theories and abelian differentials

AU - Marshakov, A.

PY - 2009

Y1 - 2009

N2 - I discuss integrable systems and their solutions arising in the context of supersymmetric gauge theories and topological string models. For the simplest cases these are particular singular solutions to the dispersionless KdV and Toda systems, and they produce in most straightforward way the generating functions for the Gromov-Witten classes, including well-known intersection and Hurwitz numbers, in terms of the "mirror" target-space rational complex curve. In order to generalize them to the higher genus curves, corresponding in this context to nonabelian gauge theories via the topological gauge/string duality, one has to solve a similar problem, using the Abelian differentials, generally with extra singularities at the branching points.

AB - I discuss integrable systems and their solutions arising in the context of supersymmetric gauge theories and topological string models. For the simplest cases these are particular singular solutions to the dispersionless KdV and Toda systems, and they produce in most straightforward way the generating functions for the Gromov-Witten classes, including well-known intersection and Hurwitz numbers, in terms of the "mirror" target-space rational complex curve. In order to generalize them to the higher genus curves, corresponding in this context to nonabelian gauge theories via the topological gauge/string duality, one has to solve a similar problem, using the Abelian differentials, generally with extra singularities at the branching points.

UR - http://www.scopus.com/inward/record.url?scp=84883635677&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-00873-3_12

DO - 10.1007/978-3-642-00873-3_12

M3 - Conference contribution

AN - SCOPUS:84883635677

SN - 9783642008726

T3 - Differential Equations: Geometry, Symmetries and Integrability - The Abel Symposium 2008, Proceedings of the 5th Abel Symposium

SP - 257

EP - 274

BT - Differential Equations

T2 - 5th Abel Symposium 2008 - Differential Equations: Geometry, Symmetries and Integrability

Y2 - 17 June 2008 through 22 June 2008

ER -