Spring 2015 GRASP Seminar, focusing on Class S theories, spectral networks, & related topics

As usual GRASP Seminar meets Fridays 3-4. This semester GRASP is in 939 Evans.

Topics to be covered

The goals of this semester are twofold: the first is to understand the integrable system associated to an N=2 supersymmetric field theory. This integrable system was first described and used in [SW], where the authors were able to derive an exact formula for the metric on the moduli space of vacua in N=2 SUSY gauge theory with G=SU(2). The first few weeks of the semester will be spent on understanding the procedure which associates an integrable system to a field theory and on understanding the mathematical structure of this integrable system.

One interesting class of N=2 theories are the Class S theories, whose associated integrable systems are Hitchin systems. (The G=SU(2) super Yang-Mills theory mentioned above is a special case.) To help compute the BPS states in these theories, Gaiotto, Moore, and Neitzke introduced in [GMN] the notion of a spectral network. The second major goal of this seminar is to understand the definition of a spectral network, how it is used in class S theories, and how it relates to other mathematical structures of interest.


19 February: Introduction and organizational meeting (Ben G.)
26 February QFT Basics (Ryan T.) ["Recommended reading:" 1 2 3 4 5 6 7]
4 March: Integrable systems from Seiberg-Witten theory [W][SW] (Alex T.)
11 March: Integrable systems from Seiberg-Witten theory, Part II [W][SW] (Alex T.)
16 March: Integrable systems from Seiberg-Witten theory, Part III [W][SW] (Alex T.)
18 March: Singular integrable systems and monodromy [N][D] (Gus S.)
25 March (No meeting: Mirror symmetry conference)
1 April (No meeting: Cluster algebras conference)
8 April: BPS states in Class S theories [N2][GMN2][N] (Ben G.)
15 April: Spectral Networks [GMN] (Ammar H.)


[D] R. Donagi, Seiberg-Witten Integrable Systems
[GMN] D. Gaiotto, G. Moore, A. Neitzke, Spectral Networks
[GMN2] ibid., Wall-crossing, Hitchin Systems, and the WKB Approximation
[H] N. Hitchin, Stable Bundles and Integrable Systems
[KS] M. Kontsevich and Y. Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
[N] A. Neitzke, Hitchin systems in N=2 field theory
[N2] A. Neitzke, What is a BPS state?
[SW] N. Seiberg, E. Witten, Monopole Condensation, and Confinement in N = 2 Supersymmetric Yang-Mills Theory
[STWZ] V. Shende, D. Treumann, H. Williams, and E. Zaslow, Cluster varieties from Legendrian knots
[W] Witten, Dynamics of Quantum FIeld Theory (lectures from IAS QFT, vol. 2)