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Hitchin Systems, Nonabelian Hodge and Wall Crossing

This is a webpage for the ZMP Seminar (Summer’ 17) on Hitchin Systems, Non Abelian Hodge and Wall Crossing

The Seminar is divided into two halves. The first half (13 April–11 May) will be an introduction to various mathematical foundations regarding Hitchin Systems. In the second half (1 June–6 July), we will study the problem of Wall crossing in four dimensional N=2 theories. The solution to this problem in specific theories turns out to intimately involve the Hitchin System. Some of the foundational material that is discussed in the first half will be useful for the second half.

References

This is a collection of some basic references for the seminar.

First half (13 April – 11 May)

Introductory Lectures/Notes

  1. What is a Higgs Bundle? (PDF) (AMS Notices) Bradlow, Garcia-Prada, Gothen.
  2. Moduli of Higgs Bundles, A. Neitzke’s notes
  3. JT's notes
  4. Higgs bundles and local systems on Riemann surfaces, R. Wentworth

Papers

  1. Hyperkahler Metrics and Supersymmetry, Hitchin-Karlhede-Lindstrom-Rocek
  2. Hitchin’s Papers:
    1. Self-duality equations on a Riemann Surface
    2. Stable bundles and Integrable Systems
    3. Bourbaki Talk : Hyperkahler Manifolds (PDF)
  3. Opers vs Non-Abelian Hodge, Dumitrescu et al
  4. Non-abelian Hodge Theory, C. Simpson
  5. Higgs Bundles and Local Systems, C. Simpson
  6. Non-abelian Hodge Theory, K. Corlette
  7. Four-dimensional wall-crossing via three-dimensional field theory, Gaiotto-Moore-Neitzke

Second half (1 June–6 July)

Introductory Lectures/Notes

  1. N=2 Supersymmetric dynamics for pedestrians, Y. Tachikawa
  2. Introduction to Seiberg-Witten Integrable Systems, R. Donagi
  3. Hitchin Systems in N=2 Field Theory, A. Neitzke

Papers

Apart from the GMN paper (above), we will also use:

  1. Seiberg-Witten’s papers:
    1. Electric Magnetic Duality, Monopole Condensation and confinement in N=2 SYM
    2. Monopoles, Duality and chiral symmetry breaking in N=2 SQCD
    3. Gauge dynamics and compactification to three dimensions
  2. Special Kahler Manifolds, D. Freed
  3. Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, M. Kontsevich and Y. Soibelman
  4. More On Gauge Theory and Geometric Langlands, E. Witten

Coordination

Murad Alim

A. Balasubramanian

Dr. Florian Beck

Adrien Brochier

Jörg Teschner