Introduction to Spin Chains and Supersymmetric Gauge Theories – FS 2014

Description

Gauge theories form the basic paradigm of our understanding of the fundamental
interactions. Their supersymmetric versions are well-controlled and a helpful
tool for gaining deeper insights and addressing open questions. Integrable
models, on the other hand, are completely solvable quantum many-body systems
used in condensed matter physics. The spin chain which mimics a one-dimensional
magnet is a prominent example. Despite being very different in nature, there are
deep connections between supersymmetric gauge theories and integrable models.

This advanced course introduces the student to both the areas of
supersymmetric gauge theories and spin chains and outlines their connections,
providing a glimpse into a current and very active research topic.

Prerequisites

Prerequisites are quantum field theory (in particular gauge theory and the
notion of a spinor). Basic knowledge of supersymmetry and group theory are
helpful.

Content

• Overview over the relations between integrable systems and supersymmetric gauge theories.
• Introduction to integrable models, in particular the Heisenberg (XXX) spin chain and the Bethe ansatz (2 lectures).
• Introduction to supersymmetric gauge theories in two and four dimensions (2 lectures).
• Advanced applications, gauge/Bethe correspondence, string theory construction.

Literature

• Supersymmetric gauge theory:
  - Hori et al.: Mirror Symmetry (Ch. 12, 15)
• Spin Chains and Bethe Ansatz:
  - Gaudin: La fonction d'onde de Bethe
  - Bethe: Zur Theorie der Metalle
  - arXiv:cond-mat/9809162
• Relations between the two:
  - arXiv:0901.4744, arXiv:0901.4748
  - arXiv:1005.4445

Credit Requirements

20 minute oral examination

Materials

Lecture Notes

• Lecture Notes (PDF, 220 kB)