SL(2, R) Chern-Simons, Liouville, and gauge theory on duality walls

Yuji Terashima, Masahito Yamazaki

Research output: Contribution to journalReview articlepeer-review

137 Citations (Scopus)


We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d SL(2,R) Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d N = 2 supercon- formal field theory on S3, which is realized as a duality domain wall in a 4d gauge theory on S 4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmüller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals.

Original languageEnglish
Article number135
JournalJournal of High Energy Physics
Issue number8
Publication statusPublished - 2011


  • Chern-Theories
  • Field Theories in Lower Dimensions
  • Matrix Models
  • Supersymmetry and Duality


Dive into the research topics of 'SL(2, R) Chern-Simons, Liouville, and gauge theory on duality walls'. Together they form a unique fingerprint.

Cite this