On three dimensional quiver gauge theories and integrability
Abstract
In this work we compare different descriptions of the space of vacua of certain three dimensional {N}=4 superconformal field theories, compactified on a circle and massdeformed to {N}=2 in a canonical way. The original {N}=4 theories are known to admit two distinct mirror descriptions as linear quiver gauge theories, and many more descriptions which involve the compactification on a segment of fourdimensional {N}=4 super YangMills theory. Each description gives a distinct presentation of the moduli space of vacua. Our main result is to establish the precise dictionary between these presentations. We also study the relationship between this gauge theory problem and integrable systems. The space of vacua in the linear quiver gauge theory description is related by NekrasovShatashvili duality to the eigenvalues of quantum integrable spin chain Hamiltonians. The space of vacua in the fourdimensional gauge theory description is related to the solution of certain integrable classical manybody problems. Thus we obtain numerous dualities between these integrable models.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2013
 DOI:
 10.1007/JHEP05(2013)126
 arXiv:
 arXiv:1304.0779
 Bibcode:
 2013JHEP...05..126G
 Keywords:

 Supersymmetry and Duality;
 Brane Dynamics in Gauge Theories;
 Supersymmetric gauge theory;
 String Duality;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 58 pages, 13 figures, references added