Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 5, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP05(2013)126
Keywords
Supersymmetry and Duality; Brane Dynamics in Gauge Theories; Supersymmetric gauge theory; String Duality
Categories
Funding
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Economic Development and Innovation
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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 mass-deformed 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 four-dimensional N = 4 super Yang-Mills 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 Nekrasov-Shatashvili duality to the eigenvalues of quantum integrable spin chain Hamiltonians. The space of vacua in the four-dimensional gauge theory description is related to the solution of certain integrable classical many-body problems. Thus we obtain numerous dualities between these integrable models.
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