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On Three Dimensional Quiver Gauge Theories and Integrability
"... 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 q ..."
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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 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. ar X iv
Irregular singularities in Liouville theory and ArgyresDouglas type gauge theories
 I, JHEP 1212 (2012) 050, [arXiv:1203.1052]. – 31
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Wild quiver gauge theories
 JHEP 1202:031 (2012) arXiv:1112.1691 [hepth
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Threeparticle Integrable Systems with Elliptic Dependence on Momenta and Theta Function Identities
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The master Toperator for inhomogeneous XXX spin chain and mKP
 hierarchy SIGMA 10 (2014) 006
"... we show how to construct the master Toperator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspon ..."
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we show how to construct the master Toperator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also characterize the class of solutions to the mKP hierarchy that correspond to eigenvalues of the master Toperator and study dynamics of their zeros as functions of the spectral parameter. This implies a remarkable connection between the quantum spin chain and the classical Ruijsenaars–Schneider system of particles. Key words: quantum integrable spin chains; classical manybody systems; quantumclassical correspondence; master Toperator; taufunction 2010 Mathematics Subject Classification: 37K10; 81Q80; 05E05