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DanieleGregori`ArXivExplore`
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To analyse pure ${\cal N}=2$ $SU(2)$ gauge theory in the Nekrasov-Shatashvili(NS) limit (or deformed Seiberg-Witten (SW)), we use the Ordinary DifferentialEquation/Integrable Model (ODE/IM) correspondence, and in particular its(broken) discrete symmetry in its extended version with {\it two} singularirregular points. Actually, this symmetry appears to be 'manifestation' of thespontaneously broken $\mathbb{Z}_2$ R-symmetry of the original gauge problemand the two deformed SW cycles are simply connected to the Baxter's $T$ and $Q$functions, respectively, of the Liouville conformal field theory at theself-dual point. The liaison is realised via a second order differentialoperator which is essentially the 'quantum' version of the square of the SWdifferential. Moreover, the constraints imposed by the broken $\mathbb{Z}_2$R-symmetry acting on the moduli space (Bilal-Ferrari equations) seem to havetheir quantum counterpart in the $TQ$ and the $T$ periodicity relations, andintegrability yields also a useful Thermodynamic Bethe Ansatz (TBA) for thecycles ($Y(\theta,\pm u)$ or their square roots, $Q(\theta,\pm u)$). A latere,two efficient asymptotic expansion techniques are presented. Clearly, the wholeconstruction is extendable to gauge theories with matter and/or higher rankgroups.
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hep-th/9108028 These lectures consisted of an elementary introduction to conform…Moody algebras and coset constructions 10. Advanced applications,105409,1
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