Toward the Pole

Abstract

We study the analytic structure of semiclassical conformal blocks, namely of the 1-point conformal block on the torus and of the 4-point conformal block on the sphere, as functions of the intermediate dimension. We interpret their discontinuities, which can be revealed with the use of a particular resummation procedure, holographically in terms of configurations of geodesics in AdS3. In other words, we study the behavior of the $\Omega$-deformed $\mathcal{N}=2$ SYM theory in the Nekrasov-Shatashvili limit near those singular points, where naively the W-boson with non-vanishing angular momentum becomes massless. Upon a proper resummation of instanton contributions, these singularities disappear, which is similar to the Seiberg-Witten solution in the undeformed case where there is no massless W-boson. It is shown that the order parameter undergoes a non-analytic behavior near positions of the poles. The jump of the order parameter is interpreted holographically in terms of geodesic networks

arXiv comment29 pages, 7 figures

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Cited by in corpus (8)

• Holographic thermal correlators from supersymmetric instantons
• Black hole perturbation theory and multiple polylogarithms
• A slow review of the AGT correspondence
• More on Wilson toroidal networks and torus blocks
• Recursion relation for instanton counting for $SU(2)$ $\mathcal{N}=2$ SYM in NS limit of $\Omega$ background
• Semiclassical torus blocks in the t-channel
• Absorption cross section in gravity's rainbow from confluent Heun equation
• Characters, Coadjoint Orbits and Duistermaat-Heckman Integrals