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 Ω-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.
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ArXiv ePrint: 1911.01334
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Alekseev, S., Gorsky, A. & Litvinov, M. Toward the pole. J. High Energ. Phys. 2020, 157 (2020). https://doi.org/10.1007/JHEP03(2020)157
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DOI: https://doi.org/10.1007/JHEP03(2020)157