Abstract
We analyze \( \mathcal{N} = 1 \) theories on S 5 and S 4 × S 1, showing how their partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. We demonstrate that, when the 5d mass parameters are analytically continued to suitable values, the S 5 and S 4 × S 1 partition functions degenerate to those for S 3 and S 2 × S 1. We explain this mechanism via the recently proposed correspondence between 5d partition functions and correlators with underlying q-Virasoro symmetry. From the q-Virasoro 3-point functions, we axiomatically derive a set of associated reflection coefficients, and show that they can be geometrically interpreted in terms of Harish-Chandra c-functions for quantum symmetric spaces. We link these particular c-functions to the types appearing in the Jost functions encoding the asymptotics of the scattering in integrable spin-chains, obtained taking different limits of the XYZ model to XXZ-type.
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ArXiv ePrint: 1312.1294v2
Unité Mixte du CNRS et de l’Ecole Normale Supérieure associée à l’Université Pierre et Marie Curie 6, UMR 8549.
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Nieri, F., Pasquetti, S., Passerini, F. et al. 5D partition functions, q-Virasoro systems and integrable spin-chains. J. High Energ. Phys. 2014, 40 (2014). https://doi.org/10.1007/JHEP12(2014)040
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DOI: https://doi.org/10.1007/JHEP12(2014)040