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We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter $\gamma$.
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C. Meusburger and B. Schroers, The Quantization of Poisson structures arising in Chern-Simons theory with gauge group G × g ∗ G\times g^{*} , Adv. Theor. Math. Phys. 7
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Y. Neiman, “The imaginary part of the gravity action and black hole entropy”, JHEP 04
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