Abstract
Recently, [JHEP 12 131 (2020)] obtained (a similar, scaled version of) the (a, b)-phase diagram derived from the Kazakov-Zinn-Justin solution of the Hermitian two-matrix model with interactions
starting from Functional Renormalization. We comment on something unexpected: the phase diagram of [JHEP 12 131 (2020)] is based on a βb-function that does not have the one-loop structure of the Wetterich-Morris equation. This raises the question of how to reproduce the phase diagram from a set of β-functions that is, in its totality, consistent with Functional Renormalization. A non-minimalist, yet simple truncation that could lead to the phase diagram is provided. Additionally, we identify the ensemble for which the result of op. cit. would be entirely correct.
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Perez-Sanchez, C.I. Comment on “The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization”. J. High Energ. Phys. 2021, 42 (2021). https://doi.org/10.1007/JHEP07(2021)042
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DOI: https://doi.org/10.1007/JHEP07(2021)042