Comment on "The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization"

Abstract

Recently, [JHEP 20 131 (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 \[\mathrm{Tr\,}\Big\{\frac{a}{4} (A^4+B^4)+\frac{b}{2} ABAB\Big\}\,,\] starting from Functional Renormalization. We comment on something unexpected: the phase diagram of [JHEP 20 131 (2020)] is based on a ${\beta }_b$-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 $\beta$-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.

10 pages, several ribbon graphs v3: a user's guide to ribbon graphs added. Conform with the published JHEP-version (v2: minor correction)

References in corpus (2)

• Exact evolution equation for the effective potential
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization

Cited by in corpus (2)

• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions