Revisited functional renormalization group approach for random matrices in the large-$N$ limit

Abstract

The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this paper, we focus on matrix models and address the question of the compatibility between the approximations used to solve the exact renormalization group equation and the modified Ward identities coming from the regulator. We show in particular that standard local potential approximation strongly violates the Ward identities, especially in the vicinity of the interacting fixed point. Extending the theory space including derivative couplings, we recover an interacting fixed point with a critical exponent not so far from the exact result, but with a nonzero value for derivative couplings, evoking a strong dependence concerning the regulator. Finally, we consider a modified regulator, allowing to keep the flow not so far from the ultralocal region and recover the results of the literature up to a slight improvement.

21 pages 9 figures. Minor modification: we changed figure 4 and remark 1

References in corpus (10)

• Exact evolution equation for the effective potential
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• Duality and KPZ in Liouville Quantum Gravity
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Phases Of Melonic Quantum Mechanics
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• Phase Transition in Tensor Models
• Pedagogical comments about nonperturbative Ward-constrained melonic renormalization group flow
• Random vector and matrix and vector theories: a renormalization group approach
• Notes on Tensor Models and Tensor Field Theories

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