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

Vincent Lahoche (1) , Dine Ousmane Samary (2)

1 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies
2 CEA - Commissariat à l'énergie atomique et aux énergies alternatives

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.

Mots clés: 71.70.Ej; 02.40.Gh; 03.65.-w; Matrix models; tensor models; quantum gravity; random geometry; String theory; gauge/gravity duality; coupling: derivative; renormalization group: nonperturbative; Ward identity: violation; potential: approximation; matrix model: random; potential: local; model: tensor; fixed point; critical phenomena; scaling; expansion 1/N; flow

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Vincent Lahoche, Dine Ousmane Samary. Revisited functional renormalization group approach for random matrices in the large-$N$ limit. Phys.Rev.D, 2020, 101 (10), pp.106015. ⟨10.1103/PhysRevD.101.106015⟩. ⟨hal-02317306⟩