Developing local RG: quantum RG and BFSS

TL;DR

This paper explores various renormalization group methods applied to the BFSS model, including standard and local RG, to investigate their potential role in gauge/gravity duality and quantum field theory in curved spacetime.

Contribution

It develops a local RG scheme with spacetime-dependent cutoff and tests the quantum RG approach as a mechanism for gauge/gravity duality in the BFSS model.

Findings

Standard Wilsonian RG preserves supersymmetry under certain conditions.

Local RG with spacetime-dependent cutoff offers new insights for QFT in curved spacetime.

Quantum RG raises questions about its applicability to AdS/CFT correspondence.

Abstract

In this paper we study various forms of RG, applying them to the BFSS model of $N$ coincident D0-branes. Firstly, as a warm-up, we perform standard Wilsonian RG, investigating the conditions under which supersymmetry is preserved along the flow. Next, we develop a local RG scheme such that the cutoff is spacetime dependent, which could have further applications to studying QFT in curved spacetime. Finally, we test the conjecture put forward in arXiv:1305.3908 that the method of quantum RG could be the mechanism responsible for the gauge/gravity duality by applying it to the BFSS model, which has a known gravitational dual. Although not entirely conclusive some questions are raised about the applicability of quantum RG as a description of the AdS/CFT correspondence.