Scaling law for membrane lifetime

TL;DR

This paper investigates the lifetime of membranes in a matrix model, revealing scaling laws with respect to energy, coupling, and cut-off, supported by numerical evaluation of scaling exponents.

Contribution

It introduces a reduced model to compute membrane lifetimes and identifies specific scaling laws and exponents, advancing understanding of membrane stability in matrix models.

Findings

Membrane lifetime scales with energy, coupling, and cut-off.

Numerical evaluation of scaling exponents shows they are not fixed by dimensional analysis.

Results have potential applications in understanding membrane decay processes.

Abstract

Membrane configurations in the Banks-Fischler-Shenker-Susskind matrix model are unstable due to the existence of flat directions in the potential and the decay process can be seen as a realization of chaotic scattering. In this note, we compute the lifetime of a membrane in a reduced model. The resulting lifetime exhibits scaling laws with respect to energy, coupling constant and a cut-off scale. We numerically evaluate the scaling exponents, which cannot be fixed by the dimensional analysis. Finally, some applications of the results are discussed.