Closed string transport coefficients and the membrane paradigm

TL;DR

This paper explores the correspondence between black hole membrane transport coefficients and highly excited closed string states, revealing similarities in their transport properties except for bulk viscosity, especially when the central charge is 6.

Contribution

It demonstrates a quantitative match between membrane and string transport coefficients at the correspondence point, highlighting the role of the central charge in this equivalence.

Findings

Membrane and string transport coefficients are of the same order.

Dimensionless transport coefficients are exactly equal when the central charge is 6.

Bulk viscosity remains an exception in the correspondence.

Abstract

I discuss a correspondence between a fictitious fluid in the black hole membrane paradigm and highly excited closed string states according to the black hole correspondence principle. I calculate the membrane transport coefficients of an electric NS-NS 2-charged black hole and transport coefficients of the highly excited closed string states which possess a Kaluza-Klein number and a winding number. Comparing both the transport coefficients at the correspondence point, I show that, except for the bulk viscosity, the membrane transport coefficients are of the same order as the transport coefficients of the closed string states on the stretched horizon. Also, I show that, except for the bulk viscosity, both the dimensionless transport coefficients, which are defined by dividing the transport coefficients by the entropy density, are exactly equal if the central charge is 6.