Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity

TL;DR

This paper computes the shear viscosity to entropy density ratio in six derivative gravity theories, clarifying how unambiguous bulk coefficients relate to boundary field theory parameters via the AdS/CFT correspondence.

Contribution

It provides a detailed calculation of /s in six derivative gravity, identifying unambiguous coefficients and expressing results in terms of boundary central charges and these coefficients.

Findings

/s depends on unambiguous coefficients and boundary parameters.

Six derivative corrections to central charges a and c are derived.

/s can be expressed in terms of boundary central charges and bulk coefficients.

Abstract

We calculate shear viscosity to entropy density ratio in presence of four derivative (with coefficient $\alpha'$) and six derivative (with coefficient $\alpha'^2$) terms in bulk action. In general, there can be three possible four derivative terms and ten possible six derivative terms in the Lagrangian. Among them two four derivative and eight six derivative terms are ambiguous, i.e., these terms can be removed from the action by suitable field redefinitions. Rest are unambiguous. According to the AdS/CFT correspondence all the unambiguous coefficients (coefficients of unambiguous terms) can be fixed in terms of field theory parameters. Therefore, any measurable quantities of boundary theory, for example shear viscosity to entropy density ratio, when calculated holographically can be expressed in terms of unambiguous coefficients in the bulk theory (or equivalently in terms of boundary parameters). We calculate $\eta/s$ for generic six derivative gravity and find that apparently it depends on few ambiguous coefficients at order $\alpha'^2$. We calculate six derivative corrections to central charges $a$ and $c$ and express $\eta/s$ in terms of these central charges and unambiguous coefficients in the bulk theory.