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We calculate shear viscosity to entropy density ratio in presence of fourderivative (with coefficient $\alpha'$) and six derivative (with coefficient$\alpha'^2$) terms in bulk action. In general, there can be three possible fourderivative terms and ten possible six derivative terms in the Lagrangian. Amongthem 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 theunambiguous coefficients (coefficients of unambiguous terms) can be fixed interms of field theory parameters. Therefore, any measurable quantities ofboundary theory, for example shear viscosity to entropy density ratio, whencalculated holographically can be expressed in terms of unambiguouscoefficients in the bulk theory (or equivalently in terms of boundaryparameters). We calculate $\eta/s$ for generic six derivative gravity and findthat apparently it depends on few ambiguous coefficients at order $\alpha'^2$.We calculate six derivative corrections to central charges $a$ and $c$ andexpress $\eta/s$ in terms of these central charges and unambiguous coefficientsin the bulk theory.

Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity