Maths HEP Lunchtime Seminars: Ward identities and transport in 2+1 dimensions
30 October 2015 13:00 in CM221
Transport properties of Quantum Hall systems can be derived in a systematic derivative expansion from a generating functional depending on external sources. Gauge plus non-relativistic diffeomorphism invariance constrain the form of the generating functional, and lead to an interesting relation between Hall conductivity and viscosity. Similar relations between shear and bulk viscosities and conductivities can be derived by means of Ward identities for momentum conservation in Galilean invariant systems. We generalize the identities to relativistic systems and to systems without boost invariance (such as Lifshitz theories) and try to derive them in AdS/CFT by constructing a ``probability current'' in the bulk and taking advantage of parity symmetry.