Speaker
Description
It is quite well known that quantum area-preserving diffeomorphisms play a key role in the fractional quantum Hall states (FQHs) and explain, for instance, the incompressibility of the quantum Hall fluids. Moreover, quantum area-preserving diffeomorphisms in two space dimensions are naturally encoded in the so-called Girvin-MacDonald-Plazman (GMP) algebra or in its dual version known as W_{\infinity} algebra. In this talk, firstly I will introduce an effective-field-theory approach that shows the relation between the GMP algebra and the emergence of a non-relativistic massive spin-2 mode in the bulk state of FQHs through the existence of a nematic order. The corresponding nematic order parameter is nothing but a symmetric rank-2 tensor that can be naturally identified with an emergent metric tensor. Secondly, I will generalize this approach by showing how higher-rank symmetric tensors and their corresponding non-relativistic massive higher-spin modes, which should naturally emerge from quantum area-preserving diffeomorphisms, can be indeed introduced and analyzed by considering generalized nematic FQHs. It remains an open question how and if these modes can be derived from a suitable non-relativistic version of linearized higher-spin gravity.
