String Theory Journal Club

Conformal field theory (CFT) in 1+1 dimensions is routinely used to effectively describe quantum many-body systems in equilibrium. Recently, CFT has been used to study such systems also out of equilibrium, and more recently, even in the presence of inhomogeneities varying on mesoscopic scales. Examples include quantum spin chains with spatially-varying couplings and trapped ultracold atoms. The resulting effective description is an inhomogeneous CFT where the propagation velocity is given by a position-dependent function, or equivalently, a CFT in curved spacetime. In this talk, I will present an exact analytical approach to such CFTs based on projective unitary representations of circle diffeomorphisms and properties of the Virasoro algebra. This approach can be used to study non-equilibrium scenarios, such as driven quantum systems, and generalizes previous results for a small subfamily of similar systems that involved only a finite-dimensional subalgebra to general inhomogeneities that require the full (infinite-dimensional) Virasoro algebra.