Virasoro algebra with central charge $c=1$ on the horizon of a two-dimensional-Rindler space–time

Using the holographic machinery built up in a previous work, we show that the hidden $SL(2,R)$ symmetry of a scalar quantum field propagating in a Rindler space–time admits an enlargement in terms of a unitary positive-energy representation of Virasoro algebra defined in the Fock representation. That representation has central charge $c=1.$ The Virasoro algebra of operators gets a manifest geometrical meaning if referring to the holographically associated quantum field theory on the horizon: It is nothing but a representation of the algebra of vector fields defined on the horizon equipped with a point at infinity. All that happens provided the Virasoro ground energy $h≔μ2/2$ vanishes and, in that case, the Rindler Hamiltonian is associated with a certain Virasoro generator. If a suitable regularization procedure is employed, for $h=1/2,$ the ground state of that generator seems to correspond to a thermal state when examined in the Rindler wedge, taking the expectation value with respect to Rindler time. Finally, under Wick rotation in Rindler time, the pair of quantum field theories which are built up on the future and past horizon defines a proper two-dimensional conformal quantum field theory on a cylinder.