We study a particular approach for analysing worldsheet conformal invariance for bosonic string propagating in a curved background using Hamiltonian formalism. We work in the Schrödinger picture of a single-particle description of the problem where the particle moves in an inﬁnite-dimensional space. Background independence is maintained in this approach by adopting DeWitt’s (Phys. Rev. 85, 653–661, 1952) coordinate-independent formulation of quantum mechanics. This enables us to construct certain background-independent notion of Virasoro generators, called DeWitt–Virasoro (DWV) generators, and invariant matrix elements of an arbitrary operator constructed out of them in spin-zero representation. We show that the DWV algebra is given by the Witt algebra with additional anomalous terms that vanish for Ricci-ﬂat backgrounds. The actual quantum Virasoro generators should be obtained by ﬁrst introducing the vacuum state and then normal ordering the DWV generators with respect to that. We demonstrate the procedure in ﬂat and pp-wave backgrounds.
Volume 94, 2020
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