An excursion into the string spectrum
C. Markou, Evgeny Skvortsov
Abstract
A bstract We propose a covariant technique to excavate physical bosonic string states by entire trajectories rather than individually. The approach is based on Howe duality: the string’s spacetime Lorentz algebra commutes with a certain inductive limit of sp (•), with the Virasoro constraints forming a subalgebra of the Howe dual algebra sp (•). There are then infinitely many simple trajectories of states, which are lowest-weight representations of sp (•) and hence of the Virasoro algebra. Deeper trajectories are recurrences of the simple ones and can be probed by suitable trajectory-shifting operators built out of the Howe dual algebra generators. We illustrate the formalism with a number of subleading trajectories and compute a sample of tree-level amplitudes.