A String Theory Which Isn't About Strings

Abstract

Quantization of closed string proceeds with a suitable choice of worldsheet vacuum. A priori, the vacuum may be chosen independently for left-moving and right-moving sectors. We construct ab initio quantized bosonic string theory with left-right asymmetric worldsheet vacuum and explore its consequences and implications. We critically examine the validity of new vacuum and carry out rst-quantization using standard operator formalism. Remarkably, the string spectrum consists only of a nite number of degrees of freedom: string gravity (massless spin-two, Kalb-Ramond and dilaton elds) and two massive spin-two Fierz-Pauli elds. The massive spin-two elds have negative norm, opposite mass-squared, and provides a Lee-Wick type extension of string gravity. We compute two physical observables: tree-level scattering amplitudes and one-loop cosmological constant. Scattering amplitude of four dilatons is shown to be a rational function of kinematic invariants, and in D = 26 factorizes into contributions of massless spin-two and a pair of massive spin-two elds. The string one loop partition function is shown to perfectly agree with one loop Feynman diagram of string gravity and two massive spin-two elds. In particular, it does not exhibit modular invariance. We critically compare our construction with recent studies and contrast dierences. Open Access (c) The Authors