A String Theory Which Isn't About Strings

TL;DR

This paper constructs a novel bosonic string theory with asymmetric vacuum choices, resulting in a finite spectrum including gravity and massive spin-two fields, and explores its physical implications and scattering amplitudes.

Contribution

It introduces a new quantization approach with asymmetric vacuum, leading to a finite spectrum and a Lee-Wick extension of string gravity, differing from traditional string theories.

Findings

Spectrum includes gravity and massive spin-two fields

Tree-level dilaton scattering amplitude is rational in kinematic invariants

One-loop partition function matches Feynman diagram calculations

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 {\sl 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 first-quantization using standard operator formalism. Remarkably, the string spectrum consists only of a finite number of degrees of freedom: string gravity (massless spin-two, Kalb-Ramond and dilaton fields) and two massive spin-two Fierz-Pauli fields. The massive spin-two fields 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 fields. The string one loop partition function is shown to perfectly agree with one loop Feynman diagram of string gravity and two massive spin-two fields. In particular, it does not exhibit modular invariance. We critically compare our construction with recent studies and contrast differences.