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A String Theory Which Isn't About Strings

Kanghoon Lee, Soo-Jong Rey, J. A. Rosabal

TL;DR

This work demonstrates that bosonic string theory can be consistently quantized over a left-right asymmetric worldsheet vacuum, leading to a finite spectrum consisting of string gravity plus two massive spin-2 ghost fields. The authors develop the ab initio canonical quantization in this new vacuum, establish backward time-ordering for the left-moving sector, and derive a massless gravity multiplet along with two negative-norm massive spin-2 states, effectively realizing a Lee-Wick extension within a string framework. Tree-level dilaton scattering yields a rational, pole-structured amplitude whose residues factorize at $D=26$ into massless and massive spin-2 exchanges, while the one-loop torus partition function is not modular invariant but correctly counts degrees of freedom, aligning with a corresponding field-theory picture. These results bridge string theory with finite-field content theories such as HSY double field theory and ambitwistor/string-inspired limits, suggesting new avenues for quantum gravity models and further supersymmetric generalizations.

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.

A String Theory Which Isn't About Strings

TL;DR

This work demonstrates that bosonic string theory can be consistently quantized over a left-right asymmetric worldsheet vacuum, leading to a finite spectrum consisting of string gravity plus two massive spin-2 ghost fields. The authors develop the ab initio canonical quantization in this new vacuum, establish backward time-ordering for the left-moving sector, and derive a massless gravity multiplet along with two negative-norm massive spin-2 states, effectively realizing a Lee-Wick extension within a string framework. Tree-level dilaton scattering yields a rational, pole-structured amplitude whose residues factorize at into massless and massive spin-2 exchanges, while the one-loop torus partition function is not modular invariant but correctly counts degrees of freedom, aligning with a corresponding field-theory picture. These results bridge string theory with finite-field content theories such as HSY double field theory and ambitwistor/string-inspired limits, suggesting new avenues for quantum gravity models and further supersymmetric generalizations.

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 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.

Paper Structure

This paper contains 20 sections, 169 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Quantization of Closed String
  3. Conventional route: quantization over conventional vacuum
  4. Unconventional route: metric sign flip prescription
  5. Unconventional route: tensionless or null string
  6. Quantized String over the New Vacuum
  7. Problem with conventional time-ordering
  8. Backward time-ordering for the new vacuum
  9. The spectrum
  10. The $b, c$ ghosts and the normal ordering constants
  11. Tree-level scattering amplitude
  12. Correlation functions of master vertex operators
  13. Four dilaton scattering amplitude
  14. The torus partition function and one-loop cosmological constant
  15. Field theory toy model
  16. ...and 5 more sections

Figures (1)

  • Figure 1: Various limits of quantized closed string theory. Different limits correspond to different order of the first-quantized worldsheet $\hbar$ and the string tension $T = (2 \pi \alpha')^{-1}$ (relative to a characteristic energy scale). It should be emphasized that $\hbar$ and $T$ limits do not commute. Ambitwistor string differs from multi-gravity, and a precise relation between higher spin theory and Gross-Mende high-energy scattering remains unsettled.