JOURNAL OF HIGH ENERGY PHYSICS, v.2017, no.11, pp.172 -
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