Vacuum energy density from the form factor bootstrap

TL;DR

This paper develops a new method to compute vacuum energy density in quantum field theories using the form factor bootstrap, providing results consistent with known approaches in 2D and proposing a universal form in 4D, with implications for the cosmological constant.

Contribution

It introduces a novel prescription for calculating vacuum energy density from the form factor bootstrap, applicable in both 2D and 4D quantum field theories, and explores its cosmological implications.

Findings

Reproduces known 2D results via a new bootstrap normalization method.

Proposes a universal form of vacuum energy density in 4D as proportional to $m^D/\mathfrak{g}$.

Suggests the existence of a particle, the 'zeron', possibly a massive Majorana neutrino, related to the cosmological constant.

Abstract

The form-factor bootstrap is incomplete until one normalizes the zero-particle form factor. For the stress energy tensor we describe how to obtain the vacuum energy density $\rho_{\rm vac}$, defined as $\langle 0| T_{\mu\nu} | 0 \rangle = \rho_{\rm vac} \, g_{\mu\nu}$, from the form-factor bootstrap. Even for integrable QFT's in D=2 spacetime dimensions, this prescription is new, although it reproduces previously known results obtained in a different and more difficult thermodynamic Bethe ansatz computation. We propose a version of this prescription in D=4 dimensions. For these even dimensions, the vacuum energy density has the universal form $\rho_{\rm vac} \propto m^D/\mathfrak{g}$ where $\mathfrak{g}$ is a dimensionless interaction coupling constant which can be determined from the high energy behavior of the S-matrix. In the limit $\mathfrak{g} \to 0$, $\rho_{\rm vac} $ diverges due to well understood UV divergences in free quantum field theories. If we assume the the observed Cosmological Constant originates from the vacuum energy density $\rho_{\rm vac}$ computed as proposed here, then this suggests there must exist a particle which does not obtain its mass from spontaneous symmetry breaking in the electro-weak sector, which we designate as the "zeron". A strong candidate for the zeron is a massive Majorana neutrino.