Semiclassical and Quantum Field Theoretic Bounds for Traversable Lorentzian Stringy Wormholes

TL;DR

This paper investigates bounds on traversable Lorentzian stringy wormholes using semiclassical and quantum field theoretic constraints, providing exact solutions that support the idea that such wormholes are only a few orders of magnitude larger than the Planck scale.

Contribution

It derives and verifies bounds on wormhole sizes within string theory using exact solutions, bridging semiclassical and quantum constraints.

Findings

Wormholes can be only a few orders of magnitude larger than the Planck scale.

Semiclassical and quantum bounds are compatible for these wormholes.

Identifies a 'wormhole' analog of naked black holes.

Abstract

A lower bound on the size of a Lorentzian wormhole can be obtained by semiclassically introducing the Planck cut-off on the magnitude of tidal forces (Horowitz-Ross constraint). Also, an upper bound is provided by the quantum field theoretic constraint in the form of the Ford-Roman Quantum Inequality for massless minimally coupled scalar fields. To date, however, exact static solutions belonging to this scalar field theory have not been worked out to verify these bounds. To fill this gap, we examine the wormhole features of two examples from the Einstein frame description of the vacuum low energy string theory in four dimensions which is the same as the minimally coupled scalar field theory. Analyses in this paper support the conclusion of Ford and Roman that wormholes in this theory can have sizes that are indeed only a few order of magnitudes larger than the Planck scale. It is shown that the two types of bounds are also compatible. In the process, we point out a "wormhole" analog of naked black holes.