String theory as a Lilliputian world

TL;DR

This paper demonstrates that the presence of a tachyon in continuum string theory enables a scaling limit that aligns with lattice string results, bridging the gap between lattice and continuum approaches in high dimensions.

Contribution

It shows how tachyon-inclusive continuum string theory can reproduce lattice string results through a specific scaling limit, clarifying their relationship in large spacetime dimensions.

Findings

Tachyon presence allows a unique scaling limit matching lattice results.

Standard continuum string results require a different scaling limit.

Lattice regularizations of string theories are akin to a Lilliputian world.

Abstract

Lattice regularizations of the bosonic string allow no tachyons. This has often been viewed as the reason why these theories have never managed to make any contact to standard continuum string theories when the dimension of spacetime is larger than two. We study the continuum string theory in large spacetime dimensions where simple mean field theory is reliable. By keeping carefully the cutoff we show that precisely the existence of a tachyon makes it possible to take a scaling limit which reproduces the lattice-string results. We compare this scaling limit with another scaling limit which reproduces standard continuum-string results. If the people working with lattice regularizations of string theories are akin to Gulliver they will view the standard string-world as a Lilliputian world no larger than a few lattice spacings.