Worldline theories with towers of internal states

TL;DR

This paper explores particle theories with internal degrees of freedom forming towers, including their origins from string theory and their potential to produce finite, modular invariant, and non-local theories with novel properties.

Contribution

It introduces a general framework for worldline theories with towers of internal states, extending beyond string-derived models to include non-geometric and non-local theories.

Findings

Truncated towers lead to non-local particle theories.

Such theories exhibit Gross-Mende-like saddle points in amplitudes.

The framework allows for constructing finite, modular invariant models.

Abstract

We study particle theories that have a tower of worldline internal degrees of freedom. Such a theory can arise when the worldsheet of closed strings is dimensionally reduced to a worldline, in which case the tower is infinite with regularly spaced masses. But our discussion is significantly more general than this, and there is scope to consider all kinds of internal degrees of freedom carried by the propagating particle. For example it is possible to consider towers corresponding to other geometries, or towers with no obvious geometric interpretation that still yield a modular invariant theory. Truncated towers generate non-local particle theories that share with string theory the property of having a Gross-Mende-like saddle point in their amplitudes. This provides a novel framework for constructing exotic theories which may have desirable properties such as finiteness and modular invariance.