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Worldline theories with towers of internal states

Abel, Steven and Lewis, Daniel (2020) 'Worldline theories with towers of internal states.', Journal of high energy physics., 2020 (12). 069.


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.

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Publisher statement:This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:29 October 2020
Date deposited:13 April 2021
Date of first online publication:10 December 2020
Date first made open access:13 April 2021

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