# UV Completion on the Worldline

## TL;DR

This paper introduces a novel framework for ultraviolet (UV) completion of particle theories using the worldline formalism, emphasizing ghost-free conditions and infinite-derivative models inspired by string theory, with potential for simplified amplitude calculations.

## Contribution

It proposes a new UV completion approach based on the worldline formalism, generalizing string-inspired infinite-derivative models and establishing criteria to avoid ghosts.

## Key findings

- Ghost-free theories include the Siegel model as a special case.
- Proper-time saddle points dominate the UV behavior, simplifying amplitude computations.
- Worldline inversion symmetry mimics modular invariance for regularization.

## Abstract

A framework for UV completing particle theories is proposed, based on the worldline formalism, which is equivalent to weighting all sums over histories with a proper-time dependent measure that has a smallest proper-time. We deduce a criterion to avoid ghosts, and find that the ghost-free theories have the (string-theory inspired) infinite-derivative model of Siegel as a special case, but represent a significant generalisation. Generically, the UV of such theories is dominated by a saddle-point in the proper-time, leading to simplification in the computation of amplitudes. We focus on a particularly attractive option which is to mimic the regulating properties of modular invariance with a worldline "inversion symmetry".