# Relations between positivity, localization and degrees of freedom: the Weinberg-Witten theorem and the van Dam-Veltman-Zakharov discontinuity

## TL;DR

This paper introduces a ghost-free string-localized field approach that addresses the quantum degrees of freedom transition between massive and massless higher-spin particles, resolving longstanding theoretical issues like the Weinberg-Witten theorem and the van Dam-Veltman-Zakharov discontinuity.

## Contribution

It provides a novel ghost-free framework using string-localized fields to reconcile massive and massless higher-spin theories and resolve key discontinuities.

## Key findings

- Overcomes Weinberg-Witten restrictions on massless higher-spin energy-momentum tensors.
- Resolves van Dam-Veltman-Zakharov discontinuity for light gravitons.
- Provides a consistent, ghost-free description of higher-spin fields.

## Abstract

The problem of accounting for the quantum degrees of freedom in passing from massive higher-spin potentials to massless ones and its inverse, the "fattening" of massless tensor potentials of helicity $\pm h$ to their massive $s = |h|$ counterparts, are solved - in a perfectly ghost-free approach - using "string-localized fields". This approach allows to overcome the Weinberg-Witten impediment against the existence of massless $|h| \geq 2$ energy-momentum tensors, and to qualitatively and quantitatively resolve the van Dam-Veltman-Zakharov discontinuity concerning, e.g., very light gravitons, in the limit $m \to 0$.