Schwinger's proper time and worldline holographic renormalisation

TL;DR

This paper demonstrates that worldline holography naturally leads to an AdS$_5$ geometry from Minkowski spacetime and shows that the effective action and source profiles solve a renormalisation group equation, ensuring regulator independence.

Contribution

It establishes a connection between worldline formalism and holographic renormalisation, showing the proper time and sources form an AdS$_5$ structure and solve RG equations.

Findings

Sources form a field theory over AdS$_5$ to all orders.

Proper time groups with spacetime dimensions into AdS$_5$.

Effective action and source profiles solve RG equations, ensuring regulator independence.

Abstract

Worldline holography states that within the framework of the worldline approach to quantum field theory, sources of a quantum field theory over Mink$_4$ naturally form a field theory over AdS$_5$ {\sl to all orders} in the elementary fields and in the sources of arbitrary spin. (Such correspondences are also available for other pairs of spacetimes, not only Mink$_4\leftrightarrow\mathrm{AdS}_5$.) Schwinger's proper time of the worldline formalism is automatically grouped with the physical four spacetime dimensions into an AdS$_5$ geometry. We show that the worldline holographic effective action in general and the proper-time profiles of the sources in particular solve a renormalisation group equation and, reversely, can be defined as solution to the latter. This fact also ensures regulator independence.