All-orders worldline holography and higher spins

TL;DR

This paper demonstrates that sources in a Minkowski quantum field theory naturally form a higher-dimensional AdS space, revealing a deep connection between quantum fields and holographic dualities through the worldline approach.

Contribution

It establishes, to all orders, that quantum field sources over Minkowski space form a holographic AdS$_5$ theory, using the worldline formalism without diagram selection.

Findings

Sources form an AdS$_5$ geometry via worldline approach

Higher-spin sources are naturally embedded in the holographic framework

A Wilson flow extends 4D sources to 5D fields, reproducing holographic results

Abstract

By using the worldline approach to quantum field theory, we demonstrate to all orders that the sources of a quantum field theory over Mink$_4$ naturally form a field theory over AdS$_5$. In particular, this holds for higher-spin sources of a free scalar theory. We work entirely within quantum-field theory and do not select a subset of diagrams. As auxiliary fifth dimension Schwinger's proper time is grouped with the physical four spacetime dimensions into an AdS$_5$ geometry. The four-dimensional sources are extended to five-dimensional fields by a Wilson flow (gradient flow). A variational principle for said flow reproduces the corresponding holographic computation.