Thermal worldline holography

TL;DR

This paper explores how worldline holography relates four-dimensional quantum field theories to five-dimensional AdS spaces, revealing temperature-dependent geometries and the influence of matter types on spacetime structure.

Contribution

It demonstrates that worldline holography can describe finite temperature effects with either thermal AdS or AdS black holes, and clarifies the role of coordinates and matter types in phase predictions.

Findings

Finite temperature holography yields thermal AdS or AdS black hole geometries.

No phase transition predicted by comparing five-dimensional actions.

Matter type (fermionic or bosonic) influences the preferred spacetime geometry.

Abstract

For a quantum field theory over four-dimensional Minkowski space at zero temperature worldline holography states, that it can be expressed as a field theory of its sources over five-dimensional AdS space to all orders in its elementary fields, the fifth dimension being Schwinger's proper time of the worldline formalism. For the finite temperatures studied here worldline holography yields either a thermal AdS space or an AdS black hole as five-dimensional manifolds. Comparing the values of the five-dimensional action for the two alternatives does not predict a phase transition as a function of the temperature. This absence is crucially linked to the used coordinates, and worldline holography predicts the Fefferman-Graham form. For these coordinates the only way to tilt the scales in favour of one or the other spacetime is to switch between fermionic or bosonic elementary matter.