New dual relations between quantum field theory and string regimes in curved backgrounds

TL;DR

This paper introduces a dual transform linking quantum field theory and string regimes in curved backgrounds, revealing new relations between their characteristic lengths and temperatures, with applications to black hole and de Sitter spacetimes.

Contribution

A novel { m R}-transform is proposed that relates QFT and string regimes in curved backgrounds, showing how their characteristic scales and temperatures are interconnected.

Findings

The { m R}-transform maps Hawking-Gibbons temperature to string critical temperature.

Explicit { m R}-relations are demonstrated in black hole and de Sitter backgrounds.

Quantum back reaction leads to phase relations between QFT and string regimes.

Abstract

A {\cal R} "dual" transform is introduced which relates Quantum Field Theory and String regimes, both in a curved background with D-non compact dimensions. This operation maps the characteristic length of one regime into the other (and, as a consequence, mass domains as well). The {\cal R}-transform is not an assumed or {\it a priori} imposed symmetry but is revealed by the QFT and String dynamics in curved backgrounds. The Hawking-Gibbons temperature and the string maximal or critical temperature are {\cal R}-mapped one into the other. If back reaction of quantum matter is included, Quantum Field Theory and String phases appear, and {\cal R}-relations between them manifest as well. These {\cal R}-transformations are explicitly shown in two relevant examples: Black Hole and de Sitter space times.