Mapping 1+1-dimensional black hole thermodynamics to finite volume effects

TL;DR

This paper explores the thermodynamic similarities between 1+1-dimensional scalar fields with boundary conditions and black holes, suggesting a deeper connection that extends to higher dimensions.

Contribution

It establishes a novel analogy between finite volume effects in quantum field theory and black hole thermodynamics, extending the comparison beyond 1+1 dimensions.

Findings

Similar thermodynamic behavior in 1+1 dimensions under specific identifications

Potential extension of the analogy to higher dimensions

Indication of a deeper connection due to boundary conditions

Abstract

Both black hole thermodynamics and finite volume effects in quantum field theory violate the null energy condition. Motivated by this, we compare thermodynamic features between two $1+1$-dimensional systems: (i) a scalar field confined to a periodic spatial interval of length $a$ and tunneling between two degenerate vacua; (ii) a dilatonic black hole at temperature $T$ in the presence of matter fields. If we identify $a\propto T^{-1}$, we find similar thermodynamic behaviour, which suggests some deeper connection arising from the presence of non-trivial boundary conditions in both systems. We then extend our results to $2+1$ and $3+1$-dimensions and, although a more complete study is necessary, the connection found in $1+1$-dimensions seems to be valid in higher dimensions too.