Classical Effective Field Theory and Caged Black Holes

TL;DR

This paper connects matched asymptotic expansion with Classical Effective Field Theory to analyze caged black holes, simplifying calculations and revealing new insights into their thermodynamics and renormalization properties.

Contribution

It demonstrates the equivalence between matched asymptotic expansion and CLEFT, introduces diagrammatic methods, and computes higher-loop corrections for caged black holes.

Findings

Simplified the computation of thermodynamic quantities for caged black holes.

Replaced multiple two-loop diagrams with a single diagram, reducing complexity.

Found that angular momentum does not renormalize at leading order.

Abstract

Matched asymptotic expansion is a useful technique in General Relativity and other fields whenever interaction takes place between physics at two different length scales. Here matched asymptotic expansion is argued to be equivalent quite generally to Classical Effective Field Theory (CLEFT) where one (or more) of the zones is replaced by an effective theory whose terms are organized in order of increasing irrelevancy, as demonstrated by Goldberger and Rothstein in a certain gravitational context. The CLEFT perspective has advantages as the procedure is clearer, it allows a representation via Feynman diagrams, and divergences can be regularized and renormalized in standard field theoretic methods. As a side product we obtain a wide class of classical examples of regularization and renormalization, concepts which are usually associated with Quantum Field Theories. We demonstrate these ideas through the thermodynamics of caged black holes, both simplifying the non-rotating case, and computing the rotating case. In particular we are able to replace the computation of six two-loop diagrams by a single factorizable two-loop diagram, as well as compute certain new three-loop diagrams. The results generalize to arbitrary compactification manifolds. For caged rotating black holes we obtain the leading correction for all thermodynamic quantities. The angular momentum is found to non-renormalize at leading order.