Testing Effective String Models of Black Holes with Fixed Scalars

TL;DR

This paper derives decoupled equations for fixed scalars in black hole backgrounds, compares greybody factors with effective string models, and discusses discrepancies caused by additional operator couplings.

Contribution

It provides a detailed analysis of fixed scalar fluctuations in black holes and examines their agreement with effective string theory predictions.

Findings

Decoupled fixed scalar equations are derived for specific black hole configurations.

Greybody factors match those from coupling to (2,2) operators on the effective string.

Couplings to chiral operators of different dimensions cause deviations from semiclassical results.

Abstract

We solve the problem of mixing between the fixed scalar and metric fluctuations. First, we derive the decoupled fixed scalar equation for the four-dimensional black hole with two different charges. We proceed to the five-dimensional black hole with different electric (1-brane) and magnetic (5-brane) charges, and derive two decoupled equations satisfied by appropriate mixtures of the original fixed scalar fields. The resulting greybody factors are proportional to those that follow from coupling to dimension (2,2) operators on the effective string. In general, however, the string action also contains couplings to chiral operators of dimension (1,3) and (3,1), which cause disagreements with the semiclassical absorption cross-sections. Implications of this for the effective string models are discussed.