The role of fixed scalars in scattering off a 5D black hole

TL;DR

This paper investigates the discrepancies in greybody factors for fixed scalars during scattering off a 5D black hole, highlighting gauge dependence and the complex mixing of fields affecting the interpretation of scalar roles.

Contribution

It clarifies how gauge choices influence the behavior of fixed scalars in semiclassical calculations and compares these with effective string theory results.

Findings

$ u$ acts as a test field with clear role.

$ ext{role of } ext{lambda}$ is ambiguous and gauge-dependent.

Discrepancies are linked to field mixing and decoupling procedures.

Abstract

We discuss the role of fixed scalars($\nu,\lambda$) in scattering off a five-dimensional balck hole. The issue is to explain the disagreement of the greybody factor for $\lambda$ between the semiclassical and effective string calculations. In the effective string approach, this is related to the operators with dimension (3,1) and (1,3). On the semiclassical calculation, this originates from a complicated mixing between $\lambda$ and other fields. Hence it may depend on the decoupling procedure. It is shown that $\lambda$ depends on the gauge choices such as the harmonic, dilaton gauges, and the Krasnitz-Klebanov setting for $h_{\mu\nu}$. It turns out that $\nu$ plays a role of test field well, while the role of $\lambda$ is obscure.