Exact Absorption Probability in the Extremal Six-Dimensional Dyonic String Background

TL;DR

This paper derives exact solutions for scalar wave absorption in a six-dimensional extremal dyonic string background, revealing detailed energy dependence and implications for dual field theories via AdS/CFT.

Contribution

It provides the first exact solutions for scalar wave absorption in this background, connecting wave behavior to the dual field theory and exploring low energy limits.

Findings

Exact solutions in terms of Mathieu functions

Explicit low energy absorption probabilities

Identification of a domain with zero absorption probability

Abstract

We show that the minimally coupled massless scalar wave equation in the background of an six-dimensional extremal dyonic string (or D1-D5 brane intersection) is exactly solvable, in terms of Mathieu functions. Using this fact, we calculate absorption probabilities for these scalar waves, and present the explicit results for the first few low energy corrections to the leading-order expressions. For a specific tuning of the dyonic charges one can reach a domain where the low energy absorption probability goes to zero with inverse powers of the logarithm of the energy. This is a dividing domain between the regime where the low energy absorption probability approaches zero with positive powers of energy and the regime where the probability is an oscillatory function of the logarithm of the energy. By the conjectured AdS/CFT correspondence, these results shed novel light on the strongly coupled two-dimensional field theory away from its infrared conformally invariant fixed point (the strongly coupled ``non-critical'' string).