Charge Quantization of Axion-Dilaton Black Holes

TL;DR

This paper explores axion-dilaton black holes in string theory, focusing on their charge quantization, duality invariance, and the stability of certain zero-entropy solutions called holons, revealing their mathematical and physical properties.

Contribution

It introduces a family of stable, zero-entropy axion-dilaton black holes called holons and analyzes their charge quantization and duality symmetry properties.

Findings

Holons are stable, zero-entropy black-hole solutions.

Charge spectrum invariance under SL(2,Z) but not SL(2,R).

Asymptotic axion-dilaton values relate to modular parameters.

Abstract

We present axion-dilaton black-hole and multi-black-hole solutions of the low-energy string effective action. Under $SL(2,R)$ electric-magnetic duality rotations only the ``hair" (charges and asymptotic values of the fields) of our solutions is transformed. The functional form of the solutions is duality-invariant. Axion-dilaton black holes with zero entropy and zero area of the horizon form a family of stable particle-like objects, which we call {\it holons}. We study the quantization of the charges of these objects and its compatibility with duality symmetry. In general the spectrum of black-hole solutions with quantized charges is not invariant under $SL(2,R)$ but only under $SL(2,Z)$ or one of its subgroups $\Gamma_{l}$. Because of their transformation properties, the asymptotic value of the axion-dilaton field of a black hole may be associated with the modular parameter $\tau$ of some complex torus and the integer numbers $(n,m)$ that label its quantized electric and magnetic charges may be associated with winding numbers.