Self-Binding Energies in AdS

TL;DR

This paper investigates the self-binding energies of charged particles in Anti de-Sitter space, exploring how scalar fields influence the Positive Binding Conjecture related to the Weak Gravity Conjecture in AdS.

Contribution

It provides analytic and numerical calculations of self-binding energies in AdS$_4$ and AdS$_5$, including effects of scalar fields with various masses, extending the Positive Binding Conjecture to AdS spaces.

Findings

Massless scalar fields reproduce flat-space results in large AdS radius limit.

Analytic expressions for self-binding energies in specific scalar mass cases.

Vanishing total self-binding energy for BPS particles in supersymmetric models.

Abstract

The Positive Binding Conjecture is a proposed formulation of the Weak Gravity Conjecture appropriate to Anti de-Sitter (AdS) space. It proposes that in a consistent gravitational theory, with a $U(1)$ gauge symmetry, there must exist a charged particle with non-negative self-binding energy. In order to formulate this as a constraint on a given effective theory, we calculate the self-binding energy for a charged particle in AdS$_4$ and AdS$_5$. In particular, we allow it to couple to an additional scalar field of arbitrary mass. Unlike the flat-space case, even when the scalar field is massive it contributes significantly to the binding energy, and therefore is an essential component of the conjecture. In AdS$_5$, we give analytic expressions for the self-binding energy for the cases when the scalar field is massless and when it saturates the Breitenlohner-Freedman (BF) bound, and in AdS$_4$ when it is massless. We show that the massless case reproduces the flat-space expressions in the large AdS radius limit, and that both analytic cases lead to vanishing total self-binding energy for BPS particles in example supersymmetric models. For other masses of the scalar we give numerical expressions for its contribution to the self-binding energy.