The Weak Gravity Conjecture and Scalar Fields (1705.04328v3)

Abstract: We propose a generalisation of the Weak Gravity Conjecture in the presence of scalar fields. The proposal is guided by properties of extremal black holes in ${\cal N}=2$ supergravity, but can be understood more generally in terms of forbidding towers of stable gravitationally bound states. It amounts to the statement that there must exist a particle on which the gauge force acts more strongly than gravity and the scalar forces combined. We also propose that the scalar force itself should act on this particle stronger than gravity. This implies that generically the mass of this particle decreases exponentially as a function of the scalar field expectation value for super-Planckian variations, which is behaviour predicted by the Refined Swampland Conjecture. In the context of ${\cal N}=2$ supergravity the Weak Gravity Conjecture bound can be tied to bounds on scalar field distances in field space. Guided by this, we present a general proof that for any linear combination of moduli in any Calabi-Yau compactification of string theory the proper field distance grows at best logarithmically with the moduli values for super-Planckian distances.

Overview of "The Weak Gravity Conjecture and Scalar Fields"

The paper "The Weak Gravity Conjecture and Scalar Fields" by Eran Palti endeavors to enhance the understanding of the Weak Gravity Conjecture (WGC) through its generalization in scenarios that involve scalar fields. Palti integrates concepts from established conjectures in quantum gravity, notably the WGC and the Refined Swampland Conjecture (RSC), to address fundamental questions about the configuration of effective field theories in potential concord with quantum gravitational principles.

The WGC proposes that in any effective theory of quantum gravity endowed with a U(1) gauge symmetry, there must exist a particle with mass $m$ and charge $q$ satisfying the relation $gqM \geq \sqrt{m}$. Here, gravity is posited as the weakest force as compared to electrostatic forces, an idea that finds its roots in the necessity for extremal black holes to be unstable against decay.

Key Results

The paper presents a comprehensive examination of how the WGC can be adapted for theories that incorporate scalar fields. This is primarily done by asserting that there must exist a particle for which the scalar force surpasses the gravitational force—a conjecture that hinges on the prevention of towers of stable gravitationally bound states. This assertion leads to an exponential decrease in the mass of a particle as a function of the scalar field expectation value when undergoing super-Planckian variations, marrying predictions with behaviors anticipated by the RSC.

Palti's paper provides a general proof that any linear combination of moduli within Calabi-Yau compactifications exhibits logarithmic growth over super-Planckian distances, underpinning this behavior with N = 2 supergravity formulations. It unravels the chemistry between the constraints posed by the WGC and bounds on scalar field distances within field space, thus supporting the RSC.

Implications and Speculations

The theoretical implications of this work are profound, especially in terms of how it informs the structure of potential quantum gravity theories. If accepted, the generalization of the WGC with scalar fields could necessitate certain structural components in our understanding of high-energy physics, particularly in how effective field theories are composed or constrained. Furthermore, practical implications could emerge in how these foundational aspects influence model building in quantum gravity and string theory scenarios.

In future explorations, the intersection of WGC and RSC may stimulate new avenues in addressing longstanding questions about the nature of force interactions at a quantum level. One potential exploration path could include delineating more precise conditions under which these conjectures hold universally or identifying additional principles from which they could originate.

In essence, Palti's exposition elaborates on the inherent complementarities between the WGC and distance conjectures within scalar field constructs, thus providing groundwork for more holistic theories that integrate gravitational with other gauge and scalar dynamics. The document provocatively engages with potential hypotheses that might not only unify known theoretical principles but also speculate on emergent behaviors or phenomena that arise in high-energy particle theories and extended quantum field theories.