Super-Planckian Spatial Field Variations and Quantum Gravity

Abstract: We study scenarios where a scalar field has a spatially varying vacuum expectation value such that the total field variation is super-Planckian. We focus on the case where the scalar field controls the coupling of a U(1) gauge field, which allows us to apply the Weak Gravity Conjecture to such configurations. We show that this leads to evidence for a conjectured property of quantum gravity that as a scalar field variation in field space asymptotes to infinity there must exist an infinite tower of states whose mass decreases as an exponential function of the scalar field variation. We determine the rate at which the mass of the states reaches this exponential behaviour showing that it occurs quickly after the field variation passes the Planck scale.

• The paper demonstrates that super-Planckian field variations trigger an exponential decay in gauge couplings through the Local Weak Gravity Conjecture.
• It applies the Weak Gravity Conjecture in both weakly and strongly curved backgrounds to link scalar behaviors with quantum gravity constraints.
• The study challenges classical moduli stabilization and opens avenues for broader applications in cosmology and high-energy physics.

Super-Planckian Spatial Field Variations and Their Implications for Quantum Gravity

The paper "Super-Planckian Spatial Field Variations and Quantum Gravity" by Daniel Klaewer and Eran Palti examines the consequences of super-Planckian spatial variations of scalar fields within the context of quantum gravity, particularly utilizing the Weak Gravity Conjecture (WGC). The authors focus on scenarios where a scalar field influences the coupling of a U(1) gauge field, thereby allowing for an exploration of the relationships between scalar field variations and mass scales in quantum gravity setups.

Main Concepts and Results

The authors explore configurations where the variation in a scalar field’s vacuum expectation value exceeds the Planck scale. By applying the WGC in such contexts, they gather evidence supporting the Swampland Conjecture (SC). The SC proposes that as scalar field variations in field space asymptotes to infinity, there exists an infinite tower of states with masses that decrease exponentially with these variations. Remarkably, it is shown that this exponential behavior is reached relatively rapidly once the field variation surpasses the Planck scale.

The main framework supporting these results is a conjectural extension termed the Local Weak Gravity Conjecture (LWGC). This extension adapts the WGC to scenarios with spatially varying gauge couplings and offers a direct way to translate local gauge coupling values to bounds on local mass scales. The authors scrutinize these concepts across weakly and strongly curved spacetime backgrounds.

Analysis in Different Backgrounds

• Weakly-Curved Backgrounds: In these regimes, the results bank on maintaining the validity of the Newtonian potential approximation of general relativity. The scalar field and energy densities exhibit behavior that aligns with logarithmic profiles leading to exponential coupling dependencies. Importantly, the nature of the exponential decay is tied to field variations becoming super-Planckian, expressing real constraints on the gauge coupling’s scalability within weak-curvature bounds.
• Strongly-Curved Backgrounds: The discourse then transitions to strongly curved settings, where the authors seek general scalar and gauge field behaviors. Utilizing spherical symmetry and the scalar field’s eigenfunction decompositions, they demonstrate that even under significant curvature, scalar fields supported by a U(1) gauge field maintain SC properties. The authors conclude that any negative eigenvalue within these setups signifies inherent constraints, reinforcing the Swampland related behavior exponentially as the scalar field extends over super-Planckian ranges.

In both contexts, the logarithmic behavior of scalar field variation transitions to SC-guided exponential decay, revealing self-consistent and universal characteristics of gauge couplings vis-à-vis large spatial scalar field displacements within quantum gravity frameworks.

Implications and Speculative Directions

The results have compelling implications for the fundamental understanding of quantum gravity. The rapid attainment of exponential behavior within field variations grounds the Swampland Conjecture's relevance and challenges us to re-evaluate the notion of moduli spaces in quantum theories. A speculative avenue presented is the broader application of the LWGC and SC across multiple gauge fields and scalar dimensions, potentially shaping the framework for more extensive moduli stabilization and cosmological applications.

Furthermore, the limitations highlighted in employing Wilsonian effective field theories with constant cut-offs stand to redefine the methodologies used in exploring these complex scalar interactions. Lastly, considering temporal variations as a parallel exploration remains an intriguing direction, linked possibly to time-dependent cosmological scalar phenomena.

In summary, Klaewer and Palti's investigative work not only fortifies the theoretical underpinnings of scalar field dynamics in quantum gravity via the Swampland lens but opens up discourse for a unified approach towards resolving moduli characterization in high-energy physics contexts.