Naturalness and the Weak Gravity Conjecture (1402.2287v2)

Abstract: The weak gravity conjecture (WGC) is an ultraviolet consistency condition asserting that an Abelian force requires a state of charge $q$ and mass $m$ with $q>m/m_{\rm Pl}$. We generalize the WGC to product gauge groups and study its tension with the naturalness principle for a charged scalar coupled to gravity. Reconciling naturalness with the WGC either requires a Higgs phase or a low cutoff at $\Lambda \sim q m_{\rm Pl}$. If neither applies, one can construct simple models that forbid a natural electroweak scale and whose observation would rule out the naturalness principle.

• The paper demonstrates that incorporating a new millicharged force challenges the naturalness principle in effective field theories.
• It analyzes how radiative corrections in scalar QED complicate maintaining a natural electroweak scale, prompting new theoretical adjustments.
• The research generalizes the weak gravity conjecture to multiple gauge forces, offering predictions for charge-to-mass ratios and signals of physics beyond the standard model.

Overview of "Naturalness and the Weak Gravity Conjecture"

The paper "Naturalness and the Weak Gravity Conjecture" by Clifford Cheung and Grant N. Remmen explores the tension between the principle of naturalness and the weak gravity conjecture (WGC) within the framework of effective field theories, specifically those integrating gravity and Abelian gauge theories. The weak gravity conjecture, formulated by Arkani-Hamed et al., postulates that in any consistent theory of gravity, there must exist a state where gravity is the weakest force, formally written as $q > \frac{m}{m_{\text{Pl}}}$. This conjecture serves as an ultraviolet (UV) consistency condition.

Tension with Naturalness

Naturalness in effective field theories is a guiding principle suggesting that parameters not protected by symmetries should not be fine-tuned. However, the coupling between naturalness and the WGC reveals potential inconsistencies, particularly noticeable when dealing with fundamental scalars and gauge theories. The authors consider scenarios where electromagnetic forces or extensions involving additional unbroken gauge symmetries conflict with Eq. (1), leading to possible violations of natural electroweak scales.

Implications for Electroweak Scale and New Physics

One of the key insights presented in this paper is that models incorporating a new millicharged force may invalidate the naturalness principle if the WGC holds true. The discovery of such forces or associated scalar fields could point towards unexplored dynamics beyond standard model interactions. Moreover, it raises intriguing possibilities for lifting the electroweak scale away from its natural value through experimental exemptions or theoretical constraints.

Radiative Corrections and Stability

The authors delve into complexities introduced by radiative corrections, especially within scalar quantum electrodynamics (QED). They argue that under certain configurations, a natural spectrum exhibiting a proper hierarchy becomes incompatible due to regularized quadratic divergences. Notably, the Higgs mechanism or the introduction of new degrees of freedom at a lower cutoff scale can potentially reconcile this tension, but each option comes with significant theoretical implications.

Generalizing the WGC for Multiple Forces

The paper extends the WGC framework to theories with multiple gauge symmetries, predicting more robust conditions for charge-to-mass ratios across species. The concept of the convex hull in charge space is utilized to encapsulate configurations where extremal black holes become decay-unstable, thereby accommodating broader charge interactions.

Future Directions and Theoretical Considerations

The paper posits that ongoing exploration into phenomenological implications of the WGC, such as identifying weakly gauged symmetries linked with new physics beyond the standard model, remains a fertile ground for discovery. In cases where potential fifth forces or millicharged particles are detected, implications for string theory and holographic principles could be profound. Additionally, the research contemplates practical assessments of such theories with current and future experimental setups capable of detecting minute equivalence principle violations, further enhancing our understanding of theoretical physics harmonizing gravity and quantum mechanics.

In conclusion, the discourse presented by Cheung and Remmen underscores significant implications for theoretical models attempting to merge quantum field theory with gravitational systems, challenging established norms of naturalness within these paradigms and urging a reevaluation of UV consistency conditions inherent to our understanding of physics.