Evidence for a Lattice Weak Gravity Conjecture

Abstract: The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index sublattice of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance. However, we present counterexamples to the stronger possibility that a superextremal particle exists at every lattice site, including an example in which the lightest charged particle is subextremal. The Sublattice Weak Gravity Conjecture has many implications both for abstract theories of quantum gravity and for real-world physics. For instance, it implies that if a gauge group with very small coupling $e$ exists, then the fundamental gravitational cutoff energy of the theory is no higher than $\sim e^{1/3} M_{\rm Pl}$.

Insights into the Lattice Weak Gravity Conjecture

The paper "Evidence for a Lattice Weak Gravity Conjecture" by Heidenreich, Reece, and Rudelius provides compelling evidence for a refined version of the Weak Gravity Conjecture (WGC), proposing the Sublattice Weak Gravity Conjecture (sLWGC). The WGC posits the existence of superextremal particles within gauge theories coupled to gravity—particles whose charge-to-mass ratio surpasses that of an extremal black hole with similar charge. The sLWGC extends this, suggesting that a finite index sublattice exists where each lattice point corresponds to a superextremal particle.

Main Contributions

• Numerical Evidences: The paper presents examples from effective Kaluza-Klein theories and perturbative string vacua supporting the sLWGC. These examples indicate that an infinite tower of superextremal particles populates a sublattice of the charge lattice.

• Perturbative String Theory and Modular Invariance: The authors argue that the sLWGC naturally arises from modular invariance in perturbative string theories. This is significant because modular invariance represents a fundamental aspect of the consistency within string theory.

• Counterexamples: The study acknowledges potential counterexamples where every lattice site may not host superextremal particles. For instance, the lightest charged particle can be subextremal, illustrating the need for refinement from the LWGC to the sLWGC.

Theoretical and Practical Implications

The implications of this work are vast, both theoretically and practically. The sLWGC refines our understanding of charged spectra in quantum gravity frameworks, particularly those derived from string theories. It serves as a tool to constrain models involving gauge theories with weak coupling constants, arguing that these theories exhibit an inevitable collapse in effective field theories at higher energy scales.

• Swampland and Quantum Gravity: This conjecture aids in delineating the boundaries of effective field theories that are consistent with gravity—a necessity for deriving predictions from string theories.

• UV Cutoffs: The sLWGC suggests an essential UV cutoff in effective theories due to the existence of a tower of charged particles becoming light as we reduce coupling constants. The authors correlate this to a cutoff energy in gravity theories, furthering the discussion initiated by earlier works.

Speculations on AI and Future Directions

The continued exploration of lattice-based conjectures will likely contribute to advancements in theoretical physics and quantum computing, where principles of symmetry and lattice formation are crucial. The alignment presented with modular invariance could inform future computational models in AI, potentially enhancing simulations in quantum algorithms or aiding the understanding of complex quantum phenomena.

The paper’s analysis opens potential paths for examining the robustness of gauge theories in varying dimensional theories, calling for more detailed exploration into supersymmetric models, non-Abelian groups, and potential extensions into realms currently unexplored by quantum gravity theorists. Further empirical testing and computational verification of these conjectures will be paramount to understanding their practical limits and applications in realistic scenarios.

In conclusion, this paper significantly contributes to the theoretical physics community by refining gravitational conjectures and incorporating intricate numerical validation, ultimately enhancing our grasp of quantum gravity dynamics and the structure of fundamental forces within the universe.