Swampland Conjecture Linked to Quantum Complexity Freezing

Amin Faraji Astaneh and Reza Ghomi Shurkaie of Sharif University of Technology, an and b, have linked the behavior of quantum complexity to a fundamental challenge in theoretical physics known as the Weak Gravity Conjecture. Their work demonstrates that as a charged black hole approaches its theoretical limit, an AdS Reissner, Nordström black hole, a “freezing” of Krylov spread complexity occurs, effectively halting the spread of the dual quantum state in what researchers call Krylov space. This cessation of nontrivial dynamics is then lifted once the discharge channel is opened, restoring the quantum state’s ability to evolve. The researchers suggest this dynamic offers a complexity-based interpretation of the Weak Gravity Conjecture, positing that the conjecture may require the absence of this exact freezing when a discharge channel is available. This analysis points to a new connection between the swampland program, black-hole physics, and quantum information theory.

Krylov Complexity and the Weak Gravity Conjecture

An unexpected freezing of quantum state complexity near black holes offers a novel lens through which to examine the Weak Gravity Conjecture, a long-standing puzzle in theoretical physics. “In this regime, the return amplitude becomes effectively a pure phase, and the dual quantum state ceases to spread nontrivially in Krylov space,” the researchers write, detailing how the system’s ability to evolve in a complex manner is suppressed as the black hole approaches extremality. This “freezing” is quantified by examining the return amplitude, which becomes dominated by a single phase, indicating a lack of complex evolution. However, this frozen state isn’t absolute. The researchers incorporated the effects of charged matter and modeled Schwinger pair production, the creation of particle-antiparticle pairs, near the black hole’s event horizon. “Within this semiclassical near-extremal analysis, the frozen behavior is lifted once the discharge channel is opened, and the dynamics become nontrivial again,” they explain.

This suggests that the creation of these particles acts as a catalyst, restoring the complexity of the quantum state and allowing it to evolve once more. This interplay between freezing and unfreezing leads to a proposed interpretation of the Weak Gravity Conjecture; the team suggests that the conjecture can be understood as a requirement for this complexity to not freeze completely when a mechanism for dissipating charge is available. Current investigations into quantum gravity increasingly focus on connections between disparate fields, including the swampland program and black hole physics informed by quantum information theory.

Researchers are actively seeking shared diagnostic tools to assess the consistency of quantum gravity theories, and a new approach leverages Krylov complexity to examine these constraints. “This suggests that the Weak Gravity Conjecture may admit a complexity-based interpretation in terms of the absence of exact freezing in the presence of an available discharge channel.” Ultimately, this research points towards a deeper connection between the swampland program, black hole physics, and the fundamental principles of quantum information theory, potentially offering new avenues for exploring the landscape of consistent quantum gravity theories.

Sharif University of Technology researchers are employing quantum information theory to probe the boundaries of gravitational physics, specifically examining the behavior of black holes nearing their theoretical limits. Their work centers on the AdS Reissner, Nordström black hole, a theoretical construct existing within Anti-de Sitter space, and its holographic dual, a charged thermofield double state, allowing them to probe the near-extremal regime.

The conventional picture of an extremal black hole, one at the theoretical limit of its charge, suggests a static, frozen existence. However, recent work challenges this notion, revealing a surprising link between particle creation and the fundamental complexity of the black hole’s quantum state.

A quantum state spreading occurs within a specific holographic model mirroring an electrically charged AdS Reissner, Nordström black hole as it nears a theoretical limit, revealing a surprising connection between gravity and quantum information. The researchers, working within the framework of the AdS/CFT correspondence, explored the behavior of a charged thermofield double state, a quantum construct allowing them to probe the near-extremal regime, to understand how the approach to extremality impacts the spread of quantum information.