Kyoto University Finds Quantum Symmetry Breaks Map to Bulk Wormholes

Kyoto University and University of Tokyo researchers have demonstrated a surprising link between a specific type of symmetry breaking and the theoretical structures of wormholes. The work centers on “strong-to-weak spontaneous symmetry breaking” (SWSSB), a critical phenomenon that, unlike traditional symmetry breaking, occurs only in mixed states like thermal ensembles. Researchers including Taishi Kawamoto demonstrate that SWSSB is realized through wormhole geometries connecting two copies within a using the BTZ black hole as a model. The researchers further propose a new swampland conjecture relating ensemble averages to quantum gravity theories, suggesting that statistical averaging may constrain viable theories of quantum gravity; they state that SWSSB can be “recast as an emergence of global symmetries under ensemble averaging.” This connection offers a geometric understanding of symmetry breaking within strongly-coupled quantum field theories.

Strong-to-Weak Symmetry Breaking in Mixed States

Recent work reveals a surprising connection between symmetry breaking and the fundamental nature of quantum states, challenging long-held assumptions about how order emerges in physical systems. This distinction is crucial because it ties SWSSB to systems commonly found in thermal ensembles and open quantum systems, expanding the scope of where this type of symmetry change can be observed. This suggests a deep link between abstract symmetry principles and the actual, albeit theoretical, structure of spacetime. This stems from their examination of the interplay between SWSSB and the swampland program, and a proposal for a new swampland conjecture for quantum-gravity theories involving ensemble averages.

The team’s analysis of Rényi-2 correlators and Wightman correlators, defined as overlaps between perturbed states, led to a conjecture: if a density matrix has no spontaneous symmetry breaking, then a specific equation relating correlation functions must hold. This conjecture, while awaiting rigorous proof, suggests a constraint on viable quantum gravity theories; a theory must accommodate the statistical behavior implied by SWSSB to avoid falling into the “swampland” of inconsistent models. The researchers emphasize that this connection extends beyond simple lattice systems, potentially applying to local quantum many-body systems, offering a new avenue for exploring the foundations of quantum gravity.

Beyond traditional symmetry breaking observed in pure quantum states, a more nuanced phenomenon is gaining attention: strong-to-weak spontaneous symmetry breaking, or SWSSB. This process, unique to mixed states like those encountered in thermal systems, is now being linked to the geometry of spacetime itself through sophisticated mathematical tools. Researchers, including Masahito Yamazaki at the University of Tokyo, are utilizing Rényi-2 and Wightman correlators, measures of state overlap, to detect and characterize SWSSB, revealing a surprising connection to wormhole geometries. Unlike conventional symmetry breaking where a unitary operator preserves the density matrix, SWSSB involves a breaking where the symmetry acts merely as a phase. Specifically, the researchers demonstrate that these correlators can reveal SWSSB even when conventional correlation functions show no long-range order, indicating a breakdown of symmetry in a way not seen in simpler systems. This detection method has profound implications for our understanding of gravity, suggesting that the emergence of wormholes, theoretical tunnels through spacetime, is directly linked to the presence of SWSSB.

The pursuit of a complete theory of quantum gravity receives an unexpected boost from investigations into symmetry breaking in condensed matter physics. This link, explored by Taishi Kawamoto and colleagues, suggests a novel constraint on what constitutes a viable quantum gravity theory, potentially narrowing the field of possibilities. The core of this research lies in understanding how symmetry breaks in systems described not by a single, definite state, but by a statistical mixture of states, a density matrix. Unlike traditional symmetry breaking occurring in pure states, SWSSB arises only in these mixed states, a critical distinction that highlights its unique character.

This distinction is not merely mathematical; the team’s analysis reveals a deep link between this type of symmetry breaking and the very fabric of reality, specifically through the existence of wormholes. This isn’t simply a mathematical curiosity; it suggests that the long-range order characterizing SWSSB physically manifests as these exotic spacetime structures. This connection extends to the broader swampland program, which seeks to identify which theoretical landscapes are consistent with quantum gravity. The researchers point out the interplay between SWSSB and the swampland program, and propose a new swampland conjecture for quantum-gravity theories involving ensemble averages. The implications are profound, potentially reshaping our understanding of how symmetry, entanglement, and spacetime itself are intertwined at the most fundamental level.