Gaillard-zumino Models Exhibit Infinite Non-Invertible Symmetries Surviving Beyond Integral Subgroup Level

The fundamental symmetries governing physical laws are now understood to be far more subtle than previously thought, and new research reveals a surprising resilience in symmetries once considered broken. Fabio Apruzzi from the University of Padova and Luca Martucci, also at the University of Padova, alongside their colleagues, demonstrate the existence of an infinite class of non-invertible symmetries within models originally studied by Gaillard and Zumino. These symmetries, which act on electric and magnetic fields, persist despite expectations to the contrary, manifesting instead through unusual defects in the system. This discovery challenges conventional understanding of symmetry breaking and opens new avenues for exploring the underlying structure of fundamental forces, potentially impacting areas such as string theory and supergravity.

Non-Invertible Symmetries in Gaillard-Zumino Models

Scientists have uncovered an infinite class of novel zero-form non-invertible symmetries within a broad family of four-dimensional models, initially studied decades ago, which includes several extended supergravities as specific instances. These models feature abelian gauge fields coupled to a neutral sector containing scalars, leading to a peculiar structure of the symmetry transformations. These symmetries are non-invertible, meaning their generators do not have well-defined inverses, profoundly impacting the consistency and interpretation of the underlying physical theory. This discovery expands the landscape of possible consistent quantum field theories and provides new insights into duality and topological order, potentially leading to the discovery of novel exotic states with unusual properties.

Non-Invertible Symmetries and Defect Interactions

The study investigates an infinite class of non-invertible symmetries within four-dimensional models originally explored by Gaillard and Zumino, which encompass extended supergravities. These models feature abelian gauge fields coupled to a neutral sector containing scalars, exhibiting classical invariance under continuous transformations acting on electric and magnetic field strengths. Contrary to established understanding, the research demonstrates that a significantly larger subgroup of these symmetries survives through non-invertible defects. Scientists explicitly constructed these defects and determined their fusion rules, providing a detailed map of their interactions.

The research involved examining how these non-invertible symmetries manifest as topological defects, boundaries or singularities in the field configuration. To characterize these defects, the team developed a method for analyzing their action on line defects, one-dimensional topological objects. This involved constructing interfaces between regions of spacetime where the symmetry is broken differently, pioneering the use of integral coprime matrix factorizations to describe these interfaces. Furthermore, scientists investigated how these non-invertible symmetries can be broken by gauging the invertible subgroup, revealing the conditions under which the symmetry is lost.

The team also explored the bulk origin of minimal topological quantum field theories and C interfaces, providing a deeper understanding of the underlying physics. The research employed half-space gauging, imposing boundary conditions on the fields, to construct interfaces and analyze their properties. This method connected the non-invertible symmetries to the behavior of the system at its boundaries. By carefully analyzing the action of these defects on line operators, the team demonstrated how the non-invertible symmetries manifest themselves in observable quantities, providing a new perspective on the symmetry structure of these models and implications for quantum gravity and string theory.

Non-Invertible Symmetries in Four-Dimensional Models

Scientists have uncovered an infinite class of novel zero-form non-invertible symmetries within a broad family of four-dimensional models, initially studied decades ago, which encompass several extended supergravities as specific instances. These models feature abelian gauge fields coupled to a neutral sector, often including scalars, and classically exhibit invariance under a continuous group acting on electric and magnetic field strengths. Contrary to established understanding, the research demonstrates that a significantly larger subgroup of these symmetries survives, albeit realized through non-invertible defects. The team explicitly constructed these defects and characterised their fusion rules, providing concrete examples using the axion-dilaton-Maxwell model and the bosonic sector of supergravities arising in type II Calabi-Yau compactifications.

Analysis reveals that when gravity is decoupled, the full subgroup of rational Gaillard-Zumino symmetries remains unbroken, with rational but non-integral symmetries realized by these non-invertible topological defects. The τ-Maxwell model, where scalars parameterize cosets G/K, serves as a simple instance of a large class of Gaillard-Zumino models, including extended supergravities with symmetry groups such as E7(7) and SL(2, R)×SO(6, 6+n). Measurements confirm the existence of these symmetries even in models with axionic shift symmetries, commonly found in perturbative type IIA Calabi-Yau compactifications. The research provides a novel perspective on duality symmetries, potentially offering insights into ultraviolet divergences within extended supergravities and encoding low-energy target space manifestations of O(d, d; Q) world-sheet topological interfaces. Furthermore, the work suggests a connection to string theory realizations, potentially offering frameworks to test qualitative ideas related to symmetry breaking and the Swampland program. The team emphasizes that while most Gaillard-Zumino models are low-energy effective field theories, they may admit a UV completion characterized by a group of invertible and non-invertible zero-form global symmetries.

Non-Invertible Symmetries in Four-Dimensional Models

This research establishes the existence of an infinite class of novel, non-invertible symmetries within a broad family of four-dimensional models originally studied decades ago. These models, incorporating abelian gauge fields and neutral scalar fields, are typically understood to possess symmetries broken down to an integral subgroup; however, this work demonstrates that a much larger symmetry group survives, albeit manifested through non-invertible defects. The team explicitly constructed these defects and characterised their fusion rules, providing concrete examples using the axion-dilaton-Maxwell model and bosonic sectors of supergravity theories arising from Calabi-Yau compactifications. The discovery significantly expands the understanding of symmetry in quantum field theory, moving beyond traditional invertible symmetries to encompass those associated with topological defects lacking inverses. This framework identifies global symmetries with extended topological defects, revealing a richer landscape of symmetries than previously recognised.