U-dualities and Spin-lifts Predict New Codimension-Two Branes in String Theories

The fundamental symmetries governing string theory and its connection to gravity present a long-standing challenge for physicists, and new research sheds light on these intricate relationships. Vivek Chakrabhavi from the University of Pennsylvania, Arun Debray from the University of Kentucky, Markus Dierigl from CERN, and Jonathan J Heckman explore these symmetries through the lens of ‘U-dualities’, transformations connecting different theoretical descriptions of the same physics. Their work determines how these dualities extend to incorporate the behaviour of fermions, particles with intrinsic angular momentum, and predicts the existence of novel ‘reflection branes’, generalisations of recently discovered objects in string theory. By combining refined duality groups with a mathematical conjecture known as Swampland Cobordism, the team establishes properties of these branes, including how they interact and combine, potentially revealing deeper insights into the underlying structure of spacetime and gravity itself.

In Philadelphia, Pennsylvania, research into the U-dualities of maximally supersymmetric non-chiral supergravity theories provides strong constraints on the non-perturbative structure of quantum gravity. This work determines the Spin- and Pin-lifts of these dualities, extending their action to include fermionic degrees of freedom. This refinement allows access to non-supersymmetric sectors of low energy effective field theories, where bosonic and fermionic degrees of freedom are treated distinctly. By combining this refined understanding of duality groups with the Swampland Cobordism Conjecture, the research predicts the existence of new codimension-two branes, representing a natural generalization of existing theoretical frameworks.

Non-Invertible Symmetries and Topological Defects

This research investigates the deep connections between generalized symmetries, topological defects, and their mathematical foundations in areas like algebraic topology and differential geometry. A central focus lies on non-invertible symmetries, which are not described by standard group theory but by more exotic algebraic structures, and how these symmetries manifest as defects in physical theories. Researchers utilize tools from algebraic topology, including bordism, K-theory, and cohomology, to classify and understand these symmetries and defects, ensuring the consistency of the underlying physical models. The study explores higher-dimensional structures and classification problems, particularly concerning manifolds, to find consistent backgrounds for string theory and understand the possible realizations of these generalized symmetries. This work requires a deep understanding of both physics and mathematics, demonstrating the breadth and depth of knowledge needed to tackle these challenging problems. Specifically, researchers aim to find a mathematical description of non-invertible symmetries, classify topological defects, connect these symmetries and defects to the underlying geometry of spacetime, and ensure anomaly cancellation, a crucial requirement for consistent quantum field theories.

Codimension-Two Branes and Global Symmetry Breaking

Scientists have uncovered new constraints on the non-perturbative structure of maximally supersymmetric gravity theories, revealing a deeper understanding of their underlying principles. The research focuses on extending these theories to include fermionic degrees of freedom through Spin- and Pin-lifts of U-dualities, allowing exploration of non-supersymmetric sectors where bosons and fermions are treated distinctly. This refinement of duality groups predicts the existence of novel codimension-two branes, generalizing recently discovered R7-branes in type II string theories. The team determined that for dimensions up to seven, the relevant bordism groups vanish, indicating no need for additional codimension-two defects to break global symmetries within the theory.

However, for dimensions eight, nine, and twelve, the story changes, as the duality groups exhibit non-trivial Abelianization, leading to the prediction of new branes. Specifically, the research demonstrates that for dimensions three through seven, the bordism group ΩSpin-g GU + 1 (pt) equals Z2, predicting a reflection brane that effectively trivializes the corresponding bordism class. Further analysis reveals that in dimensions eight and nine, the Abelianization of the extended duality group is Z2 ⊕Z2, indicating the presence of two distinct generators and, consequently, two types of codimension-two branes. One is the previously identified reflection brane, while the other is a supersymmetric object characterized by a specific T2 fibration over a complex plane with a fixed complex structure. These findings suggest a rich landscape of branes arising from internal reflections on the torus, potentially reversing the orientation of internal dimensions under monodromy. The research establishes a framework for understanding these defects and their implications for the underlying gravity theories, opening avenues for further exploration of their properties and connections to string theory and F-theory constructions.

Spin- and Pin-lifts Reveal New Branes

This research extends the understanding of U-dualities, which describe relationships between different theoretical frameworks in quantum field theory and gravity. The team investigated how these dualities can be extended to include fermionic degrees of freedom, effectively refining the symmetry groups that govern these relationships. By considering these extensions, known as Spin- and Pin-lifts, the researchers gain insight into non-supersymmetric sectors of these theories, where supersymmetry, a symmetry linking bosons and fermions, is not preserved. The study leverages the Swampland Cobordism Conjecture, a recent proposal linking mathematical topology to the consistency of theoretical physics, to predict the existence of new codimension-two branes.

These branes represent extended objects within the theory and are a generalization of previously discovered R7-branes. The researchers established basic properties of these predicted branes, including how they interact with other objects and their potential configurations, revealing details about their stability and possible arrangements within the theoretical landscape. The authors acknowledge that their work focuses on qualitative predictions of new branes and does not provide a complete description of their dynamics. Future research could explore the precise properties of these branes and their role in more complex physical scenarios.