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Global Aspects of Strongly-Coupled Gauge Theories

par Vandepopeliere, Romain
Président du jury Clerbaux, Barbara
Promoteur Argurio, Riccardo
Publication Non publié, 2025-05-23

Thèse de doctorat

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Résumé :

The rich structure of generalized symmetries, encompassing higher-form and non- invertible symmetries, plays a pivotal role in shaping the phase dynamics of strongly-coupled gauge theories. Also, many of the non-perturbative phenomena observed in such models including confinement, chiral symmetry breaking, and domain wall dynamics, are influenced by the global structure of the gauge group and its spectrum of extended operators. This motivates a careful investigation of global variants and the associated topological features, as these aspects cannot be fully captured by the local dynamics dictated solely by the gauge Lie algebra.The thesis begins with a review of the essential ingredients needed to develop the research work. We first present an introduction to generalized symmetries and the key notions that extend the classification of phases in quantum field theory (QFT). We also highlight the way non-invertible symmetries can naturally emerge in QFT. We then examine how the global structure of the gauge group impacts the spectrum of line operators, introducing the concept of global variants in non- abelian gauge theories. Finally, we explore dualities and self-duality symmetries.Then, the original material is presented. First, we apply these ideas to non- abelian gauge theories with fermions in representations that leave a Z_2 electric 1-form symmetry intact. We analyze the mixed ’t Hooft anomaly between the discrete axial symmetry and the 1-form symmetry, demonstrating that in the presence of a non-trivial anomaly, the gauging of the 1-form symmetry generates non-invertible symmetry defects. Such a pattern provides valuable insights into the low-energy physics realized in the vacua of the gauged theory. Our investi- gation further reveals that the topological field theory dressing these defects is universal, and that its emergence depends closely on the rank of the gauge group.In a second line of research, we explore the interplay between supersymmetric gauge theories and integrable systems. We focus on the N = 1* theory, which is a massive deformation of N = 4 Super Yang-Mills that exhibits a rich spectrum of discrete vacua, and the elliptic Calogero–Moser integrable system. Upon com- pactification on R3 ×S1, the vacua of the gauge theory correspond to the extrema of the integrable system. To ensure that this correspondence holds beyond the level of the Lie algebra, we introduce a notion of global variant for the integrable system. This refined matching clarifies how topological data in the gauge the- ory manifest itself in the structure and symmetries of the associated many-body system. Since the integrable model provides a better-controlled framework, this correspondence also enables us to extract non-perturbative information about the gauge theory vacua.