Matteo Bertolini

A bstract: We investigate the symmetry structure of five-dimensional Yang-Mills theories with 𝔰𝔲( N ) gauge algebra. These theories feature intertwined 0-, 1-, and 2-form symmetries, depending on the global variant one is considering. In the SU( N ) theory, there is a mixed ’t Hooft anomaly between the instantonic 0-form symmetry and the electric 1-form symmetry. We show that in the PSU( N ) theory this translates into a ℤ _N extension of the instantonic symmetry, generated by an invertible condensation defect of the magnetic 2-form symmetry. We identify the charged configurations as linked ’t Hooft surfaces, while pointlike instanton operators remain insensitive to the extension. We generalize our analysis to the SU( N )/ℤ _k global form and show that similar results hold, embedded now in a 3-group structure for generic k . We then apply our findings to SO(3) supersymmetric Yang-Mills theory. We determine the global form of the enhanced instantonic symmetry of its superconformal UV completion, showing that it arises through a similar symmetry extension mechanism from the parent E ₁ theory, which is the UV completion of SU(2) supersymmetric Yang-Mills theory. Finally, we recast our results in the language of the symmetry topological field theory. As a warm-up, we also analyze Maxwell theory, highlighting analogous features involving continuous symmetries and composite currents.

Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.

We generalize recent results regarding the phase space of the mass deformed E₁ fixed point to a full class of five-dimensional superconformal field theories, known as X_1,N. As in the E₁ case, a phase transition occurs as a supersymmetry preserving and a supersymmetry breaking mass deformations are appropriately tuned. The order of such phase transition could not be unequivocally determined in the E₁ case. For X_1,N, instead, we can show that at large N there exists a regime where the phase transition is second order. Our findings give supporting evidence for the existence of non-supersymmetric fixed points in five dimensions.

We study (orientifolded) toric Calabi-Yau singularities in search for D-brane configurations which lead to dynamical supersymmetry breaking at low energy. By exploiting dimer techniques we are able to determine that while most realizations lead to a Coulomb branch instability, a rather specific construction admits a fully stable supersymmetry breaking vacuum. We describe the geometric structure that a singularity should have in order to host such a construction, and present its simplest example, the Octagon.