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The global symmetries of a $D$ -dimensional quantum field theory (QFT) can, in many cases, be captured in terms of a ( $D+1$ )-dimensional symmetry topological field theory (SymTFT). In this work we construct a ( $D+1$ )-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large $M$ averaging where the topological sectors of different large $M$ replicas become dressed by additional extended operators associated with the SymTree. Published by the American Physical Society 2024

Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes with links given by conformal matter; a strongly coupled generalization of a bifundamental hypermultiplet. For theories obtained from M5-branes probing an ADE singularity, this was recently leveraged to extract a protected large R-charge subsector of operators, with operator mixing controlled at leading order in an inverse large R-charge expansion by an integrable spin s Heisenberg spin chain, where s is determined by the $$\mathfrak{su}$$(2)_R R-symmetry representation of the conformal matter operator. In this work, we show that this same structure extends to the full superconformal algebra $$\mathfrak{osp}$$(6, 2|1). In particular, we determine the corresponding Bethe ansatz equations which govern this super-spin chain, as well as distinguished subsectors which close under operator mixing. Similar considerations extend to 6D little string theories (LSTs) and 4D $$\mathscr{N}$$ = 2 SCFTs with the same generalized quiver structures.

We consider all 4D N = 2 theories of class S arising from the compactification of exceptional 6D (2, 0) SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4D theories has another origin as a 6D (1, 0) SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6D theory is identified with a complex structure deformation of (e_n,e_n) minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure is precisely replicated by the partial closure of the punctures in the class S construction. We explain how the plurality of origins makes manifest some aspects of 4D SCFTs, including flavor symmetry enhancements and determining if it is a product SCFT. We further highlight the string theoretic basis for this identification of 4D theories from different origins via mirror symmetry.

We use the numerical conformal bootstrap to study six-dimensional $$\mathscr{N}$$ = (1,0) superconformal field theories with flavor symmetry so_4k We present evidence that minimal ($$D_k,D_k$$) conformal matter saturates the unitarity bounds for arbitrary k. Furthermore, using the extremal-functional method, we check that the chiral-ring relations are correctly reproduced, extract the anomalous dimensions of low-lying long superconformal multiplets, and find hints for novel operator product expansion selection rules involving type-$$\mathscr{B}$$ multiplets.

We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. Accordingly, we consider complex structure deformations of elliptic fibrations with a Mordell-Weil group of rank one and identify the conditions under which the generating section becomes torsional. In the specific case of Ζ₂ torsion we construct the generic solution to these conditions and show that the associated F-theory compactification exhibits the global gauge group [SU₍₂₎ × SU₍₄₎]/Ζ₂ × SU₍₂₎. The subsolution with gauge group SU₍₂₎/Ζ₂ × SU₍₂₎, for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian has a Ζ₂ torsional section. While an analysis of the spectrum on the Jacobian fibration reveals an SU₍₂₎/Ζ₂ × Ζ₂ gauge theory, reproducing this result from the bisection geometry raises some conceptual puzzles about F-theory on genus-one fibrations.