Abstract
We study and compute supersymmetric observables for line defects in 3d \( \mathcal{N} \) ≥ 4 theories. Our setup is a novel supersymmetric configuration involving line operators and local operators living on a linked circle. The algebra of the local operators is described by a topological quantum mechanics. For operators belonging to conserved current multiplets, we propose an exact formula for their correlation functions based on a Ward identity for integrated correlators. Our formula gives a general recipe to compute the bremsstrahlung function for any \( \frac{1}{3} \)-BPS lines in \( \mathcal{N} \) = 6 SCFTs. We apply our relation to the \( \frac{1}{2} \)-BPS Wilson loop in the ABJM model, showing the validity of previous computations. Furthermore, our construction allows us to explore higher points correlators. As an example, we compute the two-point function of the stress tensor multiplet correlators in ABJM theory in the presence of the Wilson line. We also present some perturbative checks of our formulae.
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Acknowledgments
It is a pleasure to thank Luca Griguolo, Domenico Seminara, Itamar Yaakov, and Stefano Cremonesi for interesting discussions and useful insights. We are especially grateful to Luca Griguolo and Itamar Yaakov for useful comments on the draft. We also thank the Department of Mathematical Sciences at Durham University and its faculty members for hospitality, discussions, and feedback when presenting this work in the local journal club. This work has been supported in part by Della Riccia Foundation, Italian Ministero dell’Università e Ricerca (MUR), and by Istituto Nazionale di Fisica Nucleare (INFN) through the “Gauge Theories, Strings, Supergravity” (GSS) and “Gauge and String Theory” (GAST) research projects.
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Guerrini, L. On protected defect correlators in 3d \( \mathcal{N} \) ≥ 4 theories. J. High Energ. Phys. 2023, 100 (2023). https://doi.org/10.1007/JHEP10(2023)100
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DOI: https://doi.org/10.1007/JHEP10(2023)100