Abstract
We find a one-dimensional protected subsector of \( \mathcal{N} \) = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2 × S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general \( \mathcal{N} \) = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.
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Panerai, R., Pittelli, A. & Polydorou, K. Topological correlators and surface defects from equivariant cohomology. J. High Energ. Phys. 2020, 185 (2020). https://doi.org/10.1007/JHEP09(2020)185
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DOI: https://doi.org/10.1007/JHEP09(2020)185