Abstract
Via a challenging field-theory computation, we confirm a supergravity prediction for the non-supersymmetric D3-D7 probe-brane system with probe geometry AdS4 ×S2 ×S2, stabilized by fluxes. Supergravity predicts, in a certain double-scaling limit, the value of the one-point functions of chiral primaries of the dual defect version of \( \mathcal{N}=4 \) SYM theory, where the fluxes translate into SO(3) × SO(3)-symmetric, Lie-algebra-valued vacuum expectation values for all six scalar fields. Using a generalization of the technique based on fuzzy spherical harmonics developed for the related D3-D5 probe-brane system, we diagonalize the resulting mass matrix of the field theory. Subsequently, we calculate the planar one-loop correction to the vacuum expectation values of the scalars in dimensional reduction and find that it is UV finite and non-vanishing. We then proceed to calculating the one-loop correction to the planar one-point function of any single-trace scalar operator and explicitly evaluate this correction for a 1/2-BPS operator of length L at two leading orders in the double-scaling limit, finding exact agreement with the supergravity prediction.
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Grau, A.G., Kristjansen, C., Volk, M. et al. A quantum check of non-supersymmetric AdS/dCFT. J. High Energ. Phys. 2019, 7 (2019). https://doi.org/10.1007/JHEP01(2019)007
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DOI: https://doi.org/10.1007/JHEP01(2019)007