Abstract
We study a system of N D2-branes probing a generic Calabi-Yau three-fold singularity in the presence of a non-zero quantized Romans mass n. We argue that the low-energy effective c \( \mathcal{N}=2 \) Chern-Simons quiver gauge theory flows to a superconformal fixed point in the IR, and construct the dual AdS4 solution in massive IIA supergravity. We compute the free energy F of the gauge theory on S 3 using localization. In the large N limit we find F = c (nN )1/3 a 2/3, where c is a universal constant and a is the a-function of the “parent” four-dimensional \( \mathcal{N}=1 \) theory on N D3-branes probing the same Calabi-Yau singularity. It follows that maximizing F over the space of admissible R-symmetries is equivalent to maximizing a for this class of theories. Moreover, we show that the gauge theory result precisely matches the holographic free energy of the supergravity solution, and provide a similar matching of the VEV of a BPS Wilson loop operator.
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ArXiv ePrint: 1507.05817
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Fluder, M., Sparks, J. D2-brane Chern-Simons theories: F -maximization = a-maximization. J. High Energ. Phys. 2016, 48 (2016). https://doi.org/10.1007/JHEP01(2016)048
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DOI: https://doi.org/10.1007/JHEP01(2016)048