Abstract
We consider the sphere free energy F(b; mI) in \( \mathcal{N} \) = 6 ABJ(M) theory deformed by both three real masses mI and the squashing parameter b, which has been computed in terms of an N dimensional matrix model integral using supersymmetric localization. We show that setting \( {m}_3=i\frac{b-{b}^{-1}}{2} \) relates F(b; mI) to the round sphere free energy, which implies infinite relations between mI and b derivatives of F(b; mI) evaluated at mI = 0 and b = 1. For \( \mathcal{N} \) = 8 ABJ(M) theory, these relations fix all fourth order and some fifth order derivatives in terms of derivatives of m1, m2, which were previously computed to all orders in 1/N using the Fermi gas method. This allows us to compute \( {\partial}_b^4F\left|{}_{b=1}\right. \) and \( {\partial}_b^5F\left|{}_{b=1}\right. \) to all orders in 1/N, which we precisely match to a recent prediction to sub-leading order in 1/N from the holographically dual AdS4 bulk theory.
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Chester, S.M., Kalloor, R.R. & Sharon, A. Squashing, mass, and holography for 3d sphere free energy. J. High Energ. Phys. 2021, 244 (2021). https://doi.org/10.1007/JHEP04(2021)244
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DOI: https://doi.org/10.1007/JHEP04(2021)244