Squashing, mass, and holography for 3d sphere free energy

A bstract We consider the sphere free energy F ( b ; m I ) in $$ \mathcal{N} N = 6 ABJ(M) theory deformed by both three real masses and squashing parameter , which has been computed terms of an N dimensional matrix model integral using supersymmetric localization. show that setting {m}_3=i\frac{b-{b}^{-1}}{2} m 3 = i b − 1 2 relates to round energy, implies infinite relations between derivatives evaluated at 0 1. For 8 theory, these fix all fourth order some fifth 1 2 were previously orders /N Fermi gas method. This allows us compute {\partial}_b^4F\left|{}_{b=1}\right. ∂ 4 F {\partial}_b^5F\left|{}_{b=1}\right. 5 we precisely match a recent prediction sub-leading from holographically dual AdS 4 bulk theory.