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# Interpolating between a and F

@inproceedings{Giombi2015InterpolatingBA, title={Interpolating between a and F}, author={Simone Giombi and Igor R. Klebanov}, year={2015} }

- Published 2015

We study the dimensional continuation of the sphere free energy in conformal field theories. In continuous dimension d we define the quantity F̃ = sin(πd/2) logZ, where Z is the path integral of the Euclidean CFT on the d-dimensional round sphere. F̃ smoothly interpolates between (−1)d/2π/2 times the a-anomaly coefficient in even d, and (−1)(d+1)/2 times the sphere free energy F in odd d. We calculate F̃ in various examples of unitary CFT that can be continued to non-integer dimensions… CONTINUE READING