Identify a general degrees-of-freedom measure for generic d-dimensional QFTs

Determine a universally applicable quantity, analogous to F in conformal field theories, that quantifies the number of degrees of freedom for a generic d-dimensional quantum field theory and can serve as a meaningful C-function along renormalization group flows in continuous dimension.

Background

The thesis reviews how the universal part of the sphere free energy F is used to count degrees of freedom for conformal field theories in continuous dimensions and to compare UV and IR fixed points. While F works well for CFTs (interpolating between the Weyl anomaly in even d and the free energy in odd d), there is no established analogue for generic interacting QFTs away from fixed points.

The authors explicitly note that a general prescription for such a measure in arbitrary dimension remains unknown, highlighting a gap in our understanding of how to characterize degrees of freedom and monotonicity along RG flows outside fixed points.