Abstract
Using the recently established classification of 6D SCFTs we present evidence for the existence of families of weak C-functions, that is, quantities which decrease in a flow from the UV to the IR. Introducing a background R-symmetry field strength R, and a non-trivial tangent bundle T on the 6D spacetime, we consider C-functions given by the linear combinations C = m 1α + m 2 β + m 3γ, where the αi are the anomaly polynomial coefficients for the formal characteristic classes c 2(R)2, c 2(R)p 1(T ) and p 1(T )2. By performing a detailed sweep over many theories, we determine the shape of the unbounded region in “m-space” compatible with both Higgs branch flows and tensor branch flows. We also verify that — as expected — the Euler density conformal anomaly falls in the admissible region.
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Heckman, J.J., Rudelius, T. Evidence for C-theorems in 6D SCFTs. J. High Energ. Phys. 2015, 218 (2015). https://doi.org/10.1007/JHEP09(2015)218
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DOI: https://doi.org/10.1007/JHEP09(2015)218