| Summary: | Abstract We study M5-branes compactified on S 1 from the D0-D4 Witten index in the Coulomb phase. We first show that the prepotential of this index is S-dual, up to a simple anomalous part. This is an extension of the well-known S-duality of the 4d N=4 $$ \mathcal{N}=4 $$ theory to the 6d (2, 0) theory on finite T 2. Using this anomalous S-duality, we find that the asymptotic free energy scales like N 3 when various temperature-like parameters are large. This shows that the number of 5d Kaluza-Klein fields for light D0-brane bound states is proportional to N 3. We also compute some part of the asymptotic free energy from 6d chiral anomalies, which precisely agrees with our D0-D4 calculus.
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