Supersymmetric states in M5/M2 CFTs

We propose an exact, finite $N$ formula for the partition function over$1/4^{th}$ BPS states in the conformal field theory on the world volume of $N$coincident M5 branes and $1/8^{th}$ BPS states in the theory of $N$ coincidentM2 branes. We obtain our partition function by performing the radialquantization of the Coulomb Branches of these theories, and rederive the sameformula from the quantization of supersymmetric giant and dual giant gravitonsin $AdS_7 \times S^4$ and $AdS_4 \times S^7$. Our partition function isqualitatively similar to the analogous quantity in ${\cal N}=4$ Yang Mills. Itreduces to the sum over supersymmetric multi gravitons at low energies, butdeviates from this supergravity formula at energies that scale like a positivepower of $N$.Comment: 24 pages, harvmac; v2 reference adde