Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-02-09
JHEP 0712:004,2007
Physics
High Energy Physics
High Energy Physics - Theory
24 pages, harvmac; v2 reference added
Scientific paper
10.1088/1126-6708/2007/12/004
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 $N$ coincident M2 branes. We obtain our partition function by performing the radial quantization of the Coulomb Branches of these theories, and rederive the same formula from the quantization of supersymmetric giant and dual giant gravitons in $AdS_7 \times S^4$ and $AdS_4 \times S^7$. Our partition function is qualitatively similar to the analogous quantity in ${\cal N}=4$ Yang Mills. It reduces to the sum over supersymmetric multi gravitons at low energies, but deviates from this supergravity formula at energies that scale like a positive power of $N$.
Bhattacharyya Sayantani
Minwalla Shiraz
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