Witten index of BMN matrix quantum mechanics

We compute the Witten index of the Berenstein-Maldacena-Nastase matrix quantum mechanics, which counts the number of ground states as well as the difference between the numbers of bosonic and fermionic BPS states with nonzero angular momenta. The Witten index sets a lower bound on the entropy, which exhibits N^2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>N</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> growth that provides strong evidence for the existence of BPS black holes in M-theory, asymptotic to the plane-wave geometry. We also discuss a relation between the Witten index in the infinite N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> </mml:math> limit and the superconformal index of the Aharony-Bergman-Jafferis-Maldacena theory.