Shaping up BPS states with matrix model saddle points

DIEGO H. CORREA; MARTIN WOLF

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Año: 2010 vol. 43 p. 465402 - 465425

1751-8113

We provide analytical results for the probability distribution of a family ofwavefunctions of a quantum mechanics model of commuting matrices in thelarge-N limit. These wavefunctions describe the strong coupling limit of 1/8BPS states of N = 4 supersymmetric Yang–Mills theory. In the large-Nlimit, they should be dual to classical solutions of type IIB supergravity thatasymptotically approach AdS5 × S5. Each probability distribution can bedescribed as the partition function of a matrix model (different wavefunctionscorrespond to different matrix model potentials) which we study by meansof a saddle point approximation. These saddle point solutions are given interms of (five-dimensional) hypersurfaces supporting density distributions ofeigenvalues.