Duality and integrability of a supermatrix model with an external source

@article{Kimura2014DualityAI,
  title={Duality and integrability of a supermatrix model with an external source},
  author={Taro Kimura},
  journal={Progress of Theoretical and Experimental Physics},
  year={2014},
  volume={2014}
}
  • Taro Kimura
  • Published 2 October 2014
  • Mathematics
  • Progress of Theoretical and Experimental Physics
We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the duality between the characteristic polynomial and the external source with an arbitrary matrix potential function. We also show that the supermatrix integral satisfies the one and two dimensional Toda lattice equations as well as the ordinary matrix model. 
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