Large N reductions and holography

The large N reductions in gauge theories are identified with dimensional reductions with homogeneous distribution of the eigenvalues of the gauge fields, and it is used to identify the corresponding closed string descriptions in the Maldacena duality. When one does not take the zero-radii limit, the large N reductions are naturally extended to the equivalences between the gauge theories and the generalized reduced models, which naturally contain the notion of T-dual equivalence. In the dual gravitational description, T-duality relates two type IIB supergravity solutions, the near horizon geometry of D3-branes, and the near horizon geometry of D-instantons distributed densely and homogeneously on the dual torus. This is the holographic description of the generalized large N reductions.