Two-matrix model with ABAB interaction

Using recently developed methods of character expansions we solve exactly in the large N limit a new two-matrix model of hermitian matrices A and B with the action S = 12 (tr A2 + tr B2) − α4 (trA4 + trB4) −β2 tr(AB)2. This model can be mapped onto a special case of the 8-vertex model on dynamical planar graphs. The solution is parametrized in terms of elliptic functions. A phase transition is found: the critical point is a conformal field theory with central charge c = 1 coupled to 2D quantum gravity.

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