Exact Solution of Induced Lattice Gauge Theory at Large $N$

Physics – High Energy Physics – High Energy Physics - Lattice

Scientific paper

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PUPT-1323

Scientific paper

10.1142/S0217732393000374

We find the exact solution of a recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation at $ N= \infty $ for arbitrary dimension $D$. The nonlinear integral equation for the gauge invariant density of eigenvalues of the vacuum average of the scalar field is derived. In the continuum limit, the density grows as $ \phi^{\alpha} $ where $ \alpha = 1 + \frac{1}{\pi}\arccos\frac{D}{3D-2} $.

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