  We investigate the spectrum of the Dirac operator with infinite mass boundary
conditions posed in a tubular neighborhood of a smooth compact hypersurface in
$\mathbb{R}^n$ without boundary. We prove that when the tubular neighborhood
shrinks to the hypersurface, the asymptotic behavior of the eigenvalues is
driven by a Schr\"odinger operator involving electric and Yang-Mills
potentials, both of geometric nature.
