  We compute the curvature of the determinant line bundle on a family of Dirac
operators for a noncommutative two torus. Following Quillen's original
construction for Riemann surfaces and using zeta regularized determinant of
Laplacians, one can endow the determinant line bundle with a natural Hermitian
metric. By using an analogue of Kontsevich-Vishik canonical trace, defined on
Connes' algebra of classical pseudodifferential symbols for the noncommutative
two torus, we compute the curvature form of the determinant line bundle by
computing the second variation $\delta_{w}\delta_{\bar{w}}\log\det(\Delta)$.
