  We show that the global fluctuations of spectra of GOE and GUE matrices and
their principal submatrices executing Dyson's Brownian motion are Gaussian in
the limit of large matrix dimensions. For nested submatrices one obtains a
limiting three-dimensional generalized Gaussian process; its restrictions to
two-dimensional sections that are monotone in matrix sizes and time moments
coincide with the two-dimensional Gaussian Free Field with zero boundary
conditions. The proof is by moment convergence, and it extends to more general
Wigner matrices and their stochastic evolution.
