  Exploiting insights on strings moving in pp-wave backgrounds, we show how
open strings emerge from N = 4 SU(M) Yang-Mills theory as fluctuations around
certain states carrying R-charge of order M. These states are dual to spherical
D3-branes of AdS_5 x S^5 and we reproduce the spectrum of small fluctuations of
these states from Yang Mills theory. When G such D3-branes coincide, the
expected G^2 light degrees of freedom emerge. The open strings running between
the branes can be quantized easily in a Penrose limit of the spacetime. Taking
the corresponding large charge limit of the Yang-Mills theory, we reproduce the
open string worldsheets and their spectra from field theory degrees of freedom.
