  We revisit the idea that the quantum dynamics of open strings ending on $N$
D3-branes in the large $N$ limit can be described at large `t Hooft coupling by
classical closed string theory in the background created by the D3-branes in
asymptotically flat spacetime. We study the resulting thermodynamics and
compute the Hagedorn temperature and other properties of the D3-brane
worldvolume theory in this regime. We also consider the theory in which the
D3-branes are replaced by negative branes and show that its thermodynamics is
well behaved. We comment on the idea that this theory can be thought of as an
irrelevant deformation of $\mathcal{N}=4$ SYM, and on its relation to $T\bar T$
deformed $CFT_2$.
