present note in which we discuss the consequences for the physics of the BMN correspondence. In string theory single-string states $|(n,-n)p^+\ra$ with $n>1$ would be expected to be unstable, with decay to the continuum of $(k+1)$-string states $|(m,-m)p_0^+,p_1^+,\cdots p_k^+\>$ in which the total light cone momentum is divided continuously among the $k+1$ strings. The lowest case $k=1$ should correspond to single/double trace mixing in gauge theory, and it has been shown [@unp] that the relevant string theory matrix element vanishes at order $g_2$ in agreement with the vanishing gauge theory result mentioned above. Instability would then be expected in string theory via a composite (order $g_2^2$) process in which the single string first splits into two “virtual” strings and by a further interaction into three final state strings. The non-vanishing single/triple trace mixing matrix element, which is also composite in a sense described below, is the signal of this instability in gauge theory.

More generally the gauge theory has discrete single-trace states $\co^J_n$ embedded in a continuum of multi-traces, since the ratios $J_i/J$ become continuous variables with range 0 to 1 in the BMN limit. It is a well known phenomenon in quantum mechanics that a state which is purely 