Before revision:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed  .
After revision:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), we show that the integrality gap implies that branch-and-bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed .