We calculate the two-loop correction to the dispersion relation for worldsheet modes of the BMN string in AdS(n) x S(n) x T(10-2n) for n=2,3,5. For the massive modes the result agrees with the exact dispersion relation derived from symmetry considerations with no correction to the interpolating function h. For the massless modes in AdS(3) x S(3) x T(4) however our result does not match what one expects from the corresponding symmetry based analysis. We also derive the S-matrix for massless modes up to the one-loop order. The scattering phase is given by the massless limit of the Hernandez-Lopez phase. In addition we compute a certain massless S-matrix element at two loops and show that it vanishes suggesting that the two-loop phase in the massless sector is zero.

翻译：在 AdS(n) x S(n) x S(n) x T(10-2n) x T(10-2n) 中,我们计算出在 n= 2,3,5的 BMN 字符串世界表模式的散射关系的双环校正。对于大型模式,结果与对称考虑产生的确切散射关系一致,对内插函数没有纠正 h。对于AdS(3) x S(3) x T(4) 中的无质量模式,我们计算得出的结果与相应的对称分析所预期的不符。我们还得出了无质量模式的S矩阵,直到单圈顺序。散射阶段由Hernandez-Lopez 级的无质量限制给出。此外,我们在两个圆圈中计算了某种无质量的S-matrix元素,并显示它消失了表明无质量部门中的两环相位为零。