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<p>We consider the S-matrix of transverse scalar excitations on an infinite <i>D</i> = 10 GS superstring and <i>D</i> = 11 supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the <i>D</i> = 10 GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.</p>

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2-loop scattering on superstring and supermembrane in flat space

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月24日

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  • M. Beccaria,
  • R. Roiban,
  • A. A. Tseytlin

摘要

We consider the S-matrix of transverse scalar excitations on an infinite D = 10 GS superstring and D = 11 supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the D = 10 GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.