关于${\cal N}=8$超引力中天体软对称代数的进一步研究
More on the Celestial Soft Symmetry Algebra in the ${\cal N}=8$ Supergravity
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中文总结 AI 辅助
本文通过构造${\cal N}=8$超引力中${\rm w}_{1+\infty}$流与物质场的OPEs，重现并扩展了天体软对称代数，识别了扩展BMS代数及软定理。
中文摘要 AI 辅助
我们构造了${\cal N}=8$超引力中${\rm w}_{1+\infty}$流（由反全纯光变换获得）与物质场之间的算子乘积展开（OPEs）。相应的（反）对易子通过上述OPEs的双围道积分获得。通过计算由流-流-物质组成的三重（反）对易子（即固定最后元素的雅可比恒等式），我们重现了先前已知的这些流之间（在反全纯扇区中）的${\cal N}=8$天体软对称代数。我们通过取全纯光变换重复上述过程，并获得了${\cal N}=8$ ${\rm \bar{w}}_{1+\infty}$流与物质场的OPEs以及相应的（反）对易子。我们还获得了这些流之间（在全纯扇区中）另一种类型的${\cal N}=8$天体软对称代数。作为反全纯和全纯扇区中的子代数，存在${\cal N}=8$扩展BMS（Bondi, van der Burg, Metzner, and Sachs于1962年）代数。我们从反全纯（或全纯）扇区中的${\cal N}=8$共形{\it 软}${\rm w}_{1+\infty}$（或${\rm \bar{w}}_{1+\infty}$）流分析了上述结果。描述了引力子、引力微子和引力光子的非平凡软定理。最后，利用阴影变换（全纯和反全纯光变换的连续复合），我们获得了${\cal N}=8${\it 阴影}${\rm w}_{1+\infty}$（或${\rm \bar{w}}_{1+\infty}$）流与物质场的OPEs，其中识别了${\cal N}=8$扩展BMS代数的应力-能量张量、超流和超平移生成元。
英文摘要
We construct the operator product expansions (OPEs) of the ${\cal N}=8$ ${\rm w}_{1+\infty}$ currents (obtained from the antiholomorphic light transform) with the matter fields in the ${\cal N}=8$ supergravity. The corresponding (anti)commutators are obtained from the double contour integrals using the above OPEs. By computing the triple (anti)commutators consisting of current-current-matter (i.e., the Jacobi identity for fixed last element), the previously known ${\cal N}=8$ celestial soft symmetry algebra between these currents (in the antiholomorphic sector) is reproduced. We repeat the above procedure by taking the holomorphic light transform and the OPEs of the ${\cal N}=8$ ${\rm \bar{w}}_{1+\infty}$ currents with the matter fields and the corresponding (anti)commutators are obtained. We also obtain another type of ${\cal N}=8$ celestial soft symmetry algebra between these currents (in the holomorphic sector). As a subalgebra in the antiholomorphic and holomorphic sectors, there exists the ${\cal N}=8$ extended BMS (Bondi, van der Burg, Metzner, and Sachs in 1962) algebra. We analyze the above results from the ${\cal N}=8$ conformally {\it soft} ${\rm w}_{1+\infty}$ (or ${\rm \bar{w}}_{1+\infty}$) currents in the antiholomorphic (or holomorphic) sector. The nontrivial soft theorems for the graviton, the gravitinos and the graviphotons are described. Finally, using the shadow transform (the consecutive composition of holomorphic and antiholomorphic light transforms), we obtain the OPEs of the ${\cal N}=8$ {\it shadow} ${\rm w}_{1+\infty}$ (or ${\rm \bar{w}}_{1+\infty}$) currents with the matter fields where the stress-energy tensor, the supercurrents and the supertranslation generator of the ${\cal N}=8$ extended BMS algebra are identified.
发表机构
- Seoul National University of Science and Technology（首尔科学技术大学）
- Kyungpook National University（庆北国立大学）
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