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arXiv 1706.09381hep-th
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双圈超对称QCD和半最大超重力振幅

Two-loop supersymmetric QCD and half-maximal supergravity amplitudes

Henrik Johansson, Gregor Kälin, Gustav Mogull

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53 pages, 5 figures, 1 table + appendices, ancillary files; v2 published version
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摘要：

利用颜色和运动学之间的对偶性，我们构造了耦合到$N_f$基本超多重态的$\mathcal{N}=2$ super-Yang-Mills（SYM）理论中的两圈四点散射振幅.我们的结果在$D\le 6$维数下是有效的，其上界对应于六维手征$\mathcal{N}=(1,0)$ SYM理论.通过利用与$\mathcal{N}=4$ SYM理论的密切联系-以及等价的六维$\mathcal{N}=(1,1)$ SYM理论-我们发现了在最大螺旋度违反（MHV）和全手征矢量扇区中具有四维外部矢量的紧凑被积体。通过双拷贝构造，在MHV扇区和全手征扇区得到了相应的$D$维半极大超引力振幅和外部引力子多重态。适当地调整$N_f$使我们能够考虑纯超引力和物质耦合超引力，在$D=4$中具有任意数量的矢量多重态。另外，我们还得到了真六维超引力与$\mathcal{N}=(1,1)$和$\mathcal{N}=(2,0)$超对称的被积函数。最后，我们提取了$D=5-2ε$中半极大超引力的潜在紫外发散，并表明它与预期的一样非平凡地抵消了。

英文摘要：

Using the duality between color and kinematics, we construct two-loop four-point scattering amplitudes in $\mathcal{N}=2$ super-Yang-Mills (SYM) theory coupled to $N_f$ fundamental hypermultiplets. Our results are valid in $D\le 6$ dimensions, where the upper bound corresponds to six-dimensional chiral $\mathcal{N}=(1,0)$ SYM theory. By exploiting a close connection with $\mathcal{N}=4$ SYM theory - and, equivalently, six-dimensional $\mathcal{N}=(1,1)$ SYM theory - we find compact integrands with four-dimensional external vectors in both the maximally-helicity-violating (MHV) and all-chiral-vector sectors. Via the double-copy construction corresponding $D$-dimensional half-maximal supergravity amplitudes with external graviton multiplets are obtained in the MHV and all-chiral sectors. Appropriately tuning $N_f$ enables us to consider both pure and matter-coupled supergravity, with arbitrary numbers of vector multiplets in $D=4$. As a bonus, we obtain the integrands of the genuinely six-dimensional supergravities with $\mathcal{N}=(1,1)$ and $\mathcal{N}=(2,0)$ supersymmetry. Finally, we extract the potential ultraviolet divergence of half-maximal supergravity in $D=5-2ε$ and show that it non-trivially cancels out as expected.

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