关于4维$\mathcal{N}$=4和6维(2,0)共形超重力及Poincaré超重力的紫外有限性
On anomaly free 4d $\mathcal{N}$=4 and 6d (2,0) conformal supergravities and UV finiteness of Poincaré supergravities
AI总结：
本文研究4维$\mathcal{N}$=4和6维(2,0)共形超重力的异常消除条件，发现其与Poincaré超重力的紫外有限性相关，通过散射幅计算验证了理论预测。
摘要：
我们回顾了4维$\mathcal{N}$=4共形超重力（CSG）与N_v个$\mathcal{N}$=4向量多重群耦合时的超共形异常结构，以及6维(2,0)CSG与N_T个(2,0)张量多重群耦合时的异常情况。当N_v=4和N_T=26时，异常抵消。若舍去CSG部分，N_v=6+n_v时，第一理论等价于4维$\mathcal{N}$=4 Poincaré超重力（PSG）与n_v向量多重群耦合，第二理论等价于6维(2,0) PSG与n_T张量多重群耦合。我们论证这些事实表明，4维PSG中n_v向量的发散应与n_v+2成比例，6维PSG中n_T张量的发散应与n_T-21成比例。这些预测似乎与已知的散射幅计算结果一致。
英文摘要：
We review the structure of superconformal anomalies in 4d $\mathcal N$=4 conformal supergravity (CSG) coupled to a number N$_\rm v$ of $ \mathcal N$=4 vector multiplets and 6d (2,0) CSG coupled to N$_{_{\rm T}}$ of (2,0) tensor multiplets. Anomalies cancel if N$_\rm v$=4 and N$_{_{\rm T}}$=26 respectively. If the CSG part of the action is dropped and N$_{\rm v}$=6+ n$_{\rm v}$, the first theory is classically equivalent to the 4d $\mathcal N$=4 Poincaré supergravity (PSG) coupled to n$_{\rm v}$ vector multiplets, while the second one with N$_{_{\rm T}}$=5+ n$_{_{\rm T}}$ is classically equivalent to the 6d (2,0) PSG coupled to n$_{\rm T}$ tensor multiplets. We argue that these facts imply that divergences in the 4d PSG with n$_{\rm v}$ vectors should be proportional to n$_{\rm v}$+2 and similarly in the 6d PSG with n$_{_{\rm T}}$ tensors to n$_{_{\rm T}}$-21. These predictions appear to be consistent with known results of explicit scattering amplitude computations in these 4d and 6d PSG theories.
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