Lessons from crossing symmetry at large N
Lessons from crossing symmetry at large N
复制标题
大 N 交叉对称性的教训
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
T. Lukowski
中科院分区：
文献类型：
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作者：
L. Alday;A. Bissi;T. Lukowski
我们考虑了N=4 $$ \mathcal{N}=4 $$ SYM中应力张量多重集的四点相关器，构造了在中心电荷c ～ N2和g2N大的极限下符合交叉对称的所有解。虽然我们找到了无限的解塔，但我们认为它们中的大多数都被一个额外的尺度Δgap所抑制，并且与在大中心电荷的数值超共形自举中观察到的无保护算子的缩放维的上界一致。这些解决方案组织为1/c和1/Δgap的双重扩展。我们的解决方案对1/c和1/Δgap中的所有订单都有效，并重现，特别是先前发现的即时更正。进一步，我们发现了这种上界与平面空间中由因果关系引起的正性约束之间的联系。最后，我们证明了在交叉对称下，由ad散射的因果约束推导出的某些关系。
A bstractWe consider the four-point correlator of the stress tensor multiplet in N=4$$ \mathcal{N}=4 $$ SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ∼ N2 and large g2N . While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale Δgap and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/Δgap. Our solutions are valid to leading order in 1/c and to all orders in 1/Δgap and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.