AI 中文总结
本文基于AdS/CFT对应关系，研究N=4 SU(N)超对称杨-米尔斯理论的超共形指标，提出通过余维-2奇点的实洛伦兹号差时空积分计算体路径积分的方法，在大N极限下排除相关黑洞鞍点，在AdS₄的ABJM指标计算中得到类似结果。
AI 中文摘要
AdS/CFT对应关系表明，N=4 SU(N)超对称杨-米尔斯理论中的超共形指标I可通过对偶体理论计算。尤其在大N极限下，该指标应表示为合适鞍点的求和。然而，I依赖于势σ、τ、Δ，且在Im τ = Im σ很大时，CFT指标I对所有N值迅速趋近于1，这导致与指数级大N贡献相关的黑洞鞍点在该极限下无法产生贡献，特别排除了此前被认为在这类区域相关的鞍点。因此，我们提出一种受此启发的体路径积分方法，将其定义为对具有余维-2奇点的实洛伦兹号差时空的积分，该方法仅得到满足上述边界的鞍点，并通过斯托克斯现象实现该边界。我们还在体AdS₄的ABJM超共形指标计算中得到了类似结果。
英文摘要
The AdS/CFT correspondence implies that the superconformal index ${\mathcal I}$ in ${\mathcal N=4}$ SU(N) supersymmetric Yang-Mills theory can be computed using the dual bulk theory. In particular, in the limit of large $N$, the index should be given by a sum over appropriate saddles. However, ${\mathcal I}$ depends on potentials $σ, τ, \vec Δ$ and, at large ${\rm Im}\, τ= {\rm Im}\, σ$, the CFT index ${\mathcal I}$ rapidly approaches $1$ at all values of $N$. As a result, black hole saddles associated with exponentially large contributions in $N$ cannot contribute in this limit. This in particular excludes saddles that were previously suggested to be relevant in such regimes. We thus consider an approach to the bulk path integral motivated by taking it to be defined as an integral over real Lorentz-signature spacetimes with codimension-2 singularities. This approach leads only to saddles that satisfy the above bound, and to the enforcement of this bound via Stokes phenomena. We also find similar results for bulk AdS$_4$ calculations of the ABJM superconformal index.
Comments65 pages, 16 figures
