论文标题
从$ \ mathbb {rp}^4 $ on $ \ mathbb {rp}^4 $ to $ \ mathbb {rp}^2 $ on $ \ mathbb {rp}^4 $ on $ \ mathbb {rp}^4 $ on $ \ mathbb {rp}^4 $ ron $ \ super-yang-mills from $ \ mathbb {rp}^2 $上
From $\mathcal{N}=4$ Super-Yang-Mills on $\mathbb{RP}^4$ to bosonic Yang-Mills on $\mathbb{RP}^2$
论文作者
论文摘要
我们研究了不可定向的时空歧管$ \ mathbb {rp}^4 $，研究了四维$ \ mathcal {n} = 4 $ super-yang-mills（sym）理论。使用超对称性定位，我们发现，对于保留共同的增压$ \ Mathcal {q} $的一大批本地和扩展的观测值，他们的期望值是由有效的二维Bosonic Yang-Mills（ym）理论捕获的，这些理论是$ \ \ Mathbb {rp}^2^2 $ submanifold。这为理解$ \ mathcal {n} = 4 $ sym on $ \ mathbb {rp}^4 $使用ym上的ym上的已知结果铺平了道路。作为例证，我们在$ \ mathbb {rp}^4 $上得出了Sym分区函数的矩阵积分形式，当将其分解为离散的载体扇区时，它包含由于$ \ mathbb的dirac操作员的非平凡$η$ invariant而导致的微妙相位因子。我们还评论了我们的设置对AGT对应关系的潜在应用，在ADS/CFT中涉及边界上的跨上限状态的AGT对应关系，集成性和批量重建。
We study the four-dimensional $\mathcal{N}=4$ super-Yang-Mills (SYM) theory on the unorientable spacetime manifold $\mathbb{RP}^4$. Using supersymmetric localization, we find that for a large class of local and extended SYM observables preserving a common supercharge $\mathcal{Q}$, their expectation values are captured by an effective two-dimensional bosonic Yang-Mills (YM) theory on an $\mathbb{RP}^2$ submanifold. This paves the way for understanding $\mathcal{N}=4$ SYM on $\mathbb{RP}^4$ using known results of YM on $\mathbb{RP}^2$. As an illustration, we derive a matrix integral form of the SYM partition function on $\mathbb{RP}^4$ which, when decomposed into discrete holonomy sectors, contains subtle phase factors due to the nontrivial $η$-invariant of the Dirac operator on $\mathbb{RP}^4$. We also comment on potential applications of our setup for AGT correspondence, integrability and bulk-reconstruction in AdS/CFT that involve cross-cap states on the boundary.
