论文标题
$ sl（2，\ mathbb {z}）$在qfts上使用$ \ mathbb {z} _2 $ symmetry和brown-kervaire不变性
$SL(2,\mathbb{Z})$ action on QFTs with $\mathbb{Z}_2$ symmetry and the Brown-Kervaire invariants
论文作者
论文摘要
我们考虑了Witten的$ SL（2，\ Mathbb {Z}）$ ACTION在三维Qfts上使用$ u（1）$对称的$ 2K $ -Dimensional Qfts，$ \ Mathbb {z} _2 $（k-1 $（k-1）$ - symmetry-symmetry。我们表明，$ sl（2，\ mathbb {z}）$ Action仅通过可逆拓扑阶段乘以乘积的分区函数，其分区函数是时空歧管的棕色 - 凯维尔不变。我们将其解释为$ sl（2，\ mathbb {z}）$ bulk $（2k+1）$ - dimensional $ \ mathbb {z} _2 $ gauge理论的一部分。
We consider an analogue of Witten's $SL(2,\mathbb{Z})$ action on three-dimensional QFTs with $U(1)$ symmetry for $2k$-dimensional QFTs with $\mathbb{Z}_2$ $(k-1)$-form symmetry. We show that the $SL(2,\mathbb{Z})$ action only closes up to a multiplication by an invertible topological phase whose partition function is the Brown-Kervaire invariant of the spacetime manifold. We interpret it as part of the $SL(2,\mathbb{Z})$ anomaly of the bulk $(2k+1)$-dimensional $\mathbb{Z}_2$ gauge theory.
