论文标题
异常流入和$ p $ - 形状量规理论
Anomaly inflow and $p$-form gauge theories
论文作者
论文摘要
手性和非手续$ p $ - 形状量规场具有引力异常和绿色 - 雪Warz类型的异常。这意味着它们最自然地将其视为一个较高维度的散装拓扑阶段的边界模式。我们对总体体积系统进行了系统的描述，该系统类似于在大型费米昂边界上实现手性费米的。边界理论的异常是由批量理论的分区函数给出的，我们根据atiyah-patodi-singer $η$ invariant明确计算。我们使用形式主义来确定4D Maxwell理论的$ \ Mathrm {SL}（2，{\ Mathbb Z}）$异常。我们还将其应用于在有东方，Orbifolds和string，M和F理论中的外观，Orbifolds和S折中的单个D-Brane和M5-Brane的WorldVolume理论。在附录中，我们还描述了一类简单的非单身可逆拓扑理论，其分区函数并不是一个不变的界限，这说明了在可逆阶段的恢复性分类中单位性条件的必要性。
Chiral and non-chiral $p$-form gauge fields have gravitational anomalies and anomalies of Green-Schwarz type. This means that they are most naturally realized as the boundary modes of bulk topological phases in one higher dimensions. We give a systematic description of the total bulk-boundary system which is analogous to the realization of a chiral fermion on the boundary of a massive fermion. The anomaly of the boundary theory is given by the partition function of the bulk theory, which we explicitly compute in terms of the Atiyah-Patodi-Singer $η$-invariant. We use our formalism to determine the $\mathrm{SL}(2,{\mathbb Z})$ anomaly of the 4d Maxwell theory. We also apply it to study the worldvolume theories of a single D-brane and an M5-brane in the presence of orientifolds, orbifolds, and S-folds in string, M, and F theories. In an appendix we also describe a simple class of non-unitary invertible topological theories whose partition function is not a bordism invariant, illustrating the necessity of the unitarity condition in the cobordism classification of the invertible phases.
