Quiver Approach to Symmetry Theories

Abstract

Global symmetry anomalies of a quantum field theory (QFT) can be packaged as specific couplings of a higher-dimensional symmetry theory (SymTh). In this work we show that for 5D superconformal field theories (SCFTs) engineered from M-theory backgrounds $X$ a Calabi-Yau cone, this data can be extracted from the path algebra of branes probing $X$. This provides a complementary algebraic approach compared with more geometric computations based on the explicit calculation of triple intersection numbers in a resolved geometry and / or $η$-invariants extracted from the boundary geometry $\partial X$. Our method applies in situations where the counterpart geometric computation is either unknown or combinatorially unwieldy. We illustrate with several toric threefold examples, including orbifolds $\mathbb{C}^{3} / Γ$ and more general non-orbifold Calabi-Yau cones of Sasaki-Einstein five-manifolds.