The geometry of decoupling fields

• DOI: 10.1007/jhep09(2022)197
• Publication Date: 2022-09-24T07:02:48Z
• Authors: Ibrahima Bah; Federico Bonetti; Enoch Leung; Peter Weck
• Keywords: Global Symmetries; High Energy Physics - Theory; FOS: Physical sciences; Field Theories in Higher Dimensions; M-Theory; QC770-798; 01 natural sciences; High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; Anomalies in Field and String Theories

Abstract We consider 4d field theories obtained by reducing the 6d (1,0) SCFT of N M5-branes probing a ℂ2/ℤk singularity on a Riemann surface with fluxes. We follow two different routes. On the one hand, we consider the integration of the anomaly polynomial of the parent 6d SCFT on the Riemann surface. On the other hand, we perform an anomaly inflow analysis directly from eleven dimensions, from a setup with M5-branes probing a resolved ℂ2/ℤk singularity fibered over the Riemann surface. By comparing the 4d anomaly polynomials, we provide a characterization of a class of modes that decouple along the RG flow from six to four dimensions, for generic N, k, and genus. These modes are identified with the flip fields encountered in the Lagrangian descriptions of these 4d models, when they are available. We show that such fields couple to operators originating from M2-branes wrapping the resolution cycles. This provides a geometric origin of flip fields. They interpolate between the 6d theory in the UV, where the M2-brane operators are projected out, and the 4d theory in the IR, where these M2-brane operators are part of the spectrum.