The Geometry of Decoupling Fields

TL;DR

This paper investigates the geometric and anomaly-based origins of decoupling modes, known as flip fields, in 4d theories derived from 6d SCFTs of M5-branes, revealing their connection to M2-branes and resolution cycles.

Contribution

It provides a geometric interpretation of flip fields in 4d theories from 6d SCFTs, linking them to M2-branes wrapping resolution cycles and analyzing anomaly inflow from eleven dimensions.

Findings

Identification of decoupling modes with flip fields in 4d models.

Connection of flip fields to M2-branes wrapping cycles.

Geometric origin of flip fields via anomaly inflow analysis.

Abstract

We consider 4d field theories obtained by reducing the 6d (1,0) SCFT of $N$ M5-branes probing a $\mathbb C^2/\mathbb Z_k$ 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 $\mathbb C^2/\mathbb Z_k$ 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.