Generalized Families of QFTs

TL;DR

This work develops a comprehensive framework for generalized families of QFTs organized by broken generalized and categorical symmetries. It introduces the SymTFT perspective and spurion analyses to study how higher-group and non-invertible symmetries act on coupling spaces, producing family anomalies that constrain RG flows and IR phases. Through concrete 4d examples (Maxwell, Yang–Mills with various global forms, and N=2 SYM deformations), it demonstrates how higher-family and non-invertible anomalies enforce phase structure, domain-wall dynamics, and strict IR behavior, including necessary phase transitions or symmetry breaking. The results illuminate how twists, gauging, and compactification generate rich hierarchical and categorical structures that shape UV completions and IR dynamics in non-Abelian gauge theories. The findings have broad implications for understanding anomaly matching, IR dualities, and the role of generalized symmetries in high-energy theory and beyond.

Abstract

RG flows and IR phases of QFTs can be constrained by generalized symmetries and their anomalies. Broken symmetries act on the space of coupling constants of families of theories, and can also have IR-constraining family anomalies. We generalize family anomaly considerations to cases of broken generalized/categorical symmetries, including higher-group and non-invertible symmetries. We consider the anomaly inflow and SymTFTs of such generalized families of QFTs, and their implications for RG flows and constraints on the IR phases. As examples, we apply family anomalies to study the IR phases of $4d$ QCD-like theories deformed by irrelevant, multi-fermion interactions.

Figures (1)

• Figure 1: In this figure, we illustrate the idea of the SymTFT. Here, the left boundary (blue) is the QFT boundary (i.e. where the physical QFT exists) and the right boundary (orange) is the topological boundary which is labeled by a topological boundary condition $\mathfrak{B}$. In the SymTFT, these boundary conditions can also be written as states in the Hilbert space of the topological theory $\langle QFT|$ and $|\mathfrak{B}\rangle$ respectively. Here the symmetry operators $U_g$ of the QFT can be lifted directly to operators $\widehat{U}_g$ (teal) in the SymTFT whereas charged operators (red) $\mathcal{O}(x)$ are attached to topological operators $L_\gamma$ that run between the boundaries in the SymTFT.