Generalized Families of QFTs

ArXiv.org · 2026-02-09

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.

Generalized Families of QFTs

Open MIND · 2026-02-09

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.

Anomalies of 4d SpinG theories

Journal of High Energy Physics · 2024-07-18 · 10 citations

A bstract We consider ’t Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits Spin G (4) generalized spin structure, with G either gauged or a global symmetry. We discuss methods to directly compute w 2 ∪ w 3 ’t Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g. M 4 = ℂℙ 2 . Such anomalies have been discussed for SU(2) gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 SYM theory. We directly compute these anomalies for a variety of theories, including general G gauge theories with adjoint fermions, SU(2) gauge theory with fermions in general representations, and Spin(N) gauge theories with fundamental matter. We discuss aspects of matching these and other ’t Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for general G gauge theory with N f adjoint Weyl fermions. For example, in the case of N f = 2 we discuss anomaly matching in the IR phase consisting of $$ {h}_{G_{\textrm{gauge}}}^{\vee } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>h</mml:mi> <mml:msub> <mml:mi>G</mml:mi> <mml:mtext>gauge</mml:mtext> </mml:msub> <mml:mo>∨</mml:mo> </mml:msubsup> </mml:math> copies of a ℂℙ 1 non-linear sigma model, including for the w 2 w 3 anomalies when formulated with $$ {\textrm{Spin}}_{\textrm{SU}{(2)}_{\textrm{global}}}(4) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>Spin</mml:mtext> <mml:mrow> <mml:mi>SU</mml:mi> <mml:msub> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> <mml:mtext>global</mml:mtext> </mml:msub> </mml:mrow> </mml:msub> <mml:mfenced> <mml:mn>4</mml:mn> </mml:mfenced> </mml:math> structure.

Anomalies of 4d $Spin_G$ Theories

arXiv (Cornell University) · 2023-12-07

We consider 't Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits $Spin_G(4)$ generalized spin structure, with $G$ either gauged or a global symmetry. We discuss methods to directly compute $w_2\cup w_3$ 't Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g. $M_4=\mathbb{CP}^2$. Such anomalies have been discussed for $SU(2)$ gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of ${\cal N}=2$ SYM theory. We directly compute these anomalies for a variety of theories, including general $G$ gauge theories with adjoint fermions, $SU(2)$ gauge theory with fermions in general representations, and $Spin(N)$ gauge theories with fundamental matter. We discuss aspects of matching these and other 't Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for general $G_{\rm gauge}$ theory with $N_f$ adjoint Weyl fermions. For example, in the case of $N_f=2$ we discuss anomaly matching in the IR phase consisting of $h^\vee _{G_{\rm gauge}}$ copies of a $\mathbb{CP}^1$ non-linear sigma model, including for the $w_2w_3$ anomalies when formulated with $Spin_{SU(2)_{\rm global}}(4)$ structure.

2-Group global symmetries and anomalies in six-dimensional quantum field theories

Journal of High Energy Physics · 2023 · 43 citations

• Physics
• Theoretical physics
• Mathematical physics

We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength ƒ⁽²⁾, naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current <em>J</em>⁽²⁾~ _*Tr (ƒ⁽²⁾ $\wedge$ ƒ⁽²⁾). We show that suitable mixed anomalies involving the gauge field ƒ⁽²⁾ and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current <em>J</em>⁽²⁾. We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the <em>a</em>-type Weyl anomaly of all SCFTs with a tensor branch must be positive, <em>a</em> > 0.

Snowmass White Paper on SCFTs

arXiv (Cornell University) · 2022-02-15 · 9 citations

Superconformal field theories (SCFTs) occupy a central role in the study of many aspects of quantum field theory. In this white paper for the Snowmass process we give a brief overview of aspects of SCFTs in $3\leq D \leq 6$ space-time dimensions, including classification efforts and some of the vast current research trends on the physical and mathematical structures generated by this rich class of physical theories.

Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

arXiv (Cornell University) · 2022 · 113 citations

• Sociology
• Theoretical physics
• Physics

Symmetry plays a central role in quantum field theory. Recent developments include symmetries that act on defects and other subsystems, and symmetries that are categorical rather than group-like. These generalized notions of symmetry allow for new kinds of anomalies that constrain dynamics. We review some transformative instances of these novel aspects of symmetry in quantum field theory, and give a broad-brush overview of recent applications.

$$ \mathcal{N} $$ = (1, 0) anomaly multiplet relations in six dimensions

Journal of High Energy Physics · 2020-07-01 · 11 citations

A bstract We consider conformal and ’t Hooft anomalies in six-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = (1 , 0) superconformal field theories, focusing on those conformal anomalies that determine the two- and three-point functions of conserved flavor and SU(2) R currents, as well as stress tensors. By analyzing these correlators in superspace, we explain why the number of independent conformal anomalies is reduced in supersymmetric theories. For instance, non- supersymmetric CFTs in six dimensions have three independent conformal c -anomalies, which determine the stress-tensor two- and three-point functions, but in superconformal theories the three c -anomalies are subject to a linear constraint. We also describe anomaly multiplet relations, which express the conformal anomalies of a superconformal theory in terms of its ’t Hooft anomalies. Following earlier work on the conformal a -anomaly, we argue for these relations by considering the supersymmetric dilaton effective action on the tensor branch of such a theory. We illustrate the utility of these anomaly multiplet relations by presenting exact results for conformal anomalies, and hence current and stress-tensor correlators, in several interacting examples.

Multiplets of superconformal symmetry in diverse dimensions

Journal of High Energy Physics · 2019-03-01 · 39 citations

A bstract We systematically analyze the operator content of unitary superconformal multiplets in d ≥ 3 spacetime dimensions. We present a simple, general, and efficient algorithm that generates all of these multiplets by correctly eliminating possible null states. The algorithm is conjectural, but passes a vast web of consistency checks. We apply it to tabulate a large variety of superconformal multiplets. In particular, we classify and construct all multiplets that contain conserved currents or free fields, which play an important role in superconformal field theories (SCFTs). Some currents that are allowed in conformal field theories cannot be embedded in superconformal multiplets, and hence they are absent in SCFTs. We use the structure of superconformal stress tensor multiplets to show that SCFTs with more than 16 Poincaré supercharges cannot arise in d ≥ 4, even when the corresponding superconformal algebras exist. We also show that such theories do arise in d = 3, but are necessarily free.

Matching 3d N =2 vortices and monopole operators

OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2019-04-26 · 4 citations

In earlier work with N. Seiberg, we explored connections between monopole operators, the Coulomb branch modulus, and vortices for 3d, N =2 supersymmetric, U(1)_k Chern-Simons matter theories. We here extend the monopole / vortex matching analysis, to theories with general matter electric charges. We verify, for general matter content, that the spin and other quantum numbers of the chiral monopole operators match those of corresponding BPS vortex states, at the top and bottom of the tower associated with quantizing the vortices’ Fermion zero modes. There are associated subtleties from non-normalizable Fermi zero modes, which contribute non-trivially to the BPS vortex spectrum and monopole operator matching; a proposed interpretation is further discussed here.