Related papers: 't Hooft Anomaly Matching for Discrete Symmetries
We prove that in $(3+1)d$ quantum field theories with $\mathbb{Z}_N$ symmetry, certain anomalies forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, this applies to discrete chiral symmetries which are…
Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…
We analyze in detail the global symmetries of various (2+1)d quantum field theories and couple them to classical background gauge fields. A proper identification of the global symmetries allows us to consider all non-trivial bundles of…
We discuss the vacuum structure of the SU(6) model, a chiral gauge theory, from the perspective of anomaly matching. To this end, we first identify all possible 't Hooft anomalies in the UV theory using the Stora-Zumino procedure.…
We extend our earlier work on anomalies in the space of coupling constants to four-dimensional gauge theories. Pure Yang-Mills theory (without matter) with a simple and simply connected gauge group has a mixed anomaly between its one-form…
We investigate 't Hooft anomalies in the $\mathbb{CP}^{N-1}$ model in spacetime dimensions higher than two and identify two types of anomalies: One is a mixed anomaly between the $\mathrm{PSU}(N)$ flavor-rotation and magnetic symmetries,…
We critically reconsider the argument based on 't Hooft anomaly matching that aims at proving chiral symmetry breaking in confining four-dimensional QCD-like theories with $N_c>2$ colors and $N_f$ flavors. The main line of reasoning relies…
't Hooft anomalies are known to induce specific contributions to the effective action at finite temperature. We present a general method to directly calculate such contributions from the anomaly polynomial of a given theory, including a…
In this work we propose a way to promote the anomalous axial U(1) transformations to exact non-invertible U(1) symmetries. We discuss the procedure of coupling the non-invertible symmetry to a (dynamical or background) gauge field. We show…
It is customary to couple a quantum system to external classical fields. One application is to couple the global symmetries of the system (including the Poincar\'{e} symmetry) to background gauge fields (and a metric for the Poincar\'{e}…
In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a…
We use a low-energy effective approach, the extended linear sigma model, to study realizations of the $U(1)_A$ anomaly with different operators, linear and quadratic in the 't Hooft determinant. After discussing the parameterization in…
't Hooft anomaly matching is powerful for constraining the low energy phases of gauge theories. In 3d one common anomaly is the parity anomaly in a $T$-symmetric theory where one cannot gauge the global symmetry group without breaking the…
In this paper, we give a brief overview of generalized symmetries from the point of view of the lattice regularization as a fully regularized framework. At first, we illustrate the generalization of 't~Hooft anomaly matching for higher-form…
We develop a general framework for the description of anomalies using extended functorial field theories extending previous work by Freed and Monnier. In this framework, anomalies are described by invertible field theories in one dimension…
It is known that the 't Hooft anomalies of invertible global symmetries can be characterized by an invertible TQFT in one higher dimension. The analogous statement remains to be understood for non-invertible symmetries. In this note we…
We report our study of the discrete symmetry for lattice 3450 model proposed by Wang and Wen. Lattice 3450 model is expected to describe the anomaly free chiral U(1) gauge theory in 1+1 dimension using 2+1 dimensional domain-wall fermion…
We study the dynamics of $SU(N)$ chiral gauge theories with massless fermions belonging to various combinations of the symmetric, antisymmetric or fundamental representations. We limit ourselves to the gauge-anomaly-free and asymptotically…
The structure of the moduli space of N=1 supersymmetric gauge theories is analyzed from an algebraic geometric viewpoint. The connection between the fundamental fields of the ultraviolet theory, and the gauge invariant composite fields of…
We explore the consequence of generalized symmetries in four-dimensional $\mathcal{N}=1$ superconformal field theories. First, we classify all possible supersymmetric gauge theories with a simple gauge group that have a nontrivial one-form…