Related papers: Anomalies of 4d $Spin_G$ Theories
'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…
Discrete finite-group global symmetries may suffer from nonperturbative 't-Hooft anomalies. Such global anomalies can be canceled by anomalous symmetry-preserving topological quantum field theories (TQFTs), which contain no local point…
We study 't Hooft anomalies for discrete global symmetries in bosonic theories in 2, 3 and 4 dimensions. We show that such anomalies may arise in gauge theories with topological terms in the action, if the total symmetry group is a…
't Hooft anomalies of discrete global symmetries and gaugings thereof have rich mathematical structures and far-reaching physical consequences. We examine each subgroup $G$, up to automorphisms, of the permutation group $S_4$ that acts on…
We explore 4-dimensional SU(N) gauge theory with a Weyl fermion in an irreducible self-conjugate representation. This theory, in general, has a discrete chiral symmetry. We use 't Hooft anomaly matching condition of the center symmetry and…
We show that the phase structure of certain staggered fermion theories can be understood on the basis of exact anomalies. These anomalies arise when staggered fermions are coupled to gravity which can be accomplished by replacing them by…
We undertake a systematic study of the $4$-dimensional $SU(N)$ $2$-index chiral gauge theories and investigate their faithful global symmetries and dynamics. These are a finite set of theories with fermions in the $2$-index symmetric and…
We study more extensively and completely for global gauge anomalies with some semisimple gauge groups as initiated in ref.1. A detailed and complete proof or derivation is provided for the Z_2 global gauge anomaly given in ref.1 for a gauge…
We develop a theory of anomalies of fermionic topological phases of matter in (2+1)D with a general fermionic symmetry group $G_f$. In general, $G_f$ can be a non-trivial central extension of the bosonic symmetry group $G_b$ by fermion…
A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r+1/2, is inconsistent. We…
We discuss the $SU(3)/[U(1)\times U(1)]$ nonlinear sigma model in 1+1D and, more broadly, its linearized counterparts. Such theories can be expressed as $U(1)\times U(1)$ gauge theories and therefore allow for two topological…
We derive explicit anomaly-index formulas for four-dimensional Weyl fermions charged under the finite symmetries $\mathrm{Spin}\times\mathbb Z_n$ and $\mathrm{Spin}\times_{\mathbb Z_2^{\mathrm F}}\mathbb Z_{2m}^{\mathrm F}$. The strategy is…
We study the mixed anomaly between the discrete chiral symmetry and general baryon-color-flavor (BCF) backgrounds in $SU(N_c)$ gauge theories with $N_f$ flavors of Dirac fermions in representations ${\cal R}_c$ of $N$-ality $n_c$,…
We show that $2$d adjoint QCD, an $SU(N)$ gauge theory with one massless adjoint Majorana fermion, has a variety of mixed 't Hooft anomalies. The anomalies are derived using a recent mod $2$ index theorem and its generalization that…
We study the strong-interaction dynamics of a class of $4D$ chiral $SU(N)$ gauge theories with a fermion in a symmetric second-rank tensor representation and a number of fermions in an anti-antisymmetric tensor representation, extending the…
We study a class of 4-dimensional $SU(N)$ chiral gauge theories with fermions in the 2-index symmetric and antisymmetric representations and classify their infrared phases. The choice $N=4\mathbb{Z}$ corresponds to gauging the fermion…
We hypothesize a new and more complete set of anomalies of certain quantum field theories (QFTs) and then give an eclectic verification. First, we propose a set of 't Hooft higher anomalies of 4d time-reversal symmetric pure…
We study the dynamics of chiral SU(N) gauge theories. These contain Weyl fermions in the symmetric or anti-symmetric representation of the gauge group, together with further fermions in the fundamental and anti-fundamental. We revisit an…
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 $f^{(2)}$, naturally gives rise to a continuous 1-form global symmetry…
We revisit discrete gauge anomalies in chiral fermion theories in $3+1$ dimensions. We focus on the case that the full symmetry group of fermions is $\mathrm{Spin}(4)\times\mathbb{Z}_n$ or…