相关论文: 't Hooft anomalies for staggered fermions

We review the shift (translation) and time reversal symmetries of Hamiltonian staggered fermions and their connection to continuum symmetries concentrating in particular on the case of massless fermions and (3+1) dimensions. We construct…

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 $w_2\cup w_3$…

We show that massless Kaehler-Dirac (KD) fermions exhibit a mixed gravitational anomaly involving an exact $U(1)$ symmetry which is unique to KD fields. Under this $U(1)$ symmetry the partition function transforms by a phase depending only…

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 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 investigate the implications of the quantized vectorial and axial charges in the lattice Hamiltonian of multi-flavor staggered fermions in $(1+1)$ dimensions. These lattice charges coincide with those of the $U(1)_V$ and $U(1)_A$ global…

4d gauge theories with massless fermions typically have axial U(1) transformations that suffer from the ABJ anomaly. One can modify the theory of interest by adding more fields in a way that restores the axial symmetry, and use it to derive…

't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by $\sim a_1\wedge…

'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…

I consider anomalies in effective field theories (EFTs) of gauge fields coupled to fermions on an interval in AdS_5, and their holographic duals. The anomalies give rise to constraints on the consistent EFT description, which are stronger…

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…

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…

Staggered fermion shift symmetries correspond to translations of the fermion field within the unit cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean dimensions can be related to a discrete subgroup of an $SU(4)$…

We study K\"ahler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requring vielbeins and spin connections. We work in the…

Standard lore uses local anomalies to check the kinematic consistency of gauge theories coupled to chiral fermions, e.g. Standard Models (SM). Based on a systematic cobordism classification, we examine constraints from invertible quantum…

Anomalies can be elegantly analyzed by means of the Dai-Freed theorem. In this framework it is natural to consider a refinement of traditional anomaly cancellation conditions, which sometimes leads to nontrivial extra constraints in the…

We study the symmetries of lattice staggered fermions in 2+1d. Using the symmetries, we can place the system on any sheared torus or Klein bottle. These different backgrounds provide diagnostics of various 't Hooft anomalies associated with…

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 recent years tantalizing signs for a novel phase have been reported that is chirally symmetric but nevertheless exhibits massive bound states. The necessary condition for such a phase, referred to as Symmetric Mass Generation (SMG), is…

We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This…