Related papers: On anomalies and fermionic unitary operators
For any worldline reformulation of a quantum field theory for Dirac fermions, this paper shows that worldline supersymmetry may generally be enforced by the vanishing of the commutator of the Dirac operator with the worldline Hamiltonian.…
We study the constraints on models with extra dimensions arising from local anomaly cancellation. We consider a five-dimensional field theory with a U(1) gauge field and a charged fermion, compactified on the orbifold S^1/(Z_2 x Z_2'). We…
This paper reviews the well-known fact that nilpotent Hermitian operators on physical state spaces are zero, thereby indicating that the supersymmetries and "Grassmann numbers" are also zero on these spaces. Next, a positive definite inner…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
Working with anticommuting Weyl(or Mayorana) spinors in the framework of the van der Waerden calculus is standard in supersymmetry. The natural frame for rigorous supersymmetric quantum field theory makes use of operator-valued…
We present a systematic approach to supersymmetric holographic renormalization for a generic 5D $\mathcal{N}=2$ gauged supergravity theory with matter multiplets, including its fermionic sector, with all gauge fields consistently set to…
We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality…
We consider the simplest nontrivial supersymmetric quantum mechanical system involving higher derivatives. We unravel the existence of additional bosonic and fermionic integrals of motion forming a nontrivial algebra. This allows one to…
We develop a systematic framework for constructing (3+1)-dimensional topological orders or topological quantum field theories (TQFTs) that realize specified anomalies of finite symmetries, as encountered in gauge theories with fermions or…
We describe the physics of fermionic Lifschitz theories once the anisotropicscaling exponent is made arbitrarily small. In this limit the system acquires an enhanced(Carrollian) boost symmetry. We show, both through the explicit computation…
We investigate supergroups with Grassmann parameters replaced by odd Clifford parameters. The connection with non-anticommutative supersymmetry is discussed. A Berezin-like calculus for odd Clifford variables is introduced. Fermionic…
By considering the fermionic realization of $G/H$ coset models, we show that the partition function for the $U(1)/U(1)$ model defines a Topological Quantum Field Theory and coincides with that for a 2-dimensional Abelian BF system. In the…
Symmetry acting on a (2+1)$D$ topological order can be anomalous in the sense that they possess an obstruction to being realized as a purely (2+1)$D$ on-site symmetry. In this paper, we develop a (3+1)$D$ topological quantum field theory to…
We apply Schroedinger functional methods to two gauge theories with fermions in two-index representations: the SU(3) theory with Nf=2 adjoint fermions, and the SU(4) theory with Nf=6 fermions in the two-index antisymmetric representation.…
Lorentz invariant quantum field theories (QFTs) with fermions in four spacetime dimensions (4D) have a $\mathbb{Z}_4$ symmetry provided there exists a basis of operators in the QFT where all operators have even operator dimension, $d$,…
The super Macdonald polynomials indexed by the super partitions form a basis of the level zero super Fock module (combinatorial representation) of the quantum toroidal algebra $\mathcal{U}_{q,t}(\widehat{\widehat{\mathfrak{gl}}}_{1|1})$.…
Supersymmetric Yang-Mills quantum mechanics (SYMQM) in four dimensions for SU(2) gauge group is considered. In this work a two-fermionic sector with the angular momentum j=0 in discussed. Energy levels from discrete and continuous spectra…
Non-anticommutative Grassmann coordinates in four-dimensional twist-deformed N=1 Euclidean superspace are decomposed into geometrical ones and quantum shift operators. This decomposition leads to the mapping from the commutative to the…
Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are…
A bosonic operator of U_q(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of U_q(osp(1|2)) for q a root of unity (in the unrestricted specialisation). As in the…