Related papers: Determinant and Weyl anomaly of Dirac operator: a …
In this paper we discuss a connection between Dirac operators on configuration spaces and Yang-Mills quantum field theory. We first show that the Hamilton operators of the self-dual and anti-self-dual sectors of a Yang-Mills quantum field…
For two-dimensional conformal field theories driven by evolving background space-time metrics in a closed universe, we present an operator formulation as a driven inhomogeneous CFT. The Hamiltonian of this theory is given by a background…
The three dimensional abelian fermionic determinant of a two component massive spinor in flat euclidean space-time is resetted to a pure Chern-Simons action through a nonlinear redefinition of the gauge field.
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal…
On a compact manifold $M$, we consider the affine space $A$ of non self-adjoint perturbations of some invertible elliptic operator acting on sections of some Hermitian bundle, by some differential operator of lower order. We construct and…
We consider a free massive spinor field in Euclidean Anti-de Sitter space. The usual Dirac action in bulk is supplemented by a certain boundary term. The boundary conditions of the field are parametrized by a spinor on the boundary, subject…
We put fermions and define the Dirac operator and spin structures on a randomly triangulated 2d manifold.
We study the relation between boundary conditions and categorical symmetries of two-dimensional fermionic conformal field theories. We determine all anomaly-free invertible global symmetries of two free complex Weyl fermions, which take the…
This paper develops a chiral adelic operator framework in which the functional--equation symmetry of global $L$--functions is realized directly in the spectrum of a Dirac--type Hamiltonian. Working on the id\`ele class space, we place a…
The Gelfand-Yaglom formula relates functional determinants of the one-dimensional second order differential operators to the solutions of the corresponding initial value problem. In this work we generalise the Gelfand-Yaglom method by…
We find the Holographic Renormalization Group equations for the holographic duals of generic gravity theories coupled to form fields and spin-1/2 fermions. Using Hamilton-Jacobi theory we discuss the structure of Ward identities, anomalies,…
We develop the representation of bulk fields with spin one and spin two in anti-de Sitter space, as non-local observables in the dual CFT. Working in holographic gauge in the bulk, at leading order in 1/N bulk gauge fields are obtained by…
We use the boundary triplet approach to extend the classical concept of perturbation determinants to a more general setup. In particular, we examine the concept of perturbation determinants to pairs of proper extensions of closed symmetric…
We outline a novel chiral kinetic theory framework for systematic computations of the Chiral Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. The real part of the fermion determinant in the QCD effective action is expressed…
The standard formula for the change in the effective action under a conformal transformation is extended to the case when the boundary is piecewise smooth. We then find the functional determinants of the scalar Laplacian on regions of the…
We derive the bosonic sector of the AdS$_3$/CFT$_2$ correspondence from the $(1+1)$-dimensional Gross-Neveu (GN) model with $N$ fermion species and a local quartic interaction, with no stringy or geometric input. A Bargmann-Wigner fusion…
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of…
We consider the minimal coupling of a thin film Dirac semimetal Hamiltonian to a generic spin-texture. A simple unitary transformation gauges away the spatial dependence in the exchange term, leading to the generation of effective…
In this work, based on quantum operator Hermite polynomials and Weyl's mapping rule, we find a generation function of the two-variable Hermite polynomials. And then, noting that the Weyl ordering is invariant under the similar…