Related papers: On the high derivative fermionic operator and trac…
We compute the contribution to the anomalous dimension of the twist-2 operators in N=4 SYM theory, which is proportional to the number of fermion loops inside Feynman diagrams or, formally, to the number of fermions. The result was obtained…
The anomaly implies an obstruction to a fully chiral covariant calculation of the effective action in the abnormal parity sector of chiral theories. The standard approach then is to reconstruct the anomalous effective action from its…
In this article, we explicitly compute in momentum space the three and four-point correlation functions involving scalar and spinning operators in the free bosonic and the free fermionic theory in three dimensions. We also evaluate the…
We derive recursion relations for the anomalous dimensions of double-trace operators occurring in the conformal block expansion of four-point stress tensor correlators in the 6d $(2,0)$ theory, which encode higher-derivative corrections to…
Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…
The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We…
We consider a generic time-reversal invariant model of fermions hopping randomly on a square lattice. By means of the conventional replica-trick within the fermionic path-integral formalism, the model is mapped onto a non-linear sigma-model…
We study the the high spin expansion of the anomalous dimension for long operators belonging to the $sl(2)$ sector of ${\cal N}=4$ SYM. Keeping the ratio $j$ between the twist and the logarithm of the spin fixed, the anomalous dimensions…
As it is shown in previous works, discrete periodic operators with defects are unitarily equivalent to the operators of the form $$ {\mathcal A}{\bf u}={\bf A}_0{\bf u}+{\bf A}_1\int_0^1dk_1{\bf B}_1{\bf u}+...+{\bf…
We calculate the trace (conformal) anomaly for chiral fermions in a general curved background using Hadamard subtraction. While in intermediate steps of the calculation imaginary terms proportional to the Pontryagin density appear, imposing…
We discuss conformally covariant differential operators, which under local rescalings of the metric, \delta_\sigma g^{\mu\nu} = 2 \sigma g^{\mu\nu}, transform according to \delta_\sigma \Delta = r \Delta \sigma + (s-r) \sigma \Delta for…
We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which…
In this paper I propose the use of a lattice derivative operator that is equivalent to the ideal SLAC derivative operator in all lattice calculations, but without the prohibitively expensive computational cost of the latter. A pedagogical…
Let $X=G/P$ be a real projective quadric, where $G=O(p,q)$ and $P$ is a parabolic subgroup of $G$. Let $\left(\pi_{\lambda,\epsilon}, \mathcal{H}_{\lambda,\epsilon}\right)_{ (\lambda,\epsilon)\in \mathbb {C}\times \{\pm\}}$ be the family of…
We consider Hadamard fractional derivatives and integrals of variable fractional order. A new type of fractional operator, which we call the Hadamard-Marchaud fractional derivative, is also considered. The objective is to represent these…
We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the…
The axial anomaly is computed for Euclidean Dirac fermions on the plane. The dependence upon the self-adjoint extensions of the Dirac operator is investigated and its relevance concerning the second virial coefficient of the anyon gas is…
A nonstandard invariant fourth order operator acting on functions on a manifold equipped with an almost Grassmannian structure with an arbitrary trorsion is found by means of the curved translation principle. This operator can be viewed as…
We deform the well-known three dimensional $\mathcal{N}=1$ Wess-Zumino model by adding higher derivative operators (Lee-Wick operators) to its action. The effects of these operators are investigated both at the classical and quantum levels.
A remarkable feature of a lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this Ginsparg-Wilson lattice Dirac operator does not possess topological zero modes for any…