Related papers: New Integrable Structures in Large-N QCD
The local composite gluon-ghost operator $({1/2}A^{a\mu}A_{\mu}^{a}+\alpha \bar{c}^{a}c^{a})$ is analysed in the framework of the algebraic renormalization in SU(N) Yang-Mills theories in the Landau, Curci-Ferrari and maximal abelian…
In this paper, we consider a compact five dimensional spacetime with the structure $\mathcal{M}^{1,3}\times S^{1}$. Generally speaking, motion on such a structure will break Lorentz invariance, allowing for causal bulk signals to propagate…
We analyse the renormalisation properties of composite operators of scalar fields in the N=2 Super Yang-Mills theory. We compute the matrix of anomalous dimensions in the planar limit at one-loop order in the 't Hooft coupling, and show…
We propose a new method for computing the renormalization functions, which is based on the ideas of operator product expansion and large momentum expansion. In this method, the renormalization $Z$-factors are determined by the ultraviolet…
The quantum periodic XXZ chain with alternating spins is studied. The properties of the related R-matrix and Hamiltonians are discussed. A compact expression for the ground state energy is obtained. The corresponding conformal anomaly is…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
Most of the exact solutions of quantum one-dimensional Hamiltonians are obtained thanks to the success of the Bethe ansatz on its several formulations. According to this ansatz the amplitudes of the eigenfunctions of the Hamiltonian are…
We study two-loop anomalous dimension matrices in QCD and related gauge theories for products of Wilson lines coupled at a point. We verify by an analysis in Euclidean space that the contributions to these matrices from diagrams that link…
We study $(1+1)$-dimensional $SU(N)$ spin systems in the presence of the global $SU(N)$ rotation and lattice translation symmetries. By matching the mixed anomaly of the $PSU(N)\times\mathbb{Z}$ symmetry in the continuum limit, we identify…
We show that Hertz $\phi^4$ theory of quantum criticality is incomplete as it misses anomalous non-local contributions to the interaction vertices. For antiferromagnetic quantum transitions, we found that the theory is renormalizable only…
We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous. Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently…
Employing the operator algebra of the conformal group and the conformal Ward identities, we derive the constraints for the anomalies of dilatation and special conformal transformations of the local twist-2 operators in Quantum…
We discuss, in conformally invariant field theories such as QCD with massless fermions, a possible link between the perturbative signature of the conformal anomaly, in the form of anomaly poles of the 1-particle irreducible effective…
The path space of an inhomogeneous vertex model constructed from the vector representation of $U_q\bigl(gl(2|2)\bigr)$ and its dual is studied for various choices of composite vertices and assignments of $gl(2|2)$-weights. At $q=0$, the…
Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1|2) sector. For planar N=4 SYM…
The spin chains originating from large-N conformal gauge theories are of a special kind: The Hamiltonian is not invariant under the symmetry algebra, it is rather a part of it. This leads to interesting properties within the asymptotic…
The results of analysis of the one--loop spectrum of anomalous dimensions of composite operators in the scalar $ \phi^{4} $ model are presented. We give the rigorous constructive proof of the hypothesis on the hierarchical structure of the…
I present a theoretical discussion of the uncertainties related to the QCD analysis of the proton structure function $F_2(x,Q^2)$ at small $x$. The role played by the `unphysical' gluon density is pointed out. It is shown how the study of…
A two-dimensional Pauli Hamiltonian describing the interaction of a neutral spin-1/2 particle with a magnetic field having axial and second order symmetries, is considered. After separation of variables, the one-dimensional matrix…
The anomalous dimensions of four-quark operators $(\bar q_i q_j)_{V-A} (\bar q_k q_l)_{V-A}$ are calculated in the large $N_f$ limit. As expected, the result is a convergent series without renormalon ambiguities. Using the approximation of…