arXiv subjects
Publications and source records attributed to L. Mesref.
In this paper, we introduce a map between the q-deformed gauge fields defined on the GL$_{q}(N) $-covariant quantum hyperplane and the ordinary gauge fields. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing $\grave{a} $ la BRST is discussed. An other star product defined on the hybrid $(q,h) $% -plane is explicitly constructed .
The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid kit" before one ventures into the beautiful but bewildering landscape of Woronowicz's theory. First, we present an up-to-date account of the methods and definitions used in quantum gauge theories. Then, we highlight our new results. The present paper is by no means an exhaustive overview of this swiftly developing subject.
A q-analogue of four dimensional conformally invariant field theory based on the quantum algebra U_{q}(so(4,2)) is proposed. The two- and three-point correlation functions are calculated. The construction is elaborated in order to fit the Hopf algebra structure.
We introduce a new map between a (q,h)-deformed gauge theory and ordinary gauge theory in a full analogy with Seiberg-Witten map.
We introduce a new map between a q-deformed gauge theory on a general GL_{q}(N)-covariant quantum hyperplane and an ordinary gauge theory in a full analogy with Seiberg-Witten map. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing a la BRST is discussed
In complete analogy with Seiberg-Witten map defined in noncommutative geometry we introduce a new map between a q-deformed gauge theory and an ordinary gauge theory. The construction of this map is elaborated in order to fit the Hopf algebra structure.
We study the superconformal and super-BRS invariance of the supersymmetric Wess-Zumino-Witten model based on Lie superalgebra. The computation of the critical super-dimension of this model is done using the Fujikawa regularization. Finally, we recover the well-known result which fixes the relative coupling constant a2 = 1 in a rigorous way.
We show that the Woronowicz prescription using a bimodule constructed out of a tensorial product of a bimodule and its conjugate and a bi-coinvariant singlet leads to a trivial differential calculus.
We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fields obtained from chiral primary operators (CPOs) $O^I_k(x)$ and eventually their derivatives by applying operator product expansions and singling out SO(6) representations. We show that normal products of $O_2$ operators can be expressed in terms of projection operators on representations of SO(20) and discuss intertwining operators for SO(6) representations. Furthermore we derive $\mathcal{O}(\frac{1}{N^2})$ corrections to AdS/CFT 4-point functions by graphical combinatorics and finally extract anomalous dimensions by applying the method of conformal partial wave analysis. We find infinite sequences of quasi-primary fields with vanishing anomalous dimensions and interpret them as 1/2-BPS or 1/4-BPS fields.
We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of $U(1)_Y$ symmetry for four-point functions.
Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields $\tildeΦ\tildeΦ$, $\tilde{C}\tilde{C}$ and $\tildeΦ\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $δ=2+l$ or $8+l+η(l)$ and $η(l)=\mathcal{O}(N^{-2})$ are identified. The unidentified fields have dimension $δ=λ+l+η(l)$ with $λ\geq 10$. The anomalous dimensions $η(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tildeΦ\tildeΦ + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tildeΦ\tilde{C} + \tilde{C}\tildeΦ)$ and are found to be the same, proving $U(1)_Y$ symmetry. The relevant coupling constants are given at order $\mathcal{O}(1)$.
We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis.