BRST Algebra Quantum Double and Quantization of the Proper Time Cotangent Bundle

The quantum double for the quantized BRST superalgebra is studied. The corresponding R-matrix is explicitly constucted. The Hopf algebras of the double form an analytical variety with coordinates described by the canonical deformation parameters. This provides the possibility to construct the nontrivial quantization of the proper time supergroup cotangent bundle. The group-like classical limit for this quantization corresponds to the generic super Lie bialgebra of the double.Comment: 11 pages, LaTe

Four-loop verification of algorithm for Feynman diagrams summation in N=1 supersymmetric electrodynamics

A method of Feynman diagrams summation, based on using Schwinger-Dyson equations and Ward identities, is verified by calculating some four-loop diagrams in N=1 supersymmetric electrodynamics, regularized by higher derivatives. In particular, for the considered diagrams correctness of an additional identity for Green functions, which is not reduced to the gauge Ward identity, is proved.Comment: 14 pages, 9 figure

Zero Order Estimates for Analytic Functions

The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under some appropriate transformation of a polynomial ring. In particular, this result leads to a new link between the theory of polarized algebraic dynamical systems and transcendental number theory. On the other hand, it allows to establish an improvement of Nesterenko's conditional result on solutions of systems of differential equations. We also deduce, under some condition on stable varieties, the optimal multiplicity estimate in the case of generalized Mahler's functional equations, previously studied by Mahler, Nishioka, Topfer and others. Further, analyzing stable ideals we prove the unconditional optimal result in the case of linear functional systems of generalized Mahler's type. The latter result generalizes a famous theorem of Nishioka (1986) previously conjectured by Mahler (1969), and simultaneously it gives a counterpart in the case of functional systems for an important unconditional result of Nesterenko (1977) concerning linear differential systems. In summary, we provide a new universal tool for transcendental number theory, applicable with fields of any characteristic. It opens the way to new results on algebraic independence, as shown in Zorin (2010).Comment: 42 page

Variant supercurrent multiplets

In N = 1 rigid supersymmetric theories, there exist three standard realizations of the supercurrent multiplet corresponding to the (i) old minimal, (ii) new minimal and (iii) non-minimal off-shell formulations for N = 1 supergravity. Recently, Komargodski and Seiberg in arXiv:1002.2228 put forward a new supercurrent and proved its consistency, although in the past it was believed not to exist. In this paper, three new variant supercurrent multiplets are proposed. Implications for supergravity-matter systems are discussed.Comment: 11 pages; V2: minor changes in sect. 3; V3: published version; V4: typos in eq. (2.3) corrected; V5: comments and references adde

Summation of diagrams in N=1 supersymmetric electrodynamics, regularized by higher derivatives

For the massless N=1supersymmetric electrodynamics, regularized by higher derivatives, the Feynman diagrams, which define the divergent part of the two-point Green function and can not be found from Schwinger-Dyson equations and Ward identities, are partially summed. The result can be written as a special identity for Green functions.Comment: 16 pages, 10 figure

Superconformal constraints for QCD conformal anomalies

Anomalous superconformal Ward identities and commutator algebra in N = 1 super-Yang-Mills theory give rise to constraints between the QCD special conformal anomalies of conformal composite operators. We evaluate the superconformal anomalies that appear in the product of renormalized conformal operators and the trace anomaly in the supersymmetric spinor current and check the constraints at one-loop order. In this way we prove the universality of QCD conformal anomalies, which define the non-diagonal part of the anomalous dimension matrix responsible for scaling violations of exclusive QCD amplitudes at the next-to-leading order.Comment: 30 pages, 2 figures, LaTe

Decoupling of the ϵ\epsilon-scalar mass in softly broken supersymmetry

It has been shown recently that the introduction of an unphysical $\epsilon$-scalar mass $\tilde{m}$ is necessary for the proper renormalization of softly broken supersymmetric theories by dimensional reduction (\drbar). In these theories, both the two-loop $\beta$-functions of the scalar masses and their one-loop finite corrections depend on $\tilde{m}^2$. We find, however, that the dependence on $\tilde{m}^2$ can be completely removed by slightly modifying the \drbar renormalization scheme. We also show that previous \drbar calculations of one-loop corrections in supersymmetry which ignored the $\tilde{m}^2$ contribution correspond to using this modified scheme.Comment: 7 pages, LTH-336, NUB-3094-94TH, KEK-TH-40