Structure constants of beta deformed super Yang-Mills

We study the structure constants of the N = 1 beta deformed theory perturbatively and at strong coupling. We show that the planar one loop corrections to the structure constants of single trace gauge invariant operators in the scalar sector is determined by the anomalous dimension Hamiltonian. This result implies that 3 point functions of the chiral primaries of the theory do not receive corrections at one loop. We then study the structure constants at strong coupling using the Lunin-Maldacena geometry. We explicitly construct the supergravity mode dual to the chiral primary with three equal U(1) R-charges in the Lunin-Maldacena geometry. We show that the 3 point function of this supergravity mode with semi-classical states representing two other similar chiral primary states but with large U(1) charges to be independent of the beta deformation and identical to that found in the AdS(5) x S-5 geometry. This together with the one-loop result indicate that these structure constants are protected by a non-renormalization theorem. We also show that three point function of U(1) R-currents with classical massive strings is proportional to the R-charge carried by the string solution. This is in accordance with the prediction of the R-symmetry Ward identity.

Yang-Mills theory in six-dimensional superspace

The superspace approach provides a manifestly supersymmetric formulation of supersymmetric theories. For N= 1 supersymmetry one can use either constrained or unconstrained superfields for such a formulation. Only the unconstrained formulation is suitable for quantum calculations. Until now, all interacting N>1 theories have been written using constrained superfields. No solutions of the nonlinear constraint equations were known.

In this work, we first review the superspace approach and its relation to conventional component methods. The difference between constrained and unconstrained formulations is explained, and the origin of the nonlinear constraints in supersymmetric gauge theories is discussed. It is then shown that these nonlinear constraint equations can be solved by transforming them into linear equations. The method is shown to work for N=1 Yang-Mills theory in four dimensions.

N=2 Yang-Mills theory is formulated in constrained form in six-dimensional superspace, which can be dimensionally reduced to four-dimensional N=2 extended superspace. We construct a superfield calculus for six-dimensional superspace, and show that known matter multiplets can be described very simply. Our method for solving constraints is then applied to the constrained N=2 Yang-Mills theory, and we obtain an explicit solution in terms of an unconstrained superfield. The solution of the constraints can easily be expanded in powers of the unconstrained superfield, and a similar expansion of the action is also given. A background-field expansion is provided for any gauge theory in which the constraints can be solved by our methods. Some implications of this for superspace gauge theories are briefly discussed.

Manufacturing dish shaped rings on radial-axial ring rolling mills

Ring rolling is an established method to produce seamless rings of different cross-sectional geometries. For dish shaped rings, there are applications in different areas such as offshore, aeronautics or the energy sector. At the moment, dish shaped rings are produced by machining of rings with rectangular shaped cross section, by (open die) hollow forging on a conical mandrel or by using shaped ring rolling tools. These ways of manufacturing have the disadvantage of high material waste, additional costs for special tools, long process time and limited or inflexible geometries. Therefore, the manufacturing of dish shaped rings on conventional radial-axial ring rolling mills would expand the range of products for ring producers. The aim of this study is to investigate the feasibility of an alternative to the current manufacturing processes, without requiring additional tooling and material costs. Therefore, the intended formation of dish shaped rings-previously regarded as a form error-is investigated. Based on an analysis of geometrical requirements and metal flow mechanisms, a rolling strategy is presented, causing dishing and ring climbing by a large height reduction of the ring. Using this rolling strategy dish shaped rings with dishing angles up to 18° were achieved. In addition to the experiments finite element method (FEM)-simulations of the process have been successfully conducted, in order to analyze the local strain evolution. However, when the contact between ring and main roll is lost in the process the ring starts to oscillate around the mandrel and neither dishing nor ring climbing is observed. © 2013 German Academic Society for Production Engineering (WGP).