16865488
A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory
We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. The initial stages can even be computed diagrammatically. The method is formulated within the framework of an exact renormalization group for SU(N) Yang-Mills gauge theory, incorporating an effective cutoff through a manifest spontaneously broken SU(N|N) gauge invariance. We demonstrate the technique with a compact calculation of the one-loop beta function, achieving a manifestly universal result, and without gauge fixing, for the first time at finite N.
13594136
Exact scheme independence at two loops
We further develop an algorithmic and diagrammatic computational framework for very general exact renormalization groups, where the embedded regularisation scheme, parametrised by a general cutoff function and infinitely many higher point vertices, is left unspecified. Calculations proceed iteratively,by integrating by parts with respect to the effective cutoff, thus introducing effective propagators, and differentials of vertices that can be expanded using the flow equations; many cancellations occur on using the fact that the effective propagator is the inverse of the classical Wilsonian two-point vertex. We demonstrate the power of these methods by computing the beta function up to two loops in massless four dimensional scalar field theory, obtaining the expected universal coefficients, independent of the details of the regularisation scheme.
120318744
General covariance and open string interactions
Abstract It has been suggested that Witten's open string cubic interaction is independent of the background geometry. We investigate this suggestion in detail with a view to understanding the role of closed strings in Witten's open string field theory. The standard oscillator formulation of the vertex requires the use of a metric, if it is to be generally covariant, indicating that closed string interactions are required. However by changing to variables better suited to treating the midpoint, we show explicitly that it is possible to transform away all reference to the background metric. This supports the assertion that the cubic action (of Horowitz, Lykken, Rohm and Strominger) can also describe closed strings.
15153074
An exact RG formulation of quantum gauge theory
A gauge invariant Wilsonian effective action is constructed for pure SU(N) Yang-Mills theory by formulating the corresponding flow equation. Manifestly gauge invariant calculations can be performed i.e. without gauge fixing or ghosts. Regularisation is implemented in a novel way which realises a spontaneously broken SU(N|N) supergauge theory. As an example we sketch the computation of the one-loop ? function, performed for the first time without any gauge fixing.
13411572
New Developments in the Continuous Renormalization Group
Over the last several years, there has been a resurgence of interest in using non-perturbative approximation methods based on Wilson's continuous renormalization group. In this lecture, I review progress particularly in the past year, concentrating on theoretical issues in the structure of the exact renormalization group and its approximations.
14167872
Exact scheme independence at one loop
The requirement that the quantum partition function be invariant under a renormalization group transformation results in a wide class of exact renormalization group equations, differing in the form of the kernel. Physical quantities should not be sensitive to the particular choice of the kernel. We demonstrate this scheme independence in four dimensional scalar field theory by showing that, even with a general kernel, the one-loop beta function may be expressed only in terms of the effective action vertices, and thus, under very general conditions, the universal result is recovered.
17891976
A Shack¿Hartmann wavefront sensor projected on to the sky with reduced focal anisoplanatism
A method for producing a laser guide star wavefront sensor for adaptive optics with reduced focal anisoplanatism is presented. A theoretical analysis and numerical simulations have been carried out and the results are presented. The technique, named Sky-Projected Laser Array Shack-Hartmann (SPLASH), is shown to suffer considerably less from focal anisoplanatism than a conventional laser guide star system. The method is potentially suitable for large telescope apertures (∼8 m), and possibly for extremely large telescopes.
55583676
EAGLE multi-object AO concept study for the E-ELT
EAGLE is the multi-object spatially-resolved near-IR spectrograph instrument concept for the E- ELT, relying on a distributed Adaptive Optics, so-called Multi Object Adaptive Optics. This paper presents the results of a phase A study. Using 84x84 actuator deformable mirrors, the performed analysis demonstrates that 6 laser guide stars and up to 5 natural guide stars of magnitude R < 17, picked-up in a 7.3 � diameter patrol field of view, allow us to obtain an overall performance in terms of Ensquared Energy of 35% in a 75x75mas 2 spaxel at H band whatever the target direction in the centred 5 � science field for median seeing conditions. The computed sky coverage at galactic latitudes |b |∼ 60 is close to 90%.
2587128
Shack-Hartmann sensor improvement using optical binning.
We present a design improvement for a recently proposed type of Shack-Hartmann wavefront sensor that uses a cylindrical (lenticular) lenslet array. The improved sensor design uses optical binning and requires significantly fewer detector pixels than the corresponding conventional or cylindrical Shack-Hartmann sensor, and so detector readout noise causes less signal degradation. Additionally, detector readout time is significantly reduced, which reduces the latency for closed loop systems and data processing requirements. We provide simple analytical noise considerations and Monte Carlo simulations, we show that the optically binned Shack-Hartmann sensor can offer better performance than the conventional counterpart in most practical situations, and our design is particularly suited for use with astronomical adaptive optics systems.