The Duties of a Mathematician

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## Monday, October 08, 2007

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Whatever Happened to Twistor Strings?

For those of you wondering if twistor strings vanished into obscurity, I found some recent arxiv papers on the subject. There was an august phenomenology paper on the twistor string entitled A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes.

The abstract is as follows:

Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and implement the method in a numerical procedure. Our technique can be applied to any one-loop scattering amplitude and offers the possibility that one-loop calculations can be performed in an automatic fashion, as tree-level amplitudes are currently done. Instead of individual Feynman diagrams, the ingredients for our one-loop evaluation are tree-level amplitudes, which are often already known. To study the practicality of this method we evaluate the cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically, using the analytically known 4, 5 and 6 gluon tree-level amplitudes. Comparisons with analytic answers are performed to ascertain the numerical accuracy of the method.

Others which deserve honorable mention are Twistor Strings with Flavour and Balanced Superprojective Varieties. I especially have to find the time to digest the latter, as the notion of a superprojective space as a functor-of-points seems useful.

For those of you wondering if twistor strings vanished into obscurity, I found some recent arxiv papers on the subject. There was an august phenomenology paper on the twistor string entitled A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes.

The abstract is as follows:

Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and implement the method in a numerical procedure. Our technique can be applied to any one-loop scattering amplitude and offers the possibility that one-loop calculations can be performed in an automatic fashion, as tree-level amplitudes are currently done. Instead of individual Feynman diagrams, the ingredients for our one-loop evaluation are tree-level amplitudes, which are often already known. To study the practicality of this method we evaluate the cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically, using the analytically known 4, 5 and 6 gluon tree-level amplitudes. Comparisons with analytic answers are performed to ascertain the numerical accuracy of the method.

Others which deserve honorable mention are Twistor Strings with Flavour and Balanced Superprojective Varieties. I especially have to find the time to digest the latter, as the notion of a superprojective space as a functor-of-points seems useful.

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## 3 comments:

Hi Kneemo,

1- Jacques Distler ’Musings’ comments on this paper with responses by 1st author:

Authors: Rutger Boels, Lionel Mason, David Skinner,

‘From Twistor Actions to MHV Diagrams’

(Submitted on 5 Feb 2007)

http://golem.ph.utexas.edu/~distler/blog/archives/001441.html

2 - I still speculate that the helix may be more informative than suspected by many physicists in areas other than nucleic acids, music and conventional solenoids

Since Witten has began to look at the Monster of Borcherds, the string-D may be helical which may bring us back to some forn of twistor string theory?

3 - Check out this summary report at:

USA Today, ‘New spin on how stars are born’

By Ker Than, SPACE.com

Copyright 2007, SPACE.com Inc. ALL RIGHTS RESERVED.

http://www.usatoday.com/tech/

science/space/2007-11-01-star-birth_N.htm

Original Letter:

Nature 450, 71-73 (1 November 2007) | doi:10.1038/nature06220; Received 8 June 2007;

Accepted 4 September 2007

http://www.nature.com/nature/

journal/v450/n7166/abs/

nature06220.html

Antonio Chrysostomou, Philip W Lucas and James H Hough,

‘Circular polarimetry reveals helical magnetic fields in the young stellar object HH 135–136’.

Excellent find Doug! I'll get a new post going after I read the papers you mentioned.

Hi Kneemo,

Elliptical functions are planar helical functions.

Applied Mathematics in EE and ME appears to have two publications that may link to the physics of David Hestenes 'zitterbewegung' and Edward Witten twistor string theory.

1a-look on Google books for:

Hamish Meikle

A New Twist to Fourier Transforms

1b-Maple Product Description:

A New Twist to Fourier Transforms

http://www.adeptscience.co.uk/products/mathsim/mapleconnect/fourier.html

2-A. Mahalov1, 2, 3, E. S. Titi1, 2, 3 and S. Leibovich1, 2, 3

(1) Center for Applied Mathematics, Cornell University, Ithaca, New York

(2) Department of Mathematics, University of California, California, Irvine

(3) Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York Received: 21 December 1989

Invariant helical subspaces for the Navier-Stokes equations

http://www.springerlink.com/content/u233538u255206u3/

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