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Mason L.,Mathematical Institute andrew Wiles Building | Skinner D.,Wilberforce Road
Journal of High Energy Physics | Year: 2014

We show that string theories admit chiral infinite tension analogues in which only the massless parts of the spectrum survive. Geometrically they describe holomorphic maps to spaces of complex null geodesics, known as ambitwistor spaces. They have the standard critical space-time dimensions of string theory (26 in the bosonic case and 10 for the superstring). Quantization leads to the formulae for tree-level scattering amplitudes of massless particles found recently by Cachazo, He and Yuan. These representations localize the vertex operators to solutions of the same equations found by Gross and Mende to govern the behaviour of strings in the limit of high energy, fixed angle scattering. Here, localization to the scattering equations emerges naturally as a consequence of working on ambitwistor space. The worldsheet theory suggests a way to extend these amplitudes to spinor fields and to loop level. We argue that this family of string theories is a natural extension of the existing twistor string theories. © 2014 The Author(s). Source

Lipstein A.E.,Mathematical Institute andrew Wiles Building | Reid-Edwards R.A.,University of Hull
Journal of High Energy Physics | Year: 2014

Abstract: We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be U(1), the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also explore a very simple and natural non-abelian generalization with gauge group U(N) × U(N). In the classical continuum limit, it reduces to a free theory, but at non-zero lattice spacing it is an interacting theory which gives rise to U(N) Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling. © 2014, The Author(s). Source

Zhu Y.,Hong Kong University of Science and Technology | Chapman S.J.,Mathematical Institute andrew Wiles Building
Materials Science and Engineering A | Year: 2013

The motion of gliding screw dislocation segments in channel-veins and persistent slip band structure is analysed mathematically and the shape of these segments is determined. The model provides a possible explanation of the "length effect" of such dislocation segments observed in magnesium. Finally, the possible implications for the cross-slip of screw segments in fatigue testing are discussed. © 2013 Elsevier B.V. Source

Penrose R.,Mathematical Institute andrew Wiles Building
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | Year: 2015

A key obstruction to the twistor programme has been its so-called 'googly problem', unresolved for nearly 40 years, which asks for a twistor description of right-handed interacting massless fields (positive helicity), using the same twistor conventions that give rise to left-handed fields (negative helicity) in the standard 'nonlinear graviton' and Ward constructions. An explicit proposal for resolving this obstruction - palatial twistor theory - is put forward (illustrated in the case of gravitation). This incorporates the concept of a non-commutative holomorphic quantized twistor 'Heisenberg algebra', extending the sheaves of holomorphic functions of conventional twistor theory to include the operators of twistor differentiation. © 2015 The Author(s) Published by the Royal Society. All rights reserved. Source

Zhu S.-X.,Mathematical Institute andrew Wiles Building | Zhu S.-X.,Mathematical Institute andrew Wiles Building | Gu T.-X.,CAS Beijing Institute of Applied Physics And Computational Mathematics | Liu X.-P.,CAS Beijing Institute of Applied Physics And Computational Mathematics
Computers and Mathematics with Applications | Year: 2014

Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrate how to minimize global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and verified by numerical experiments. The experiments also show the local communications for some structured sparse matrix-vector multiplications and global communications in the underlying supercomputers increase in the order P1/2.5 and P4/5 respectively, where P is the number of processors. © 2013 Elsevier Ltd. All rights reserved. Source

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