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# Some dual relations in twistor theory

HEP Experiments. Learn more. Nima Arkani-Hamed Princeton, Inst. Advanced Study. Freddy Cachazo Perimeter Inst. Clifford Cheung Princeton, Inst. Advanced Study and Harvard U. Jared Kaplan Princeton, Inst. Published in: JHEP 03 DOI: Citations per year 0 5 10 15 20 Abstract: arXiv. Less telegraphic abstract in the body of the paper. Largely expanded set of references included. Some diagrammatic clarifications added, minor typo fixed. Supersymmetric gauge theory Duality in Gauge Field Theories Classical Theories of Gravity twistor S-matrix duality tree approximation gauge field theory: Yang-Mills signature scattering amplitude.

References Figures 0. Multiparton amplitudes in gauge theories Michelangelo L. Stephen J. Parke Fermilab. Calculating scattering amplitudes efficiently Lance J. Dixon SLAC.

Peter Svrcek Princeton, Inst. PoS RTN Lance J. David A. Kosower Saclay, SPhT.

### twistor string theory

Annals Phys. Taylor Fermilab.

Apple id apiBerends Leiden U.I believe they provide a remarkable possibility for how internal and space-time symmetries become integrated at short distances, without the usual problem of introducing a host of new degrees of freedom. Twistor theory has a long history going back to the s, and it is such a beautiful idea that there always has been a good argument that there is something very right about it.

But it never seemed to have any obvious connection to the Standard Model and its pattern of internal symmetries. One of the wonderful things about twistor theory is that it includes both Minkowski and Euclidean space as real slices of a complex, holomorphic, geometry. The points in these spaces are best understood as complex lines in another space, projective twistor space. It is on projective twistor space that the internal symmetries of the Standard Model become visible.

The draft paper contains the details, but I should make clear what some of the arguments are for taking this seriously:. Two of the main problems are:. What I think is probably most important here is that this picture gives a new and compelling idea about how internal and space-time symmetries are related.

What is most bizarre about this proposal is the way in which, by going to Euclidean space-time, you change what is a space-time and what is an internal symmetry. If the identification of the direction of the Higgs field with a choice of imaginary time direction makes sense, perhaps a full theory will give Higgs physics in some way observably different from the usual Standard Model.

One thing not discussed in this paper is gravity. Twistor geometry can also describe curved space-times and gravitational degrees of freedom, and since the beginning, there have been attempts to use it to get a quantum theory of gravity. Perhaps the new ideas described here, including especially the Euclidean point of view with its breaking of Euclidean rotational invariance, will indicate some new way forward for a twistor-based quantum gravity. This discusses the Euclidean version of the twistor story, in the context it was used back in the late s to relate solutions of the instanton equations to holomorphic bundles.

The chiral nature of twistor geometry fits naturally with a long tradition going back to Plebanski and Ashtekar of formulating gravity theories using just the self-dual part of the spin connection. This is meant as a proposal for short-distance physics, conformally-invariant physics. Still, I am impressed that you have put it out to allow all those whom you have criticized to take their shots at you.

Also, does your theory predict anything and how can it be experimentally verified? John C. Rodney, At this point in my life, the last thing I want to waste my time on is dumb arguments about these ideas, string theory, testability, etc.

## Twistor theory

For a truly completely convincing prediction, what you want is a calculation of one of the Standard Model parameters, or, better, some prediction from a model based on these ideas that is different than what the Standard Model predicts. There are many unification models out there. Even I have one easily found on arXiv — using category theory, it allows you to discuss fermion generations, automatically includes gravity, works only in 4D, and has potential to circumvent Coleman-Mandula.

And some other stuff. So the lack of unification proposals, with various interesting properties, is not the problem. The majority of researchers will not bother to pay any attention to unification models. Even if one explicitly demonstrates that some model reduces the number of free parameters, it is tough to convince people.

A typical example is the noncommutative SM, developed by Chamseddine, Connes and their collaborators. Does the hep-th community pay any attention to it? Not much, really. I share your point of view that proposing unification models and studying them is a worthwhile endeavour, but it appears that any such model requires a substantial number of people to drive the research in order to flesh out a convincing prediction. But attention of other researchers can apparently be obtained only if one already has a prediction.

And thus you reach Catch 22, having a nontrivial manpower-problem to move the idea off the ground. Math is always beautiful, various algebraic structures have some captivating properties, and offer tempting ways to explain various properties of nature that we do not yet understand. Since this is your pre-? Have you discussed this with or gotten feedback from others with deep interest in twistors? Traditionally the way the field made progress was by focusing on explaining experimental results that contradicted the best available model.In theoretical physicstwistor theory was proposed by Roger Penrose in [1] as a possible path [2] to quantum gravity and has evolved into a branch of theoretical and mathematical physics.

Penrose proposed that twistor space should be the basic arena for physics from which space-time itself should emerge. It leads to a powerful set of mathematical tools that have applications to differential and integral geometrynonlinear differential equations and representation theory and in physics to general relativity and quantum field theoryin particular to scattering amplitudes. It has the physical interpretation of the space of massless particles with spin.

Usaa pay dates 2020This definition can be extended to arbitrary dimensions except that beyond dimension four, one defines projective twistor space to be the space of projective pure spinors for the conformal group. In its original form, twistor theory encodes physical fields on Minkowski space into complex analytic objects on twistor space via the Penrose transform. This is especially natural for massless fields of arbitrary spin. In the first instance these are obtained via contour integral formulae in terms of free holomorphic functions on regions in twistor space.

These constructions have had wide applications. The self-duality condition is a major limitation for incorporating the full nonlinearities of physical theories, although it does suffice for Yang—Mills—Higgs monopoles and instantons see ADHM construction.

These apply to general fields but the field equations are no longer so simply expressed. Twistorial formulae for interactions beyond the self-dual sector first arose from Witten's twistor string theory.

Despite its shortcomings, twistor string theory led to rapid developments in the study of scattering amplitudes. One was the so-called MHV formalism [16] loosely based on disconnected strings, but was given a more basic foundation in terms of a twistor action for full Yang—Mills theory in twistor space. Twistor string theory was extended first by generalising the RSV Yang—Mills amplitude formula, and then by finding the underlying string theory. They extend to give formulae for loop amplitudes [33] [34] and can be defined on curved backgrounds.

Points in Minkowski space are related to subspaces of twistor space through the incidence relation. Supertwistors are a supersymmetric extension of twistors introduced by Alan Ferber in The nonlinear graviton construction encodes only anti-self-dual, i. The task of using such twistor functions in a fully nonlinear way so as to obtain a right-handed nonlinear graviton has been referred to as the gravitational googly problem the word " googly " is a term used in the game of cricket for a ball bowled with right-handed helicity using the apparent action that would normally give rise to left-handed helicity.

From Wikipedia, the free encyclopedia. Redirected from Twistor mathematics. Journal of Mathematical Physics. Bibcode : JMP Physics Reports.

Bibcode : PhR Spinors and Space-Time.For nearly four decades, Penrose has been exploring his own mathematical approach — twistor theory. Penrose developed the theory out of a strong general relativity approach the theory requires only four dimensions. Penrose maintains a belief that any theory of quantum gravity will need to include fundamental revisions to the way physicists think about quantum mechanics, something with which most particle physicists and string theorists disagree.

One of the key aspects of twistor theory is that the relation between events in space-time is crucial. Instead of focusing on the events and their resulting relationships, twistor theory focuses on the causal relationships, and the events become byproducts of those relationships.

If you take all of the light rays in space-time, it creates a twistor space, which is the mathematical universe in which twistor theory resides.

Comunicato ufficiale n. 42 del 11/02/2020In fact, there are some indications that objects in twistor space may result in objects and events in our universe.

The major flaw of twistor theory is that even after all of these years it was originally developed in the sit still only exists in a world absent of quantum physics. The space-time of twistor theory is perfectly smooth, so it allows no discrete structure of space-time. Edward Witten and other string theorists have begun to investigate ways that twistor theory may relate to string theory. One approach has been to have the strings exist not in physical space, but in twistor space.

Andrew Zimmerman Jones received his physics degree and graduated with honors from Wabash College, where he earned the Harold Q. Fuller Prize in Physics. String Theory and Twistor Theory.In theoretical physics, twistor theory was proposed by Roger Penrose in as a possible path to quantum gravity and has evolved into a branch of theoretical and mathematical physics.

Penrose proposed that twistor space should be the basic arena for physics from which space-time itself should emerge. This article or section 's content is very similar or exactly the same as that at Wikipedia. This is considered a major breakthrough by many as till Witten's paper, Twistor theory was only applicable to Classical General Relativity. Via the nonlinear graviton construction, these integrable complex structure deformations of e.

PT Moreover there are other string theories one can construct which reproduce the same tree-level amplitudes but apparently differ at loop level. Take your favorite fandoms with you and never miss a beat. Prior to the First Superstring Revolution. To illustrate this, lets consider the six-particle NMHV amplitude originally calculated by summing Feynman diagrams. The resulting theory is closely related to the multi-dimensional residue calculus in G k,n introduced in Cachazo's talk.

This article is a stub. Penrose, Roger; McCallum M.

Download link right click and 'save-as' for playing in VLC or other compatible player. Related entries. This is because the contributor of this article had initially contributed it to wikipedia. I'll give an introduction to twistor-string theory, which is an attempt to reformulate supersymmetric gauge theory in four-dimensional space-time in terms of a certain generalisation of Gromov-Witten theory in twistor space. For nearly four decades, Penrose has been exploring his own mathematical approach — twistor theory.

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