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D-Instantons and Twistors
Home Search Collections Journals About Contact us My IOPscience D-instantons and twistors This article has been downloaded from IOPscience. Please scroll down to see the full text article. JHEP03(2009)044 (http://iopscience.iop.org/1126-6708/2009/03/044) The Table of Contents and more related content is available Download details: IP Address: 132.166.22.147 The article was downloaded on 26/02/2010 at 16:55 Please note that terms and conditions apply. Published by IOP Publishing for SISSA Received: January 5, 2009 Accepted: February 11, 2009 Published: March 6, 2009 D-instantons and twistors JHEP03(2009)044 Sergei Alexandrov,a Boris Pioline,b Frank Saueressigc and Stefan Vandorend aLaboratoire de Physique Th´eorique & Astroparticules, CNRS UMR 5207, Universit´eMontpellier II, 34095 Montpellier Cedex 05, France bLaboratoire de Physique Th´eorique et Hautes Energies, CNRS UMR 7589, Universit´ePierre et Marie Curie, 4 place Jussieu, 75252 Paris cedex 05, France cInstitut de Physique Th´eorique, CEA, IPhT, CNRS URA 2306, F-91191 Gif-sur-Yvette, France dInstitute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, 3508 TD Utrecht, The Netherlands E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by relating the quaternionic-K¨ahler metric on the hy- permultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. -
Atiyah, M.F. 1. Geometry of Yang-Mills Fields, Lezioni Fermiani, Pisa 1979 2
BIBLIOGRAPHY Atiyah, M.F. 1. Geometry of Yang-Mills fields, Lezioni Fermiani, Pisa 1979 2. Green's functions for seH-dual four manifolds, Adv. in Math. 7 A (1981) 130-158 Atiyah, M. F., Drin'feld, V.G., Hitchin, N. J. 3. Construction of instantons, Phys. Lett. 65A (1978) 185-187 Atiyah, MF., Hitchin, N.J., Singer, I.M. 4. SeH-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. Lon don 362 (1978), 425-461 Atiyah, M. F., Jones, J. S. 5. Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978), 97-118 Atiyah, M.F., Ward, R.S. 6. Instantons and algebraic geometry, Comm. Math. Phys. 55 (1977), 117-124 Barth, W. 7. Moduli of vector bundles on the projective plane, Invent. Math 42 (1977), 63-91 Barth, W., Hulek, K. 8. Monads 8.lJ.d moduli of vector bundles, manuscripta math. 25 (1978),323- 347 Beilinson, A. A. 9. Coherent sheaves on pn and problems in linear algebra, Funct. Anal. Appl. 12 (1978), 214-216 Beilinson, A. A., Gel'fand, S. I, Manin, Yu. I. 10. An instanton is determined by its complex singularlties, Funct. Anal. Appl. 14 (1980), 118-119 Belavin, A. A., Polyakov, A. M., Schwartz, A. S., Tyupkin, Yu. 11. Pseudo-particle solutions of the Yang-Mills equations, Phys. Lett. 59B (1975), 85-87 288 Bibliography Belavin, A. A., Zakharov, V. E. 12. Multidimensional method of the inverse scattering problem and duality equations for the Yang-Mills field, JETP Letters 25 (1977), 567-570 Berezin, F. A. 13. The mathematical basis of supersymmetrie field theories, Sov. -
Twistor-Strings, Grassmannians and Leading Singularities
Twistor-Strings, Grassmannians and Leading Singularities Mathew Bullimore1, Lionel Mason2 and David Skinner3 1Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom 2Mathematical Institute, 24-29 St. Giles', Oxford, OX1 3LB, United Kingdom 3Perimeter Institute for Theoretical Physics, 31 Caroline St., Waterloo, ON, N2L 2Y5, Canada Abstract We derive a systematic procedure for obtaining explicit, `-loop leading singularities of planar = 4 super Yang-Mills scattering amplitudes in twistor space directly from their momentum spaceN channel diagram. The expressions are given as integrals over the moduli of connected, nodal curves in twistor space whose degree and genus matches expectations from twistor-string theory. We propose that a twistor-string theory for pure = 4 super Yang-Mills | if it exists | is determined by the condition that these leading singularityN formulæ arise as residues when an unphysical contour for the path integral is used, by analogy with the momentum space leading singularity conjecture. We go on to show that the genus g twistor-string moduli space for g-loop Nk−2MHV amplitudes may be mapped into the Grassmannian G(k; n). For a leading singularity, the image of this map is a 2(n 2)-dimensional subcycle of G(k; n) and, when `primitive', it is of exactly the type found from− the Grassmannian residue formula of Arkani-Hamed, Cachazo, Cheung & Kaplan. Based on this correspondence and the Grassmannian conjecture, we deduce arXiv:0912.0539v3 [hep-th] 30 Dec 2009 restrictions on the possible leading singularities of multi-loop NpMHV amplitudes. In particular, we argue that no new leading singularities can arise beyond 3p loops. -
Twistor Theory and Differential Equations
IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 42 (2009) 404004 (19pp) doi:10.1088/1751-8113/42/40/404004 Twistor theory and differential equations Maciej Dunajski Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK E-mail: [email protected] Received 31 January 2009, in final form 17 March 2009 Published 16 September 2009 Online at stacks.iop.org/JPhysA/42/404004 Abstract This is an elementary and self-contained review of twistor theory as a geometric tool for solving nonlinear differential equations. Solutions to soliton equations such as KdV,Tzitzeica, integrable chiral model, BPS monopole or Sine–Gordon arise from holomorphic vector bundles over T CP1. A different framework is provided for the dispersionless analogues of soliton equations, such as dispersionless KP or SU(∞) Toda system in 2+1 dimensions. Their solutions correspond to deformations of (parts of) T CP1, and ultimately to Einstein– Weyl curved geometries generalizing the flat Minkowski space. A number of exercises are included and the necessary facts about vector bundles over the Riemann sphere are summarized in the appendix. PACS number: 02.30.Ik (Some figures in this article are in colour only in the electronic version) 1. Introduction Twistor theory was created by Penrose [19] in 1967. The original motivation was to unify general relativity and quantum mechanics in a non-local theory based on complex numbers. The application of twistor theory to differential equations and integrability has been an unexpected spin off from the twistor programme. -
Causal Dynamical Triangulations and the Quest for Quantum Gravity?
Appendices: Mathematical Methods for Basic and Foundational Quantum Gravity Unstarred Appendices support Part I’s basic account. Starred Appendices support Parts II and III on interferences between Problem of Time facets. Double starred ones support the Epilogues on global aspects and deeper levels of mathematical structure being contemplated as Background Independent. If an Appendix is starred, the default is that all of its sections are starred likewise; a few are marked with double stars. Appendix A Basic Algebra and Discrete Mathematics A.1 Sets and Relations For the purposes of this book, take a set X to just be a collection of distinguishable objects termed elements. Write x ∈ X if x is an element of X and Y ⊂ X for Y a subset of X, ∩ for intersection, ∪ for union and Yc = X\Y for the complement of Y in X. Subsets Y1 and Y2 are mutually exclusive alias disjoint if Y1 ∩ Y2 =∅: the empty set. In this case, write Y1 ∪ Y2 as Y1 Y2: disjoint union.Apartition of a set X is a splitting of its elements into subsets pP that are mutually exclusive = and collectively exhaustive: P pP X. Finally, the direct alias Cartesian product of sets X and Z, denoted X × Z, is the set of all ordered pairs (x, z) for x ∈ X, z ∈ Z. For sets X and Z,afunction alias map ϕ : X → Z is an assignation to each x ∈ X of a unique image ϕ(x) = z ∈ Z. Such a ϕ is injective alias 1to1if ϕ(x1) = ϕ(x2) ⇒ x1 = x2, surjective alias onto if given z ∈ Z there is an x ∈ X such that ϕ(x) = z, and bijective if it is both injective and surjective. -
Twistor Theory at Fifty: from Rspa.Royalsocietypublishing.Org Contour Integrals to Twistor Strings Michael Atiyah1,2, Maciej Dunajski3 and Lionel Review J
Downloaded from http://rspa.royalsocietypublishing.org/ on November 10, 2017 Twistor theory at fifty: from rspa.royalsocietypublishing.org contour integrals to twistor strings Michael Atiyah1,2, Maciej Dunajski3 and Lionel Review J. Mason4 Cite this article: Atiyah M, Dunajski M, Mason LJ. 2017 Twistor theory at fifty: from 1School of Mathematics, University of Edinburgh, King’s Buildings, contour integrals to twistor strings. Proc. R. Edinburgh EH9 3JZ, UK Soc. A 473: 20170530. 2Trinity College Cambridge, University of Cambridge, Cambridge http://dx.doi.org/10.1098/rspa.2017.0530 CB21TQ,UK 3Department of Applied Mathematics and Theoretical Physics, Received: 1 August 2017 University of Cambridge, Cambridge CB3 0WA, UK Accepted: 8 September 2017 4The Mathematical Institute, Andrew Wiles Building, University of Oxford, Oxford OX2 6GG, UK Subject Areas: MD, 0000-0002-6477-8319 mathematical physics, high-energy physics, geometry We review aspects of twistor theory, its aims and achievements spanning the last five decades. In Keywords: the twistor approach, space–time is secondary twistor theory, instantons, self-duality, with events being derived objects that correspond to integrable systems, twistor strings compact holomorphic curves in a complex threefold— the twistor space. After giving an elementary construction of this space, we demonstrate how Author for correspondence: solutions to linear and nonlinear equations of Maciej Dunajski mathematical physics—anti-self-duality equations e-mail: [email protected] on Yang–Mills or conformal curvature—can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang– Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang–Mills equations, and Einstein–Weyl dispersionless systems are reductions of ASD conformal equations. -
Twistor Theory 1St Edition Free Download
FREE TWISTOR THEORY 1ST EDITION PDF Stephen Huggett | 9781351406550 | | | | | String Theory and Twistor Theory - dummies This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate lectures given in London and Oxford and the authors have aimed to retain the informal tone of those lectures. The book will provide graduate students with an introduction to the literature of twistor theory, presupposing some knowledge of special relativity and differential geometry. It would also be of use for a short course on space-time structure independently of twistor theory. The physicist could be introduced gently to some of the mathematics Twistor Theory 1st edition has proved useful in these areas, and the mathematician could be shown where sheaf cohomology and complex manifold theory can be used in physics. Previous page. Roger Penrose. Robert J. Jakob Schwichtenberg. Physics from Finance: A gentle introduction to gauge theories, fundamental interactions and fiber bundles. Next page. Burstall, Contemporary Physics. I believe that spinors and twistors are very important and that they reveal clearly profound structure that is not easily noticed using other formalisms. There can be no doubt that Sir Roger Penrose has been the leading exponent of this line of thinking for a long, long time. His book, Spinors and Spacetime is indispensable and a great classic, but it isn't Twistor Theory 1st edition the easiest book to read. In particular, I've spent a lot of time sorting through Twistor Theory 1st edition first chapter, trying to see clearly just what a Twistor Theory 1st edition "really is. -
JHEP10(2020)127 Springer July 4, 2020 : October 20, 2020 : September 22, 2020 : Boundary Action
Published for SISSA by Springer Received: July 4, 2020 Accepted: September 22, 2020 Published: October 20, 2020 Higher-spin symmetry vs. boundary locality, and a JHEP10(2020)127 rehabilitation of dS/CFT Adrian David and Yasha Neiman Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa 904-0495, Japan E-mail: [email protected], [email protected] Abstract: We consider the holographic duality between 4d type-A higher-spin gravity and a 3d free vector model. It is known that the Feynman diagrams for boundary correlators can be encapsulated in an HS-algebraic twistorial expression. This expression can be evaluated not just on separate boundary insertions, but on entire finite source distributions. We do so for the first time, and find that the result ZHS disagrees with the usual CFT partition function. While such disagreement was expected due to contact corrections, it persists even in their absence. We ascribe it to a confusion between on-shell and off-shell boundary calculations. In Lorentzian boundary signature, this manifests via wrong relative signs for Feynman diagrams with different permutations of the source points. In Euclidean, the signs are instead ambiguous, spoiling would-be linear superpositions. Framing the situation as a conflict between boundary locality and HS symmetry, we sacrifice locality and choose to take ZHS seriously. We are rewarded by the dissolution of a long-standing pathology in higher-spin dS/CFT. Though we lose the connection to the local CFT, the precise form of ZHS can be recovered from first principles, by demanding a spin-local boundary action. -
Twistor Theory of Symplectic Manifolds
Twistor Theory of Symplectic Manifolds R. Albuquerque [email protected] Departamento de Matem´atica Universidade de Evora´ 7000 Evora´ Portugal J. Rawnsley [email protected] Mathematics Institute University of Warwick Coventry CV47AL England November 2004 Abstract This article is a contribuition to the understanding of the geometry of the twistor space of a symplectic manifold. We consider the bundle l with fibre the Siegel domain Sp(2n, R)/U(n) Z existing over any given symplectic manifold M. Then, while recalling the construction of the celebrated almost complex structure induced on l by a symplectic connection on M, we Z arXiv:math/0405516v2 [math.SG] 17 Oct 2005 study and find some specific properties of both. We show a few examples of twistor spaces, develop the interplay with the symplectomorphisms of M, find some results about a natural almost-hermitian structure on l and finally discuss the holomorphic completeness of the Z respective “Penrose transform”. Let (M,ω) be a smooth symplectic manifold of dimension 2n. Then we may consider 2 the bundle π : l M (0.1) Z −→ of all complex structures j on the tangent spaces to M compatible with ω. Having fibre a cell, the bundle becomes interesting if it is seen with a particular and well known l almost complex structure, denoted ∇, — with which we start to treat by the name J Z of “Twistor Space” of the symplectic manifold M. The almost complex structure is induced by a symplectic connection on the base manifold and its integrability equation has already been studied ([13, 14, 6, 21]). -
Spacetime Structuralism
Philosophy and Foundations of Physics 37 The Ontology of Spacetime D. Dieks (Editor) r 2006 Elsevier B.V. All rights reserved DOI 10.1016/S1871-1774(06)01003-5 Chapter 3 Spacetime Structuralism Jonathan Bain Humanities and Social Sciences, Polytechnic University, Brooklyn, NY 11201, USA Abstract In this essay, I consider the ontological status of spacetime from the points of view of the standard tensor formalism and three alternatives: twistor theory, Einstein algebras, and geometric algebra. I briefly review how classical field theories can be formulated in each of these formalisms, and indicate how this suggests a structural realist interpre- tation of spacetime. 1. Introduction This essay is concerned with the following question: If it is possible to do classical field theory without a 4-dimensional differentiable manifold, what does this suggest about the ontological status of spacetime from the point of view of a semantic realist? In Section 2, I indicate why a semantic realist would want to do classical field theory without a manifold. In Sections 3–5, I indicate the extent to which such a feat is possible. Finally, in Section 6, I indicate the type of spacetime realism this feat suggests. 2. Manifolds and manifold substantivalism In classical field theories presented in the standard tensor formalism, spacetime is represented by a differentiable manifold M and physical fields are represented by tensor fields that quantify over the points of M. To some authors, this has 38 J. Bain suggested an ontological commitment to spacetime points (e.g., Field, 1989; Earman, 1989). This inclination might be seen as being motivated by a general semantic realist desire to take successful theories at their face value, a desire for a literal interpretation of the claims such theories make (Earman, 1993; Horwich, 1982). -
Quantum Gravity Past, Present and Future
Quantum Gravity past, present and future carlo rovelli vancouver 2017 loop quantum gravity, Many directions of investigation string theory, Hořava–Lifshitz theory, supergravity, Vastly different numbers of researchers involved asymptotic safety, AdS-CFT-like dualities A few offer rather complete twistor theory, tentative theories of quantum gravity causal set theory, entropic gravity, Most are highly incomplete emergent gravity, non-commutative geometry, Several are related, boundaries are fluid group field theory, Penrose nonlinear quantum dynamics causal dynamical triangulations, Several are only vaguely connected to the actual problem of quantum gravity shape dynamics, ’t Hooft theory non-quantization of geometry Many offer useful insights … loop quantum causal dynamical gravity triangulations string theory asymptotic Hořava–Lifshitz safety group field AdS-CFT theory dualities twistor theory shape dynamics causal set supergravity theory Penrose nonlinear quantum dynamics non-commutative geometry Violation of QM non-quantized geometry entropic ’t Hooft emergent gravity theory gravity Several are related Herman Verlinde at LOOP17 in Warsaw No major physical assumptions over GR&QM No infinity in the small loop quantum causal dynamical Infinity gravity triangulations in the small Supersymmetry string High dimensions theory Strings Lorentz Violation asymptotic Hořava–Lifshitz safety group field AdS-CFT theory dualities twistor theory Mostly still shape dynamics causal set classical supergravity theory Penrose nonlinear quantum dynamics non-commutative geometry Violation of QM non-quantized geometry entropic ’t Hooft emergent gravity theory gravity Discriminatory questions: Is Lorentz symmetry violated at the Planck scale or not? Are there supersymmetric particles or not? Is Quantum Mechanics violated in the presence of gravity or not? Are there physical degrees of freedom at any arbitrary small scale or not? Is geometry discrete i the small? Lorentz violations Infinite d.o.f. -
Twistor String Theory
Progress and Prospects in Twistor String Theory Marcus Spradlin An Invitation to Twistor String Theory Formulas for scattering amplitudes in gauge theory exhibit simplicity that is completely obscure in the underlying Feynman diagrams. Invitation Page 2 An Invitation to Twistor String Theory Formulas for scattering amplitudes in gauge theory exhibit simplicity that is completely obscure in the underlying Feynman diagrams. In December 2003, Witten uncovered several new layers of previously hidden mathematical richness in gluon scattering amplitudes and argued that the unexpected simplicity could be understood in terms of twistor string theory. Invitation Page 3 An Invitation to Twistor String Theory Formulas for scattering amplitudes in gauge theory exhibit simplicity that is completely obscure in the underlying Feynman diagrams. In December 2003, Witten uncovered several new layers of previously hidden mathematical richness in gluon scattering amplitudes and argued that the unexpected simplicity could be understood in terms of twistor string theory. Today, twistor string theory has blossomed into a very diverse and active community, which boasts an impressive array of results. Invitation Page 4 An Invitation to Twistor String Theory Formulas for scattering amplitudes in gauge theory exhibit simplicity that is completely obscure in the underlying Feynman diagrams. In December 2003, Witten uncovered several new layers of previously hidden mathematical richness in gluon scattering amplitudes and argued that the unexpected simplicity could be understood in terms of twistor string theory. Today, twistor string theory has blossomed into a very diverse and active community, which boasts an impressive array of results. However, most of those results have little to do with twistors, and most have little to do with string theory! Invitation Page 5 An Invitation to Twistor String Theory Formulas for scattering amplitudes in gauge theory exhibit simplicity that is completely obscure in the underlying Feynman diagrams.