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Journal articles on the topic 'Twistor theory : Sheaf theory'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Bunke, Ulrich, Thomas Schick, and Markus Spitzweck. "Sheaf theory for stacks in manifolds and twisted cohomology forS1–gerbes." Algebraic & Geometric Topology 7, no. 2 (June 20, 2007): 1007–62. http://dx.doi.org/10.2140/agt.2007.7.1007.

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2

BOOHER, JEREMY, ANASTASSIA ETROPOLSKI, and AMANDA HITTSON. "EVALUATIONS OF CUBIC TWISTED KLOOSTERMAN SHEAF SUMS." International Journal of Number Theory 06, no. 06 (September 2010): 1349–65. http://dx.doi.org/10.1142/s1793042110003538.

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We prove some conjectures of Evans and Katz presented in a paper by Evans regarding twisted Kloosterman sheaf sums Tn. These conjectures give explicit evaluations of the sums Tn where the character is cubic and n = 4. There are also conjectured relationships between evaluations of Tn and the coefficients of certain modular forms. For three of these modular forms, each of weight 3, it is conjectured that the coefficients are related to the squares of the coefficients of weight 2 modular forms. We prove these relationships using the theory of complex multiplication.

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3

PARK, Q.-HAN. "2D SIGMA MODEL APPROACH TO 4D INSTANTONS." International Journal of Modern Physics A 07, no. 07 (March 20, 1992): 1415–47. http://dx.doi.org/10.1142/s0217751x92000624.

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4D self-dual theories are proposed to generalize 2D conformal field theory. We identify 4D self-dual gravity as well as self-dual Yang-Mills theory with 2D sigma models valued in infinite-dimensional gauge groups. It is shown that these models possess infinite-dimensional symmetries with associated algebras—“CP1 extensions” of respective gauge algebras of 2D sigma models—which generalize the Kac-Moody algebra as well as W∞. We address various issues concerning 2D sigma models, twistors and sheaf cohomology. An attempt to connect 4D self-dual theories with 2D conformal field theory is made through sl (∞) Toda field theory.

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4

Gibbons, G. W. "Twistor theory." Contemporary Physics 33, no. 3 (May 1992): 187–88. http://dx.doi.org/10.1080/00107519208211058.

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5

Putinar, Mihai. "Spectral theory and sheaf theory. II." Mathematische Zeitschrift 192, no. 3 (September 1986): 473–90. http://dx.doi.org/10.1007/bf01164022.

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6

Choukri, R., A. el Kinani, and A. Oukhouya. "On the sheaf theory." Rendiconti del Circolo Matematico di Palermo 55, no. 2 (June 2006): 185–91. http://dx.doi.org/10.1007/bf02874701.

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7

Hodges, Andrew. "Theory with a twistor." Nature Physics 9, no. 4 (April 2013): 205–6. http://dx.doi.org/10.1038/nphys2597.

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8

Mason, Lionel, and David Skinner. "Heterotic twistor–string theory." Nuclear Physics B 795, no. 1-2 (May 2008): 105–37. http://dx.doi.org/10.1016/j.nuclphysb.2007.11.010.

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9

Penrose, Roger. "Palatial twistor theory and the twistor googly problem." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2047 (August 6, 2015): 20140237. http://dx.doi.org/10.1098/rsta.2014.0237.

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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.

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10

Roe, John, and Paul Siegel. "Sheaf theory and Paschke duality." Journal of K-Theory 12, no. 2 (August 28, 2013): 213–34. http://dx.doi.org/10.1017/is013006016jkt233.

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AbstractLet X be a locally compact metrizable space. We show that the Paschke dual construction, which associates to a representation of C0(X) its commutant modulo locally compact operators, can be sheafified. We use this observation to simplify several constructions in analytic K-homology.

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11

Penrose, R. "On Ricci-flat twistor theory." Surveys in Differential Geometry 7, no. 1 (2002): 555–64. http://dx.doi.org/10.4310/sdg.2002.v7.n1.a17.

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12

Pantilie, Radu. "TWISTOR THEORY FOR EXCEPTIONAL HOLONOMY." Mathematika 67, no. 1 (October 26, 2020): 54–60. http://dx.doi.org/10.1112/mtk.12060.

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13

Chi, Quo-Shin. "Twistor theory and Blaschke manifolds." Annals of Global Analysis and Geometry 9, no. 3 (1991): 197–204. http://dx.doi.org/10.1007/bf00136811.

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14

Penrose, Roger. "On Ricci-flat twistor theory." Asian Journal of Mathematics 3, no. 4 (1999): 749–56. http://dx.doi.org/10.4310/ajm.1999.v3.n4.a2.

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15

Woodhouse, N. M. J. "Real methods in twistor theory." Classical and Quantum Gravity 2, no. 3 (May 1, 1985): 257–91. http://dx.doi.org/10.1088/0264-9381/2/3/006.

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16

Dunajski, Maciej. "Twistor theory and differential equations." Journal of Physics A: Mathematical and Theoretical 42, no. 40 (September 16, 2009): 404004. http://dx.doi.org/10.1088/1751-8113/42/40/404004.

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17

Albuquerque, R., and J. Rawnsley. "Twistor theory of symplectic manifolds." Journal of Geometry and Physics 56, no. 2 (February 2006): 214–46. http://dx.doi.org/10.1016/j.geomphys.2005.01.007.

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18

Singer, M. A. "Duality in twistor theory without Minkowski space." Mathematical Proceedings of the Cambridge Philosophical Society 98, no. 3 (November 1985): 591–600. http://dx.doi.org/10.1017/s0305004100063799.

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AbstractA modified form of the generalized Penrose-Ward Transform [4, 6] is set up to investigate the correspondence between twistor space and dual twistor space. The ways in which it differs from the ‘usual’ transform are discussed and it is used to give an alternative proof of Eastwood's recent generalization [7] of the twistor transform [9, 5] which avoids all mention of Minkowski space.

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19

Atiyah, Michael, Maciej Dunajski, and Lionel J. Mason. "Twistor theory at fifty: from contour integrals to twistor strings." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2206 (October 2017): 20170530. http://dx.doi.org/10.1098/rspa.2017.0530.

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We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space–time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold—the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics—anti-self-duality equations 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. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function.

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20

Jacobs, Philippe. "A sheaf homology theory with supports." Illinois Journal of Mathematics 44, no. 3 (September 2000): 644–66. http://dx.doi.org/10.1215/ijm/1256060422.

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21

KIKUCHI, Hideyuki. "Sheaf cohomology theory for measurable spaces." Hokkaido Mathematical Journal 24, no. 1 (February 1995): 151–60. http://dx.doi.org/10.14492/hokmj/1380892541.

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22

Rodríguez González, Beatriz, and Agustí Roig. "Godement resolutions and sheaf homotopy theory." Collectanea Mathematica 66, no. 3 (September 9, 2014): 423–52. http://dx.doi.org/10.1007/s13348-014-0123-x.

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23

Kashiwara, Masaki, and Pierre Schapira. "Persistent homology and microlocal sheaf theory." Journal of Applied and Computational Topology 2, no. 1-2 (September 18, 2018): 83–113. http://dx.doi.org/10.1007/s41468-018-0019-z.

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24

SAHU, S. K., and A. V. ASHA. "PARAMETRIC RESONANCE CHARACTERISTICS OF ANGLE-PLY TWISTED CURVED PANELS." International Journal of Structural Stability and Dynamics 08, no. 01 (March 2008): 61–76. http://dx.doi.org/10.1142/s0219455408002557.

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The present study deals with the dynamic stability of laminated composite pre-twisted cantilever panels. The effects of various parameters on the principal instability regions are studied using Bolotin's approach and finite element method. The first-order shear deformation theory is used to model the twisted curved panels, considering the effects of transverse shear deformation and rotary inertia. The results on the dynamic stability studies of the laminated composite pre-twisted panels suggest that the onset of instability occurs earlier and the width of dynamic instability regions increase with introduction of twist in the panel. The instability occurs later for square than rectangular twisted panels. The onset of instability occurs later for pre-twisted cylindrical panels than the flat panels due to addition of curvature. However, the spherical pre-twisted panels show small increase of nondimensional excitation frequency.

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25

Metzner, Norman. "Twistor theory of higher dimensional black holes: I. Theory." Classical and Quantum Gravity 30, no. 9 (April 10, 2013): 095001. http://dx.doi.org/10.1088/0264-9381/30/9/095001.

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26

Penrose, Roger. "The Central Programme of Twistor Theory." Chaos, Solitons & Fractals 10, no. 2-3 (February 1999): 581–611. http://dx.doi.org/10.1016/s0960-0779(98)00333-6.

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27

(Jr.), R. O. Wells. "Twistor geometry and classical field theory." Russian Mathematical Surveys 40, no. 4 (August 31, 1985): 121–28. http://dx.doi.org/10.1070/rm1985v040n04abeh003618.

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28

PENG, Chia-Kuei. "Twistor bundle theory and its application." Science in China Series A 47, no. 4 (2004): 605. http://dx.doi.org/10.1360/03ys0368.

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29

Wolf, Martin. "Self-dual supergravity and twistor theory." Classical and Quantum Gravity 24, no. 24 (November 29, 2007): 6287–327. http://dx.doi.org/10.1088/0264-9381/24/24/010.

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30

Hartnoll, Sean A., and Giuseppe Policastro. "Spacetime foam in twistor string theory." Advances in Theoretical and Mathematical Physics 10, no. 2 (2006): 181–216. http://dx.doi.org/10.4310/atmp.2006.v10.n2.a2.

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31

Penrose, Roger. "Twistor theory and the Einstein vacuum." Classical and Quantum Gravity 16, no. 12A (November 16, 1999): A113—A130. http://dx.doi.org/10.1088/0264-9381/16/12a/306.

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32

Berkovits, Nathan, and Edward Witten. "Conformal Supergravity in Twistor-String Theory." Journal of High Energy Physics 2004, no. 08 (August 5, 2004): 009. http://dx.doi.org/10.1088/1126-6708/2004/08/009.

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33

Huggett, S. A. "Recent work in twistor field theory." Classical and Quantum Gravity 9, S (December 1, 1992): S127—S135. http://dx.doi.org/10.1088/0264-9381/9/s/006.

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34

Bette, A., and S. Zakrzewski. "Extended phase spaces and twistor theory." Journal of Physics A: Mathematical and General 30, no. 1 (January 7, 1997): 195–209. http://dx.doi.org/10.1088/0305-4470/30/1/014.

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35

Wells, R. O. "Nonlinear field equations and twistor theory." Mathematical Intelligencer 7, no. 2 (June 1985): 26–32. http://dx.doi.org/10.1007/bf03024171.

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36

Mo, M. Y. "The twistor theory of Whitham hierarchy." Journal of Geometry and Physics 56, no. 11 (November 2006): 2237–60. http://dx.doi.org/10.1016/j.geomphys.2005.11.017.

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37

Baird, Paul, and Mohammad Wehbe. "Twistor Theory on a Finite Graph." Communications in Mathematical Physics 304, no. 2 (April 22, 2011): 499–511. http://dx.doi.org/10.1007/s00220-011-1245-6.

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38

AHN, CHANGHYUN. "${\mathcal N} = 2$ CONFORMAL SUPERGRAVITY FROM TWISTOR-STRING THEORY." International Journal of Modern Physics A 21, no. 18 (July 20, 2006): 3733–59. http://dx.doi.org/10.1142/s0217751x06033787.

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A chiral superfield strength in [Formula: see text] conformal supergravity at linearized level is obtained by acting two superspace derivatives on [Formula: see text] chiral superfield strength which can be described in terms of [Formula: see text] twistor superfields. By decomposing SU (4)R representation of [Formula: see text] twistor superfields into the SU (2)R representation with an invariant U (1)R charge, the surviving [Formula: see text] twistor superfields contain the physical states of [Formula: see text] conformal supergravity. These [Formula: see text] twistor superfields are functions of homogeneous coordinates of weighted complex projective space WCP3|4 where the two weighted fermionic coordinates have weight -1 and 3.

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39

Pitts, Andrew M. "Applications of Sup-Lattice Enriched Category Theory to Sheaf Theory." Proceedings of the London Mathematical Society s3-57, no. 3 (November 1988): 433–80. http://dx.doi.org/10.1112/plms/s3-57.3.433.

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40

Witten, Edward. "Perturbative Gauge Theory as a String Theory in Twistor Space." Communications in Mathematical Physics 252, no. 1-3 (October 7, 2004): 189–258. http://dx.doi.org/10.1007/s00220-004-1187-3.

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41

Donagi, Ron, Josh Guffin, Sheldon Katz, and Eric Sharpe. "A mathematical theory of quantum sheaf cohomology." Asian Journal of Mathematics 18, no. 3 (2014): 387–418. http://dx.doi.org/10.4310/ajm.2014.v18.n3.a1.

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42

Rodríguez González, Beatriz, and Agustí Roig. "Godement resolution and operad sheaf homotopy theory." Collectanea Mathematica 68, no. 3 (May 2, 2016): 301–21. http://dx.doi.org/10.1007/s13348-016-0171-5.

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43

Ilgen, Fre. "Extensionalism and Twistor Space: Similarities and Relations between Art and Twistor Theory." Leonardo 28, no. 3 (1995): 177. http://dx.doi.org/10.2307/1576072.

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44

Machida, Yoshinori, and Hajime Sato. "Twistor theory of manifolds with Grassmannian structures." Nagoya Mathematical Journal 160 (2000): 17–102. http://dx.doi.org/10.1017/s0027763000007698.

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AbstractAs a generalization of the conformal structure of type (2, 2), we study Grassmannian structures of type (n, m) forn, m≥ 2. We develop their twistor theory by considering the complete integrability of the associated null distributions. The integrability corresponds to global solutions of the geometric structures.A Grassmannian structure of type (n, m) on a manifoldMis, by definition, an isomorphism from the tangent bundleTMofMto the tensor productV ⊗ Wof two vector bundlesVandWwith ranknandmoverMrespectively. Because of the tensor product structure, we have two null plane bundles with fibresPm-1(ℝ) andPn-1(ℝ) overM. The tautological distribution is defined on each two bundles by a connection. We relate the integrability condition to the half flatness of the Grassmannian structures. Tanaka’s normal Cartan connections are fully used and the Spencer cohomology groups of graded Lie algebras play a fundamental role.Besides the integrability conditions corrsponding to the twistor theory, the lifting theorems and the reduction theorems are derived. We also study twistor diagrams under Weyl connections.

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45

Rahman, Abdul. "A perverse sheaf approach toward a cohomology theory for string theory." Advances in Theoretical and Mathematical Physics 13, no. 3 (2009): 667–94. http://dx.doi.org/10.4310/atmp.2009.v13.n3.a3.

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46

Newman, Ezra T. "Asymptotic twistor theory and the Kerr theorem." Classical and Quantum Gravity 23, no. 10 (April 24, 2006): 3385–92. http://dx.doi.org/10.1088/0264-9381/23/10/009.

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47

Dunajski, Maciej. "Harmonic functions, central quadrics and twistor theory." Classical and Quantum Gravity 20, no. 15 (July 16, 2003): 3427–40. http://dx.doi.org/10.1088/0264-9381/20/15/311.

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48

Adamo, Tim, and Lionel Mason. "Einstein supergravity amplitudes from twistor-string theory." Classical and Quantum Gravity 29, no. 14 (June 19, 2012): 145010. http://dx.doi.org/10.1088/0264-9381/29/14/145010.

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49

Huggett, S. A. "The development of ideas in twistor theory." International Journal of Theoretical Physics 24, no. 4 (April 1985): 391–400. http://dx.doi.org/10.1007/bf00670806.

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50

Brain, S. J., and S. Majid. "Quantisation of Twistor Theory by Cocycle Twist." Communications in Mathematical Physics 284, no. 3 (October 8, 2008): 713–74. http://dx.doi.org/10.1007/s00220-008-0607-1.

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