Conformal supergravity, twistors, and the super-BMS group

Awada, M.; Gibbons, G. W.; Shaw, W T

doi:10.1016/s0003-4916(86)80023-9

Cited by 66 publications

(112 citation statements)

References 13 publications

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“…In dimension four a null line in C4 singles out a unique a-plane and a unique P-plane containing the line. This leads to an isomorphism between null curves in C4 and certain curves in ambitwistor space (Shaw 1986). This uniqueness no longer holds in dimension six; instead, a null 2-plane singles out a unique a -and P-plane.…”

Section: Pt-mentioning

confidence: 97%

“…We remark that the curve in twistor space is not unique, and the freedom is precisely the freedom in choosing P as a linear combination of A and B. The possible values of P and Q The pure curve ( P ( s ) , Q ( s ) ) is obtained by choice of point on i(s), This curve has to satisfy (21), so at this stage the twistor description is subject to constraints similar to those we started out with, qualitatively different to the situation in four dimensions (Shaw 1985(Shaw ,1986 where the constraints disappear in the twistor description of null curves. The present situation is rather more closely analogous to the ambitwistor description of null curves in four dimensions, where constraints persist.…”

Section: Null Curves and Twistorsmentioning

confidence: 99%

“…0264-9381/87/040869+ 24$02.50 0 1987 I O P Publishing Ltd 870 L P Hughston and W T Shaw The parametric solution to Plateau's problem in dimension four was given by Montcheuil (1905) and Eisenhart (191 1, 1912), following earlier investigations by Darboux (1873Darboux ( , 1887. These solutions have a twistor interpretation in terms of holomorphic curves in CP' (Shaw 1985, Hughston 1986) and may be described also in terms of curves on the space of null lines in complex Minkowski space (Shaw 1986). Certain types of minimal surface in S4 can also be described in twistor terms (Bryant 1982).…”

Section: Introductionmentioning

confidence: 99%

“…This space was employed by Witten (1978) to provide a twistor description of supersymmetric Yang-Mills theory in dimension four (cf also Ferber 1978, Isenberg er a1 1978. Certain curves in this space define a natural notion of superstring (Shaw 1986).…”

Section: Introductionmentioning

confidence: 99%

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Ferroelectric Properties of Sol-Gel-Derived PbTiO₃ Type Thin Films

Iijima¹,

Sanada

1996

Jpn. J. Appl. Phys.

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Classical strings and minimal surfaces in a flat spacetime correspond to pairs of 'minimal' (i.e. null) curves in its complexification. We show how to find null curves in dimension six by use of twistor methods. The twistor space for C6 is the space of pure spinors for C'. We review the geometry of this space and establish a correspondence between 'pure' curves in twistor space and null ruled 2-surfaces in C6. This correspondence generates an explicit parametrisation of null curves in C 6 , thereby generalising the Weierstrass-Eisenharf parametrisation of null curves in C 3 or C4. We also describe covariant methods for finding the periodic real null curves for string theory in real 6-space of any signature.

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Section: Pt-mentioning

confidence: 97%

Section: Null Curves and Twistorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ferroelectric Properties of Sol-Gel-Derived PbTiO₃ Type Thin Films

Iijima¹,

Sanada

1996

Jpn. J. Appl. Phys.

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“…The theory of scattering in a gravitational theory in Minkowski space is best formulated by viewing the scattering states as a representation of the super-BMS algebra [66]. In four dimensions, this algebra has the form…”

Section: The Quantum Theories Of Minkowski and De Sitter Spacementioning

confidence: 99%