Two-twistor description of a membrane

Abstract

We describe D = 4 twistorial membrane in terms of two twistorial three-dimensional world-volume fields. We start with the D-dimensional p-brane generalizations of two phase space string formulations: the one with p + 1 vectorial fourmomenta, and the second with tensorial momenta of (p + 1)-th rank. Further we consider tensionful membrane case in D = 4. By using the membrane generalization of Cartan-Penrose formula we express the fourmomenta by spinorial fields and obtain the intermediate spinor-space-time formulation. Further by expressing the world-volume dreibein and the membrane space-time coordinate fields in terms of two twistor fields one obtains the purely twistorial formulation. It appears that the action is generated by a geometric three-form on twotwistor space. Finally we comment on higher-dimensional (D > 4) twistorial p-brane models and their superextensions.

Supertwistor formulation for massless superparticle in AdS5 × S5 superspace

“…(Super)twistor formulation is known to combine manifest and linearly realized (super)conformal symmetry with the simple and irreducible realization of the gauge symmetries. These features provided strong motivation to study (super)twistor formulations also for massive (super)particles [10], [11], [12], [13], [14], null and tensile (super)strings [15], [16], [17], [18] and membranes [19] in 4-dimensional Minkowski (super)space and in higher string-theoretic dimensions [20], [21], [22], [23], [24], [25], [26] [27], [28]. 3 (Super)twistors also appear rather efficient in presenting scattering amplitudes of massless particles not limiting to 4-dimensional space-time (see, e.g.…”

“…mn ,Qλ C ] = −iσ mnρλQρC , [M mn , S λ C ] = −iσ mnρ λ S ρ C , [M mn ,Sλ C ] = iσ mnλρSρ C , [P I ′ , Q C λ ] = −γ I ′ C D Q D λ , [P I ′ ,Qλ C ] = γ I ′ D CQλ D , [P I ′ , S λ C ] = γ I ′ D C S λ D , [P I ′ ,Sλ C ] = −γ I ′ C DSλ D , [M I ′ J ′ , Q C λ ] = −γ I ′ J ′ C D Q D λ , [M I ′ J ′ ,Qλ C ] = γ I ′ J ′ D CQλ D , [M I ′ J ′ , S λ C ] = γ I ′ J ′ D C S λ D , [M I ′ J ′ ,Sλ C ] = −γ I ′ J ′ C DSλ D . (B 19). …”

Maxwell Symmetries and Some Applications

“…(1)) of the Maxwell Lie algebra also defines a ten-dimensional extended D = 4 spacetime that we call Maxwell D = 4 tensorial space. One can consider as well a spinorial particle model on this new Maxwell tensorial space which, after first quantization, should also provide an infinite-dimensional multiplet of D = 4 HS fields; such a model is under consideration [23].…”

Purely twistorial string with canonical twistor field quantization

“…It is known that the description of massive (super)particles requires in the Penrose framework the introduction of two-(super)twistor geometry (see [8,9,24]). Following [11], using twotwistor target space purely twistorial tensionful string action was given [25], which is classically equivalent to Nambu-Goto (NG) string action with composite spacetime string fields. Unfortunately, our twistorial action from [25] is fourlinear, what presents a serious difficulty in performing the quantization procedure.…”

“…Following [11], using twotwistor target space purely twistorial tensionful string action was given [25], which is classically equivalent to Nambu-Goto (NG) string action with composite spacetime string fields. Unfortunately, our twistorial action from [25] is fourlinear, what presents a serious difficulty in performing the quantization procedure. In this paper we resolve this difficulty.…”