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Register a new userOscillator approach to quantization of $AdS_5times S^5$ superparticle in twistor formulation
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Authors
D.V. Uvarov
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Using known relation between $SU(2,2|4)$ supertwistors and $SU(2)$ bosonic and fermionic oscillators we identify the physical states of quantized massless $AdS_5times S^5$ superparticle in supertwistor formulation and discuss how they fit into the spectrum of fluctuations of IIB supergravity on $AdS_5times S^5$ superbackground.
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Supertwistors relevant to $AdS_5times S^5$ superbackground of IIB supergravity are studied in the framework of the $D=10$ massless superparticle model in the first-order formulation. Product structure of the background suggests using $D=1+4$ Lorentz-harmonic variables to express momentum components tangent to $AdS_5$ and $D=5$ harmonics to express momentum components tangent to $S^5$ that yields eight-supertwistor formulation of the superparticles Lagrangian. We find incidence relations of the supertwistors with the $AdS_5times S^5$ superspace coordinates and the set of the quadratic constraints they satisfy. It is shown how using the constraints for the (Lorentz-)harmonic variables it is possible to reduce eight-supertwistor formulation to the four-supertwistor one. Respective supertwistors agree with those introduced previously in other models. Advantage of the four-supertwistor formulation is the presence only of the first-class constraints that facilitates analysis of the superparticle model.
Using the pure spinor formalism for the superstring in an $AdS_5times S^5$ background, a simple expression is found for half-BPS vertex operators. At large radius, these vertex operators reduce to the usual supergravity vertex operators in a flat background. And at small radius, there is a natural conjecture for generalizing these vertex operators to non-BPS states.
Motivated by recent studies related to integrability of string motion in various backgrounds via analytical and numerical procedures, we discuss these procedures for a well known integrable string background $(AdS_5times S^5)_{eta}$. We start by revisiting conclusions from earlier studies on string motion in $(mathbb{R}times S^3)_{eta}$ and $(AdS_3)_{eta}$ and then move on to more complex problems of $(mathbb{R}times S^5)_{eta}$ and $(AdS_5)_{eta}$. Discussing both analytically and numerically, we deduce that while $(AdS_5)_{eta}$ strings do not encounter any irregular trajectories, string motion in the deformed five-sphere can indeed, quite surprisingly, run into chaotic trajectories. We discuss the implications of these results both on the procedures used and the background itself.
We construct massless infinite spin irreducible representations of the six-dimensional Poincar{e} group in the space of fields depending on twistor variables. It is shown that the massless infinite spin representation is realized on the two-twistor fields. We present a full set of equations of motion for two-twistor fields represented by the totally symmetric $mathrm{SU}(2)$ rank $2s$ two-twistor spin-tensor and show that they carry massless infinite spin representations. A field twistor transform is constructed and infinite spin fields are found in the space-time formulation with an additional spinor coordinate.
Using twistor space intuition, Cachazo, Svrcek and Witten presented novel diagrammatic rules for gauge-theory amplitudes, expressed in terms of maximally helicity-violating (MHV) vertices. We define non-MHV vertices, and show how to use them to give a recursive construction of these amplitudes. We also use them to illustrate the equivalence of various twistor-space prescriptions, and to determine the associated combinatoric factors.
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