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Register a new userHalf-BPS Vertex Operators of the $AdS_5times S^5$ Superstring
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Authors
Nathan Berkovits
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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.
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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.
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.
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.
The classical spectral curve for the worldsheet theory of the AdS_5 x S^5 lambda superstring is constructed. The lambda string is interpreted as a regularized, non-abelian T dual of the AdS_5 x S^5 superstring with respect to full PSU(2,2|4) symmetry. The form of the curve is identified as the semi-classical limit of a set of Bethe ansatz equations for an XXZ type spin chain for the supergroup PSU(2,2|4) in contrast to the string in AdS_5 x S^5 which is XXX type.
We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for these correlators and present them in a universal form. We then solve these identities, employing Jack polynomial expansions. We show that the general solution is parameterized by a set of arbitrary two-variable functions, with the exception of the case d=4, where in addition functions of a single variable appear. We also discuss the operator product expansion using recent results on conformal partial wave amplitudes in arbitrary dimension.
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