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Register a new userProbing analytical and numerical integrability: The curious case of $(AdS_5times S^5)_{eta}$
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Added by
Arpan Bhattacharyya
Publication date
2018
fields
Physics
and research's language is
English
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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.
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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.
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 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.
We explore integrability properties of superstring equations of motion in AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges and construct a Lax representation for the corresponding Hamiltonian dynamics on subspace of physical superstring degrees of freedom. We present some explicit results for the corresponding conserved charges by consistently reducing the dynamics to AdS_3 x S^3 and AdS_3 x S^1 subsectors containing both bosonic and fermionic fields.
We describe an effective theory of a scalar field, motivated by some features expected in the low energy theory of gluodynamics in 3+1 dimensions. The theory describes two propagating massless particles in a certain limit, which we identify with the Abelian QED limit, and has classical string solutions in the general case. The string solutions are somewhat unusual as they are multiply degenerate due to spontaneous breaking of diffeomorphism invariance. Nevertheless all solutions yield identical electric field and have the same string tension.
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