Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction

Abstract

We study the extended supersymmetric integrable hierarchy underlying the Pohlmeyer reduction of superstring sigma models on semi-symmetric superspaces F/G. This integrable hierarchy is constructed by coupling two copies of the homogeneous integrable hierarchy associated to the loop Lie superalgebra extension f of the Lie superalgebra f of F and this is done by means of the algebraic dressing technique and a Riemann-Hilbert factorization problem. By using the Drinfeld-Sokolov procedure we construct explicitly, a set of 2D spin \pm1/2 conserved supercharges generating supersymmetry flows in the phase space of the reduced model. We introduce the bi-Hamiltonian structure of the extended homogeneous hierarchy and show that the two brackets are of the Kostant-Kirillov type on the co-adjoint orbits defined by the light-cone Lax operators L_\pm. By using the second symplectic structure, we show that these supersymmetries are Hamiltonian flows, we compute part of the supercharge algebra and find the supersymmetric field variations they induce. We also show that this second Poisson structure coincides with the canonical Lorentz-Invariant symplectic structure of the WZNW model involved in the Lagrangian formulation of the extended integrable hierarchy, namely, the semi-symmetric space sine-Gordon model (SSSSG), which is the Pohlmeyer reduced action functional for the transverse degrees of freedom of superstring sigma models on the cosets F/G. We work out in some detail the Pohlmeyer reduction of the AdS_2xS^2 and the AdS_3xS^3 superstrings and show that the new conserved supercharges can be related to the supercharges extracted from 2D superspace. In particular, for the AdS_2xS^2 example, they are formally the same.

arXiv commentV2: Two references added, V3: Modifications in section 2.6, V4: Published version

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Cited by in corpus (16)

• An Integrable Deformation of the AdS5 x S5 Superstring
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• Two-dimensional S-matrices from unitarity cuts
• Deformed Supersymmetric Mechanics
• Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
• The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
• A Relativistic Relative of the Magnon S-Matrix
• Alleviating the non-ultralocality of the AdS_5 x S^5 superstring
• Worldsheet Supersymmetry of Pohlmeyer-Reduced AdS_n x S^n Superstrings
• The Semi-Classical Spectrum of Solitons and Giant Magnons
• Lambda Models From Chern-Simons Theories
• Exploring The Lambda Model Of The Hybrid Superstring
• Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction
• Giant Magnons of String Theory in the Lambda Background
• Novel aspects of integrability for NLSMs in symmetric spaces