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Light-cone gauge Hamiltonian for \(AdS_{4} \times \mathbb {CP}^{3}\) superstring. (English) Zbl 1193.81088

Summary: We develop the phase-space formulation for the Type IIA superstring on the \(AdS_{4} \times \mathbb C\mathbb P^{3}\) background in the \(\kappa \)-symmetry light-cone gauge for which the light-like directions are taken from the \(D = 3\) Minkowski boundary of \(AdS_{4}\). After fixing bosonic light-cone gauge, the superstring Hamiltonian is expressed as a function of the transverse physical variables and in the quadratic approximation corresponds to the light-cone gauge-fixed IIA superstring in flat space.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
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