The classical exchange algebra of a Green-Schwarz sigma model on supercoset target space with \(\mathbb{Z}_{4m}\) grading. (English) Zbl 1272.81120
Summary: We investigate the classical exchange algebra of the monodromy matrix for a Green-Schwarz sigma model on supercoset target space with \(\mathbb{Z}_{4m}\) grading by using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution in the Poisson bracket sense. Our calculation is based on a general world-sheet metric. Taking a particular case of \(m = 1\) (and a particular choice of supergroup), our results coincide with those of the Green-Schwarz superstring theory in \(AdS_5 \times S^5\) background obtained by M. Magro [J. High Energy Phys. 2009, No. 1, 021, 33 p. (2009; Zbl 1243.81167)]. {
©2011 American Institute of Physics}
©2011 American Institute of Physics}
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 70H45 | Constrained dynamics, Dirac’s theory of constraints |
| 70S05 | Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 17C70 | Super structures |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
Citations:
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