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Nonlinear relativistic string equation in de Sitter space can be reduced to the following system of PDE’s [1] $$ \langle {q_\xi }J{q_\xi }\rangle = 0,{\text{ }}\langle {q_\eta }J{q_\eta }\rangle = 0 $$ (1) where q〉 ∈ R N+1 is a real vector of unit pseudolength $$ \left\langle {qJq} \right\rangle {\mkern 1mu} = {\mkern 1mu} 1,(J = diag( - 1,\underbrace {1,{\mkern 1mu} 1,{\mkern 1mu} \ldots {\mkern 1mu} ,{\mkern 1mu} 1}_N)), $$ (2) with conformai string constraints $$ \langle {q_\xi }J{q_\xi }\rangle = 0,{\text{ }}\langle {q_\eta }J{q_\eta }\rangle = 0 $$ (3) and the periodicity condition $$ q(\eta + 2\pi ,\xi - 2\pi )\rangle = q(\eta ,\xi )\rangle $$ (4) . |
