Worldsheet supersymmetry of Pohlmeyer-reduced AdS_n × Sn superstrings

摘要

As was observed by Grigoriev and Tseytlin, the Pohlmeyer-reduced AdS ₂ × S 2 superstring theory possesses N = ( 2,2 ) mathcal{N} = left( {2,2} right) worldsheet supersymmetry. We show, at the classical level, that the AdS ₃ × S 3 and AdS ₅ × S 5 superstring theories in the Pohlmeyer-reduced form reveal hidden N = ( 4,4 ) mathcal{N} = left( {4,4} right) and N = ( 8,8 ) mathcal{N} = left( {8,8} right) worldsheet supersymmetries. Our consideration is based on the modified mass-deformed gauged WZW action for the superstring equations. We present the explicit form of the supersymmetry transformations for both the off-shell action and the superstring equations. The characteristic feature of these transformations is the presence of non-local terms.