Chandia, O., Mikhailov, A., & Vallilo, B. C. (2013). A construction of integrated vertex operator in the pure spinor sigma-model in AdS(5) x S-5. J. High Energy Phys., 2013(11), 11 pp.
Abstract: Vertex operators in string theory me in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically involving the b-ghost. In the pure spinor formalism vertex operators can be identified as cohomology classes of an infinite-dimensional Lie superalgebra formed by covariant derivatives. We show that in this language the construction of the integrated vertex from an unintegrated vertex is very straightforward, and amounts to the evaluation of the cocycle on the generalized Lax currents.
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Hojman, S. A., Gamboa, J., & Mendez, F. (2012). Dynamics Determines Geometry. Mod. Phys. Lett. A, 27(33), 14 pp.
Abstract: The inverse problem of calculus of variations and s-equivalence are re-examined by using results obtained from non-commutative geometry ideas. The role played by the structure of the modified Poisson brackets is discussed in a general context and it is argued that classical s-equivalent systems may be non-equivalent at the quantum mechanical level. This last fact is explicitly discussed comparing different approaches to deal with the NairPolychronakos oscillator.
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