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This thesis presents recent developments within the pure spinor formalism, which has simplified amplitude computations in perturbative string theory, especially when spacetime fermions are involved. Firstly the worldsheet action of both the minimal and the non-minimal pure spinor formalism is derive
This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded in string theory. Secondly, this model is generalized to a web of dualitie
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