A geometric formulation using integral forms on super Riemann surfaces derives descent equations for superstring vertex operators, establishes a supergeometric correspondence to ghost superfields, and organizes operators into a universal descent structure in BRST cohomology.
New Geometrical Approach to Superstrings
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abstract
We present a new geometrical approach to superstrings based on the geometrical theory of integration on supermanifolds. This approach provides an effective way to calculate multi-loop superstring amplitudes for arbitrary backgrounds. It makes possible to calculate amplitudes for the physical states defined as BRST cohomology classes using arbitrary representatives. Since the new formalism does not rely on the presence of primary representatives for the physical states it is particulary valuable for analyzing the discrete states for which no primary representatives are available. We show that the discrete states provide information about symmetries of the background including odd symmetries which mix Bose and Fermi states. The dilaton is an example of a non-discrete state which cannot be covariantly represented by a primary vertex. The new formalism allows to prove the dilaton theorem by a direct calculation.
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Vertex Operators in Superstring Theory from Integral Forms and Descent Equations
A geometric formulation using integral forms on super Riemann surfaces derives descent equations for superstring vertex operators, establishes a supergeometric correspondence to ghost superfields, and organizes operators into a universal descent structure in BRST cohomology.