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Abstract:

Perturbative superstring theory is revisited, with the goal of giving a simpler

and more direct demonstration that multi-loop amplitudes are gauge-invariant (apart from

known anomalies), satisfy space-time supersymmetry when expected, and have the ex-

pected infrared behavior. The main technical tool is to make the whole analysis, including

especially those arguments that involve integration by parts, on supermoduli space, rather

than after descending to ordinary moduli space.

Supplements of this paper are:

Notes On Super Riemann Surfaces And Their Moduli

Abstract:

These are notes on the theory of super Riemann surfaces and their moduli

spaces, aiming to collect results that are useful for a better understanding of superstring

perturbation theory in the RNS formalism.

Notes On Supermanifolds and Integration

Abstract:

These are notes on the theory of supermanifolds and integration on them, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.