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arXiv · 2605.30759

Vertex Operators in Superstring Theory from Integral Forms and Descent Equations

Isao Kishimoto·Shigenori Seki·Haruka Shimogaki·Tomohiko Takahashi
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Abstract

We develop a geometric formulation of vertex operators in superstring theory based on integral forms on super Riemann surfaces. Starting from the integrated NS-NS vertex operator, we derive descent equations that relate operators with different ghost and picture numbers. A key result is a correspondence between supergeometric objects and ghost superfields, in which the one-form $dz-\theta d\theta$ and the even differential $d\theta$ are identified with the ghost superfield and its superderivative. This provides a geometric realization of the superghost structure. We further extend the construction by incorporating inverse picture-changing operators, which generate new descent sequences across different picture sectors. We also introduce a superfield construction of higher-ghost-number operators, for which additional terms are required compared to the bosonic case. All operators are organized into a universal descent structure and are well-defined in BRST cohomology.

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Isao Kishimoto, Shigenori Seki, Haruka Shimogaki, Tomohiko Takahashi. 2026-05-29. Vertex Operators in Superstring Theory from Integral Forms and Descent Equations. https://arxiv.org/abs/2605.30759

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