Deformation of Schild String

TL;DR

This paper explores deforming the Schild string action to include Majorana fermions, resulting in three new superstring actions with different symmetries and interactions, highlighting the challenges in constructing Schild-type superstring models.

Contribution

It introduces three novel Schild string actions incorporating Majorana fermions, expanding the understanding of supersymmetric string formulations.

Findings

First action is invariant under N=1 supersymmetry and area-preserving diffeomorphisms.

Second action includes Yukawa-type interactions.

Third action exhibits non-locality due to bilinear fermion terms.

Abstract

We attempt to construct new superstring actions with a $D$-plet of Majorana fermions $\psi^{\cal B}_A$, where ${\cal B}$ is the $D$ dimensional space-time index and $A$ is the two dimensional spinor index, by deforming the Schild action. As a result, we propose three kinds of actions: the first is invariant under N=1 (the world-sheet) supersymmetry transformation and the area-preserving diffeomorphism. The second contains the Yukawa type interaction. The last possesses some non-locality because of bilinear terms of $\psi^{\cal B}_A$. The reasons why completing a Schild type superstring action with $\psi^{\cal B}_A$ is difficult are finally discussed.