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The Kappa Symmetric transformations would be:

So that:

It is also clear that:

If we let

Now, to determine , we see that:

Switching to the exterior derivative ("d") notation,

here is a 2-form, independent of the worldsheet metric. Introducing a three-form , we obtain the desired equation through Stokes' Theorem\\. is the boundary of / . In 10 dimensions, a Majorana spinor satisfies:

Where is a real number with an absolute value of 1. In order to ensure that is closed, i.e., that , which can be trivjially seen from explicitly writing the superspace embedding function in terms of and .

itself would be given by:

Here,

We finally conclude that this modified action is invariant under the following kappa symmetric transformations: