Transformation of auxiliary field

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The discussion centers on the transformation of the auxiliary field e in the context of string theory as presented in West's "Introduction to Strings and Branes." The transformation e'(\tau')d\tau' = e(\tau)d\tau is questioned, emphasizing the need for clarity on the conditions imposed on the action. The transformation of auxiliary fields is linked to the requirement of gauge invariance, similar to the transformation laws for Yang-Mills gauge fields. Understanding these transformations is crucial for maintaining consistency in the theoretical framework. The conversation highlights the importance of deriving transformation laws from imposed conditions in theoretical physics.
rbwang1225
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In West's book "Introduction to Strings and Branes", page 2, I don't understand why the auxiliary field e transformed as e'(\tau')d\tau'=e(\tau)d\tau.
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By construction :-)

You impose several conditions on your action and then get how auxilary fields should transform. Just like with YM gauge field, you want gauge invarianceand from this you get transformation law
 

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