Transformation of auxiliary field

[rbwang1225]

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$\tau$.

 

[Korybut]

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