Transformation of auxiliary field

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SUMMARY

The discussion centers on the transformation of auxiliary fields as described in West's "Introduction to Strings and Branes". Specifically, it addresses the transformation of the auxiliary field e, where e'(\tau')d\tau' equals e(\tau)d\tau. The transformation is derived from the conditions imposed on the action, similar to the transformation laws for Yang-Mills gauge fields, emphasizing the necessity of gauge invariance in determining these laws.

PREREQUISITES
  • Understanding of auxiliary fields in theoretical physics
  • Familiarity with gauge invariance principles
  • Knowledge of Yang-Mills theory
  • Basic concepts of string theory as outlined in West's work
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  • Study the transformation laws of auxiliary fields in string theory
  • Explore the principles of gauge invariance in Yang-Mills theory
  • Read West's "Introduction to Strings and Branes" for deeper insights
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The discussion is beneficial for theoretical physicists, string theorists, and students studying advanced concepts in gauge theories and auxiliary fields.

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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