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On page 116 of this book it is said, that reparameterization invariance of the string action is analogous to the gauge invariance in electrodynamices.

Whereas Maxwell's equations are symmetric under a gauge transformation which allows to describe the same $\vec{E}$ and $\vec{B}$ fields by different potentials $A_{\mu}$, reparameterization invariance makes it possible to use different grids on the world sheet to describe the same physical motion of a string.

So is reparameterization invariance some kind of gauge invariance too? What would take the role of the gauge potential $A_{\mu}$ and what would the corresponding "gauge invariant" action look like?

Dilaton
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1 Answers1

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Reparametrization invariance here means worldsheet diffeomorphism invariance, which is a gauge symmetry in the sum over string histories formulation of perturbative string theory. It acts non-trivially on the worldsheet metric and on the sigma model fields, and tells you that most things you can build using them aren't valid observables. The relevant 'gauge theory' is 2d gravity, which is why QMechanic gave you those links.

user1504
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