# A Glimpse of String Theory and Conformal Geometry

I am taking String Theory this quarter with Joe Polchinski, reading from his Little Book of String. We have been covering bosonic string (no fermions) arising from the Polyakov string action .

Technically, we should Wick rotate the time parameter , the Lorentzian worldsheet metric becomes Riemannian . We can pick normal coordinates and complexify and . Then the action looks like the Nambu-Goto action again (measuring the area of the worldsheet).

This action is invariant under conformal symmetries of the worldsheet

, where parameterizes the worldsheet. In 2 dimensions, the conformal group is especially large and there are infinitely many generators .

I couldn’t picture them so I drew them with mathematica. Technically, these are infinitesimal transformations but I drew them globally.

## About this entry

You’re currently reading “A Glimpse of String Theory and Conformal Geometry,” an entry on monsieurcactus

- Published:
- April 3, 2012 / 10:42 pm

- Category:
- String Theory, Uncategorized

- Tags:
- conformal geometry, string theory

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