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Introduction to Strings and Branes by Peter West

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8 Conformal symmetry and two-dimensional field theory

 

 

 

 

He cooks with water doesn’t he?

German saying

In this chapter we begin by finding the conformal algebra in a Minkowski space-time, that is, the set of transformations that leave the metric invariant up to a scale factor. In dimensions greater than two the conformal algebra is finite dimensional, but in two dimensions it is infinite-dimensional. We will find that if a field theory possesses conformal symmetry, then its energy-momentum tensor is traceless. For a two-dimensional classical theory conformal invariance implies the theory has an infinite number of conserved quantities, which are moments of the energy-momentum tensor.

In two-dimensional quantum theories one finds that the ...

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