Re: Modular Invariance

Hi Rusty,

Thanks for the reply.

Modular invariance on the torus means invariance under the group
SL(2,Z).
I suppose there are other groups corresponding to higher genus
surfaces.

The mapping class group of the Riemann sphere is just 1.
So if I want to do conformal field theory only on the plane/Riemann
sphere, then I do not have to impose any discrete/modular symmetry on
my theory. Is that correct?

If I stay confined to the sphere, will such a theory be
inconsistent/unphysical in any way?

Thanks,
Marvin

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