- argue that your non-linear sigma-model may be constructed from a gauged linear sigma-model (GLSM) and RG flow
- show that the volume of the moduli space is finite in the GLSM - it's because the moduli space is something like CP^{125} with a non-singular metric
- demonstrate that the finiteness does not change by the RG flow: although the total "time" of the flow is infinite, most of the changes appear in a particular finite interval where the RG scale is comparable to the typical scales of the GLSM given by its coupling(s)

## Friday, September 30, 2005

### Finiteness of moduli spaces

Zhiqin Lu and Mike Douglas propose a physics proof of the finiteness of the moduli spaces - where the volume is measured by the Zamolodchikov metric - that was recently promoted by Cumrun Vafa in his Swampland. It is not quite clear how general their proof is but it has essentially the following parts:

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