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Most string theory compactifications analyzed so far have as backgrounds a conformal field theory corresponding to...

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Physics

Most string theory compactifications analyzed so far have asbackgrounds a conformal field theory corresponding to a nonlinearsigma model with a Calabi-Yau target space, or some relativelyclassical background, possibly with orbifolding. But as long as thecentral charge of the Virasoro algebra is right, and worldsheetsuperconformal symmetry is respected, any other superconformalfield theory will do just as well. Why haven't string theoristslooked at such models more often?

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Such models have been looked at in a fair amount of detail For example Gepner models are constructed by tensoring together superconformal minimal models Asymmetric orbifolds which have the correct superconformal worldsheet symmetry have also been    See Answer
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