# The 4D Physics of a Superstring Background

Suppose I have a compactification of string theory to four Minkowski dimensions of the form $M^{1,3}\times X$, where the internal CFT on $X$ is a $c=9$, $(2,2)$ SCFT. For example, let the SCFT on $X$ be described by the IR fixed point of an LG model with the superpotential $W(\Phi)=\Phi^p$. Can someone explain to me (hopefully in details) how can we extract the space-time physics in $M^{1,3}$ from the data of the internal CFT. What is the relation between the world-sheet superpotential $W(\Phi)=\Phi^p$ and the space-time superpotential? What is the space-time interpretation of the chiral ring of $W(\Phi)$? How does the non-perturbative corrections to the space-time superpotential are related to the correction to $W(\Phi)$. I know this is a basic question in string theory and it should be easy to find an answer in Polchinski but I hope someone will clarify things further.

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