Conformal bootstrap and Heterotic string Gepner models

In Gepner's pioneering work, the requirement that leads to a model having the desired $N=1$ Spacetime supersymmetry and $E\left(8\right)\times E\left(6\right)$ Gauge symmetry was the requirement that the spacetime symmetry is compatible with modular invariance. In this work we show that the requirement for the simultaneous fulfillment of mutual locality of the left-moving vertices of physical states with the space-time symmetry generators and of right-moving vertices with generators of $E\left(8\right)\times E\left(6\right)$-gauge symmetry, which arises after some special reduction together with the requirement of mutual locality of complete (left-right) vertices of physical states among themselves leads to the same Gepner models.