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We prove that the swampland for D=10 N=1 SUGRA coupled to D=10 N=1 SYM isonly populated by U(1)^496 and E_8 x U(1)^248. With this goal in mind, wereview the anomalies for classical and exceptional groups, retrieving traceidentities up to the sixth power of the curvature for each class of groups. Weexpand this idea for low-dimensional groups, for which the trace of the sixthpower is known to factorize, and we retrieve such factorization. We obtain thetotal anomaly polynomials for individual low dimensional groups andcombinations of them and finally we investigate their non-factorization, insuch a way that U(1)^496and E_8 xU(1)^248 are non-trivially shown to be theonly anomaly-free theories allowed in D=10. Using the method developed forchecking the factorization of gauge theories, we retrieve the Green-Schwarzterms for the two theories populating the swampland.

An Analysis of Anomaly Cancellation for Theories in D=10