Anomaly-free m-fold product representations of su_n form rational projective varieties for all n and m, and bounded-size chiral solutions are rare, with known upper and lower bounds.
Heath-Brown, The density of rational points on cubic surfaces , Acta Arith
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More varieties of 4-d gauge theories: product representations
Anomaly-free m-fold product representations of su_n form rational projective varieties for all n and m, and bounded-size chiral solutions are rare, with known upper and lower bounds.