Yukawa interactions Sample Clauses

Yukawa interactions. ‌ The codimension 3 locus of enhanced symmetry is characterized by z = b3 = b4 = 0, along which the fourfold equation reduces to 0 =δ5δ6δ7y2 − δ5ζ2 ζ346ζ12347x3 + b1δ5δ6δ7ζ47ζ235ζ346ζ12347ζ01x2y7 2 3 2 3 5 (4.2.26) − b2δ5δ6δ7ζ47ζ235ζ346ζ12347ζ01x2 − b6δ6δ7 ζ47ζ235ζ346ζ12347ζ01 . All matter surfaces remain irreducible except for Γδ5b4 : δ5 = b4x2 + b6δ6ζ346 = 0 , (4.2.27) which splits into two components in the classes ([b4] − [δ6]) · [δ5] · ([b3] − [ζ235] − [ζ346]) and [δ6] · [δ5] · ([b3] − [ζ235] − [ζ346]) . (4.2.28) Their respective Cartan charges are (−1, 1, 0, −1, 1, 0) and (0, −1, 0, 1, 0, 0) , (4.2.29) which are Cartan charges of other matter divisors, adding up to the Cartan charge of the corresponding matter surface (−1, 0, 0, 0, 1, 0). Thus at the locus b3 = b4 = 0, three matter surfaces become homologous, corresponding to the Yukawa interaction (−1, 0, 0, 0, 1, 0) → (−1, 1, 0, −1, 1, 0) + (0, −1, 0, 1, 0, 0) µ27 − 2α1 − 2α2 − 3α3 − α4 − α6 → − (µ27 − α1 − 2α2 − 2α3 − α4 − α5 − α6) − (µ27 − α1 − α2 − 2α3 − 2α4 − α5 − α6) This exactly amounts to the generation of a 27 × 27 × 27 Yukawa coupling at the b3 = b4 = 0 locus.