mrgreen

Hello, this Semester I have my first QFT class and we have a homework where I got stuck at the beginning. I have some ideas but I am not sure if they are correct, We have to assume the SM with two Generations. Now we extend the gauge group of SM with SU(2)H X SU(3)D and introduce new SM-neutral right handed fermion which is a doublet under SU(2)H and a triplet under SU(3)D and two left handed fermions which are singlets under SU(2)H and triplets under SU(3)D . Now we have to consider the gauge anomalies in this SM Extension and have to assign the charges so that we keep the cancellation of this anomlies. (There are soe more parts to do but I want to understand the beginning first) What I understand: My new gauge group is: SU(3)C X SU(3)D X SU(2)H X SU(2)W X U(1)Y Does this mean that my SM fermions also interact with the new part of the gauge Group? I think so, but that would only mean that I get more different interaction particles (more Bosons) If I look at the anomalies, which I get from the triangle diagrams, the extension of my gauge group should not provoke new anomalies because if I look at the triangle diagrams (where I couple the gauge current with two Bosons or the gravitons), all new diagrams with just SU(2) and SU(3) should be zero because I always get a trace over the representations of SU(2) and SU(3) and they are traceless. The only other new anomalies come frome U(1) with the extension, but this anomalies should allready be cancled by the choosen hypercharge Y from the normal SM. (Is that correct?) Does this also mean that I could extend my gauge group by as many new SU(2) and SU(3) as I want? Now I include the new fermions. Because they are SM-neutral the do not interact with the gauge group from the SM. So they only interact with the Extension of the gauge group? (I am not sure what SM-neutral means) Can I see the new fermions as Quarks but coupling righthanded and, because they do not transform under U(1), electrically chargeless? Now I want to consider the anomalies for the new fermions. Because they transform only under the extension SU(2)H X SU(3)D I only have to consider triangle diagrams with SU(2) and SU(3), but now the same happens as in Point 3 and there are no anomalies Does the H and D at the gauge group stand for something or is this freely choosen by our teacher? There has to be something wrong in my thoughts :/ Can someone explain what I do wrong? Greetings Christoph