# SUSY and SUGRA

1. Aug 31, 2014

### latentcorpse

Hi,

I'm curious as to the differences between gauged and ungauged SUSY and gauged and ungauged SUGRA. Perhaps I can break down my problems into the following few questions:

(i) I understand that to go from SUSY to SUGRA, one must make the supersymmetry local. What does this mean? I've read that it involves gauging the superpoincare group - how do you do this?

(ii) Within the context of SUGRA (or SUSY), what's the difference between the gauged and ungauged versions? I've read online that essentially the gauged version essentially just has some additional gauge group (as the name suggests). However, we are able to add matter multiplets (in particular vector/gauge multiplets) to the ungauged theory and surely this would correspond to some gauge symmetry? What's going on here? This is really confusing me!

(iii) In the ungauged case, as I said above, it is possible to have electric charges i.e. some U(1) gauge symmetry but then why do we need gauged supergravity to describe the dyonic case of electric and magnetic charges?

(iv) What is the "flux potential" in the gauged case and what is its role as well as the role of fluxes in the gauged case?

(v) Are we allowed Fayet-Iliopoulos terms in both cases?

Thank you.

2. Aug 31, 2014

### nrqed

Hi there. I think this would deserve to be in the Beyond the Standard Model forum.

Are you familiar with the way non SUSY gauge theories are obtained? The process is the same for SUGRA. A supersymmetric theory is invariant under global SUSY transformations. When we make the transformation parameters space-time dependent, we have to introduce a new "gauge" field to keep the theory invariant. This gauge field is essentially the graviton.

I am not sure what you have in mind by gauged vs ungauged theories (do you have a reference with more details). Normally it simply means that some global symmetries are not made local. You can then add matter multiplet, scalars and spin 1 fields but the latter are not called gauge fields.
You say that the engaged case there can be some U(1) gauge symmetry. But that is a gauged theory, at least with respect to U(1). There might be some other groups that are still engaged but it is a bit confusing to me to call this an ungauged theory. Do you have a reference?