I was wondering, is supergravity the result of adding supersymmetry to the graviton...

That is one (very informal) way to think of it. In practice, I've never seen symmetries being introduced to an already-quantized model, so at the point where susy comes in, no such thing as the graviton exists in the theory, but only some crude notion of "gravity", at best. Supersymmetry is kind of special in an additional way since it already is an extended version of the concept which (in naive approaches) later gives rise to gravitons.

It's more like supergravity being the result of adding gravitons to supersymmetry.

A much better way to think of supergravity is as the localisation or gauging of supersymmetry. Doing so almost automatically gives you a supersymmetric theory that includes gravity.

Yes, that is how I think of it. Local supersymmetry. In fact, it is so elegant, I find it hard to believe that it is not correct (at least on some level).

what is 'gauge' in physics, or a least in the sense that it is being used...

what is 'gauge' in physics, or a least in the sense that it is being used...

 

You have global and local symmetries.

 

Global: No dependence on the location on spacetime.

Local: Dependence of the location on spacetime.

 

To make sense of local symmetries an extra field is required: a gauge field. This field can be though of as compensating for the "ill effects" that arise when you make the symmetry depend on the location. More technically, gauge fields allow us to construct covariant derivatives.

 

When localising supersymmetry we have to introduce the graviton and it's superpartner the gravitino.