When studying supersymmetric QFT's, it is very common to compute the moduli space of the theory by solving all F-term equation (derivatives of the superpotential). More precisely, one should also quotient by the complexified gauge group.
Here are three fact that I believe to be true about moduli space and IR flow:
- Let us consider a supersymmetric QFT, dumbed theory A. Let us now take flow towards the IR and obtain an affective theory, called theory B. The moduli spaces of theory A and theory B are not necessarily the same. More generally, the moduli space of a theory changes with the flow.
- Now, on the contrary, a moduli space can be seen as the space of theories, i.e. the set of all possible vev's configurations for all the scalars. Choosing a point in the moduli space therefore introduces a scale, and implies that we are at a certain point in the flow of the theory. Certain regions of the moduli space can then correspond to strongly coupled or weakly coupled regimes.
- The moduli space of a theory, i.e. its space of vacua is the most low-energy thing you can do, no fields can be excited so they all take their minimum values, i.e. their moduli. So the moduli space could be seen as the bottom of the IR flow.
Those three pictures are clearly in contradiction. What is the problem with this way of thinking ?
I would be very interested by references about the link between RG flow, low energy-limits, and the moduli space.
