I have read in a paper (arXiv:1507.07709v3 [hep-th]) that the $(2,0)$ superconformal field theory (SCFT) in $d = 6$ when dimensionally reduced on $S^1$ yields a $d = 5$ $\mathcal{N} = 2^\star$ theory. In an effort to learn more about this $\star$, I figured out that the theory consists of the $\mathcal{N} = 2$ gauge vector multiplet along with an adjoint hypermultiplet of mass $m$. I have a number of questions about such a construction:

**Question 1**: In what sense is this *mass deformation* of $\mathcal{N} = 4$ Super Yang-Mills (SYM) theory?

The N=4 SYM multiplet consists of an N=2 vector multiplet and an N=2 hypermultiplet, and if you make the hypermultiplet infinitely massive, it is tantamount to integrating the hypermultiplet out, yielding an N=2 SYM. In the opposite limit (of taking the mass to zero), one gets back N=4 SYM. Is this all one means by a mass deformation?

The context of my question is the so called twisted compactification of (a stack of) M5-branes on $S^1$ which leads to this five-dimensional $\mathcal{N} = 2^\star$ theory.

**Question 2**: In this setting, what does the mass parameter *m* translate to in terms of the branes? What kind of "twist" relates to the mass?

This post imported from StackExchange Physics at 2016-08-11 19:19 (UTC), posted by SE-user leastaction