SCFT should be unique. We will see how this expectation bears out in Section \[Sec:HoloRG\], where we construct explicitly the holographic duals of those RG flows in gauged supergravity.

We would like to emphasize that the RG flows from $\mathcal{N}=4$ SYM obtained by a twisted compactification and a simultaneous mass deformation are different from the RG flows studied in [@Benini:2012cz; @Benini:2013cda] where the $\mathcal{N}=4$ theory is deformed *only* by a twisted compactification with no mass deformation. Then the effective two-dimensional $(0,2)$ SCFT has a $U(1)^3$ global symmetry (the Cartan of $SO(6)$) and in the $c$-extremization calculation one must take an arbitrary linear combination of *all* three $U(1)$ symmetries. In contrast, in the presence of the mass deformation , we have only $U(1)^2$ global symmetry (the Cartan of $U(1)_R\times SU(2)_F $) in the effective two-dimensional theory. This modifies the $c$-extremization calculation and the resulting central charge. The difference between the two deformations is most clearly visible by simply plugging the values of the background fluxes given in into the formula for the central charge in equation (3.12) of [@Benini:2013cda]. This does not reproduce the correct result in above.

The supergravity model and BPS equations
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\[Sec:SUGRAtrunc\] Our goal now is to 