constant, $\kappa$, in is the normalized curvature of the Riemann surface, with $\kappa=1$ for $\mathfrak{g}=0$, $\kappa=0$ for $\mathfrak{g}=1$, $\kappa=-1$ for $\mathfrak{g}>1$. The coefficient $\mathfrak{b}$ is real and, since it measures the flux through a compact Riemann surface, it is quantized as $2(\mathfrak{g}-1)\mathfrak{b} \in \mathbb{Z}$ for $\mathfrak{g}\neq 1$ and $\mathfrak{b} \in \mathbb{Z}$ for $\mathfrak{g}= 1$.

[@ c c c r r]{} Field & $U(1)_R^{\rm LS}$ & $U(1)_F$ & $U(1)_\mathfrak{b}$ & $U(1)_{\text{tr}}$\
$\lambda$ & $\phantom{-}1$ & $\phantom{-}0$ & ${\kappa\over 2}$ & $1$\
$\chi_2$ & $-{1\over 2}$ & $-{1\over 2}$ & $-{\kappa\over 4}-{\mathfrak{b}\over 2}$ & $-{1\over 2}-{\epsilon\over 2}$\
$\chi_3$ & $-{1\over 2}$ & $\phantom{-}{1\over 2}$ & $-{\kappa\over 4}+{\mathfrak{b}\over 2}$ & $-{1\over 2}+{\epsilon\over 2}$\

An analysis similar to the one in Appendix E of [@Benini:2013cda] shows that for $\mathfrak{g}\neq 1$ and any value of $\frak{b}$ there is $(0,2)$ supersymmetry preserved in the two-dimensional theory. When $\mathfrak{g}=1$ the discussion is slightly different. For $\mathfrak{g}=1$ and $\frak{b}=0$ there is $(2,2)$ supersymmetry preserved in two dimensions since the torus is flat. However, for $\mathfrak{g}=1$ and $\frak{b}\neq 0$, only two supercharges are preserved and one has $(0,2)$ supersymmetry [@Almuhairi:2011ws; @Benini:2013cda; @Kutasov:2013ffl]. Finally, one can preserve more supersymmetry in two-dimensions if the relevant deformation in is switched off and 