# How to determine R charge?

Ref. 1, page 15, equation (23) defines the $U(1)_V$ and $U(1)_A$ actions as $$e^{i\alpha F_V}: \Phi(x,\theta^{\pm},\bar{\theta}^{\pm}) \rightarrow e^{i\alpha q_V}: \Phi(x,e^{-i\alpha }\theta^{\pm},e^{i\alpha }\bar{\theta}^{\pm})$$ The superfield can be written as $$\Phi(x,\theta^{\pm},\bar{\theta}^{\pm}) =x+\theta^+ \psi_+ +\theta^- \psi_- + \bar{\theta}^+ \bar{\psi}_+ + \bar{\theta}^- \bar{\psi}_- \ldots$$

The question is how to judge the $U(1)_V$ charge of $\psi_+$, $\psi_-$, $\bar{\psi}_+$ and $\bar{\psi}_-$ like table 2 in page 17. that the $U(1)_V$ charge of $\psi_\pm$ is -1 and the $U(1)_V$ charge of $\bar{\psi}_\pm$ is +1.

References:

1. A. Klemm, Introduction to topological string theory on Calabi-Yau manifolds, lecture notes, 2005. The pdf file is available here.

In two dimensions one can choose the chirality operator to be diagonal (i.e., the Pauli matrix $\sigma_3$), please, see for example the following lecture notes by Rhys Davies. In this basis the Dirac operator becomes also diagonal (its components in flat space are just the holomorphic and antiholomorphic derivatives), and the Dirac Lagrangian decomposes to two independent Weyl components left and right moving.
The vector transformation does not depend on the chirality thus can be taken as $-1$ on both the right and left movers. Since the chirality operator is the Pauli matrix $\sigma_3$, the axial transformation can be taken as $+1$ on the left mover and $-1$ on the right mover. Complex conjugation reverses the charges of all vectors.