Saturday, 22 August 2015

supersymmetry - 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.





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