Quick notes on Supersymmetric Quantum Mechanics III

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$\{Q,Q^{\dagger}\} = H$

           ----- See later, but for central extension  :  $\{Q,Q^{\dagger}\} = H  + Z_{ij}$


$\{Q,Q\} = 0$

$\{Q^{\dagger},Q^{\dagger}\}= 0$

$\{Q_{\alpha}^I,Q_{\beta}^J\}= \sigma^0_{\alpha, \beta} H \delta^{IJ}$

Central Extension.

$\{Q_{\alpha}^I,Q_{\beta}^J\}= \epsilon_{\alpha, \beta} H Z^{IJ}$

Central charges

$Z^{IJ} = Z^{JI}$  

$[Z^{IJ}, H] = 0$


Partial symmetry breaking

     Given a few supercharges:

            --Say two of them $Q_1$, $Q_2$

            --It is possible to have

                            -- $Q_2| 0 \rangle \neq 0$

                            -- $Q_1| 0 \rangle = 0$

         This is partial symmetry breaking


R-Symmetry

Given a global symmetry + A supersymmetry.

Let $T_l$ be the generator of the global symmetry 

$[T_l,  Q^I_\alpha] = 0$

$[T_l,  Q^I_\alpha] \neq 0$  R-symmetry

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