 $$H_{J_t}^{(0,0)}(M) \;=\; {\mathbb{C}}\left\langle \left[ \varphi_t^0 \right] \right\rangle \qquad\text{and}\qquad   H_{J_t}^{(0,0)}(M) \;=\; {\mathbb{C}}\left\langle \left[ \bar\varphi_t^{0} \right] \right\rangle \;