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I am working on a Matrix Quantum Mechanics model that is related to 2d string theory as defined here: http://arxiv.org/abs/hep-th/0311273 §Chapter III

The action is defined as $$ S = \text{Tr} \int dt \left( \frac{1}{2} \dot{M}^2 + V(M) \right) \qquad \text{with } \qquad V(M) = \sum_{k>0} \frac{g_k}{k}M^k . $$

I have choosen $k =2$ and $g_2 = m^2$, and I calculate the 2-point function to be $$ \langle (M_{ij}(t_1) M_{ji}(t_2)) \rangle = \frac{N}{2m} e^{-im |t_1 - t_2|} $$

I would like to ask if there is a well defined way to take the massless limit $m \rightarrow 0$ of this theory, such that the correlators do not diverge?

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