I am working on a 1D Conformally invariant Matrix Model with the following Partition function:

$$ Z(g) = \int \mathcal{D}M(t) \exp \left[ -\text{tr}\int dt \left( \frac{1}{2} \dot{M}^2(t)+V(M) \right)\right] \qquad \text{with} \qquad V(M) =\frac{g}{2} \text{tr}\left(M^{-2}(t)\right), $$ where $M(t)$ is an $N \times N$ hermitian matrix whose components are functions of $t$. The potential is similar to the $1/x^2$ potential. I want to calculate the 2-point function to 1st order in the coupling $g$.

This requires the calculation of $\left \langle \text{tr}\left( M(t)M^{-3}(t')\right)\right\rangle$.

I would like to ask if there is a way of calculating such an expectation value?


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