The hep-th section of arXiv if often filled with beautiful semi-rigorous computations on Mathematics. However sometimes it is very difficult to understand what is being stated.
Here I take from: Aspects of 3d-3d Correspondence by Gang + Kim + Romo + Yamazaki. They show the asyptotics of a certain Gaussian integral is related to the entropy of a pseudo-Anosov map on the torus. In particular they work this out for the case $\mathrm{S} \, \mathrm{T}^k$ where one $\mathrm{S}$ is the flip and $\mathrm{T}$ is the shear.
Their Gaussian integral the partition function of some 3D gauge theory with no mathematical definition, so I have no way of checking their conjecture for other maps.
Are there conjectures of this kind on the math literature connecting Gaussians and hyperbolic maps? How do I get a formula to check for general maps in $\pi_1 (\mathbb{T}^2 \backslash \{ pt\})$ on the once-punctured torus.
