jaxvacua.conifold.conifold_utils.compute_a_matrix

jaxvacua.conifold.conifold_utils.compute_a_matrix#

compute_a_matrix(intnumstensor)#

Computes the \(a\)-matrix from the triple intersection number tensor.

Details

The \(a\)-matrix appears in the polynomial part of the LCS prepotential

\[F_{\rm poly}(z) = -\frac{1}{6}\,\kappa_{ijk}\,z^i z^j z^k + \frac{1}{2}\,a_{ij}\,z^i z^j + b_i\,z^i + \frac{i}{2}\,\tilde{\xi} \,,\]

where \(\kappa_{ijk}\) are the triple intersection numbers of the mirror Calabi-Yau. The entries of \(a\) are

\[\begin{split}a_{ij} = \begin{cases} \kappa_{iij}/2 & i \geq j \\ \kappa_{ijj}/2 & i < j \end{cases} \,.\end{split}\]

This convention is used for the coniLCS, coniLCS_series, and coniLCS_bulk limits in jaxvacua.lcs.lcs_tree._prepare_prepot().

Parameters:

intnumstensor (Array) – Triple intersection number tensor \(\kappa_{ijk}\) of shape \((h^{1,2}, h^{1,2}, h^{1,2})\).

Returns: