jaxvacua.conifold.coniLCS_prepotential.F_coniLCS_series

F_coniLCS_series(self, moduli, conj=False)

Calculates the full conifold-LCS prepotential \(F_{\mathrm{coniLCS}}\) in terms of the complex structure moduli \(z^i\).

Details

At the conifold-LCS (coni-LCS) limit, the prepotential can be decomposed as

\[F_{\mathrm{coni-LCS}}(z_{\mathrm{cf}}, z^a) = F_{\mathrm{coni}}(z_{\mathrm{cf}}) + \sum_{n=0}^{n_{\mathrm{max}}} F_{\mathrm{LCS}}^{(n)}(z^a) z_{\mathrm{cf}}^n\]

where \(z_{\mathrm{cf}}\) is the conifold modulus and \(z^a\) are the bulk complex structure moduli.

The conifold part \(F_{\mathrm{coni}}\) encodes the singular behavior near the conifold point:

\[F_{\mathrm{coni}}(z_{\mathrm{cf}}) = \dfrac{1}{2}\, n_{\mathrm{cf}}\, \left ( \dfrac{z_{\mathrm{cf}}^2}{2\pi \mathrm{i}}\, \log \left ( -2\pi \mathrm{i} z_{\mathrm{cf}} \right ) \right )\]

The corrections \(F_{\mathrm{LCS}}^{(n)}\) involve polynomials and polylogarithms and are summed over powers of \(z_{\mathrm{cf}}\).

Parameters:

• moduli (Array) – Complex structure moduli values, where the first component is the conifold modulus \(z_{\mathrm{cf}}\) and the remaining components are bulk moduli \(z^a\).

• conj (bool) – If True, computes the complex conjugate. Defaults to False.

Returns:

complex – Value of the coni-LCS prepotential \(F_{\mathrm{coni-LCS}}\).

Return type:

complex