jaxvacua.conifold.coniLCS_prepotential.F_coniLCS_exp

F_coniLCS_exp(self, bulk_moduli, conj=False, n=1)

Calculates the expansion coefficients of the prepotential \(F\) around the conifold point in terms of the complex structure moduli \(z^i\).

Details

The prepotential \(F\) can be expanded around the conifold point as \(F(z) = \sum_{n=0}^{\infty}\, \dfrac{1}{n!}\, \dfrac{\partial^n F}{\partial (z_{\mathrm{cf}})^n}\Bigg |_{z_{\mathrm{cf}}=0}\, (z_{\mathrm{cf}})^n\, .\) This function computes the coefficient of \((z_{\mathrm{cf}})^n\) in this expansion, i.e. it computes \(\tfrac{1}{n!}\,\partial^n_{\!z_{\mathrm{cf}}} F\big|_{z_{\mathrm{cf}}=0}\). The full coniLCS prepotential is reconstructed in F_coniLCS_series() by summing these coefficients up to order nmax.

Parameters:

• bulk_moduli (Array) – Bulk structure moduli values.

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

• n_exp (int, optional) – Order of expansion in the conifold modulus. Defaults to 1.

Returns:

complex – Value of the \(n\)-th derivative of the prepotential \(F\) around the conifold point.

Return type:

complex

See also: F_coniLCS_series()