jaxvacua.conifold.coniLCS_prepotential.F_coniLCS_series_per

F_coniLCS_series_per(self, XPer, conj=False)

Computes the coniLCS prepotential as a Taylor series in the conifold period \(X^{\mathrm{cf}}\) up to order nmax.

Details

Near the conifold locus \(X^{\mathrm{cf}} \to 0\), the prepotential takes the form

\[F_{\mathrm{coniLCS}}(X) = F_{\mathrm{coni}}(X^0, X^{\mathrm{cf}}) + \sum_{n=0}^{n_{\mathrm{max}}} c_n\, (X^{\mathrm{cf}})^n \,,\]

where \(F_{\mathrm{coni}}\) is the logarithmic conifold contribution

\[F_{\mathrm{coni}}(X^0, X^{\mathrm{cf}}) = \frac{n_{\mathrm{cf}}}{4\pi\mathrm{i}}\, (X^{\mathrm{cf}})^2\, \log\!\left(-\frac{2\pi\mathrm{i}\, X^{\mathrm{cf}}}{X^0}\right)\]

and the coefficients \(c_n\) are the Taylor coefficients of the remaining (polynomial + instanton) part of the prepotential around \(X^{\mathrm{cf}}=0\), computed by F_coniLCS_exp_per().

Worldsheet instanton contributions are included in the coefficients \(c_n\) when maximum_degree > 0 (via F_inst_per_coni()).

This expansion replaces the full dilogarithm resummation of the standard coniLCS prepotential with a finite polynomial series, providing a simpler analytic handle on the vacuum structure at small \(|X^{\mathrm{cf}}|\). The accuracy improves as nmax increases.

Parameters:

• XPer (Array) – Period vector \((X^0, X^{\mathrm{cf}}, X^2, \ldots, X^{h^{1,2}})\).

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

Returns:

complex – Value of the series-expanded coniLCS prepotential.

Return type:

complex

See also: F_coni_per(), F_coniLCS_exp_per(), F_inst_per_coni()