jaxvacua.conifold.coniLCS_prepotential

jaxvacua.conifold.coniLCS_prepotential#

coniLCS prepotential functions.

Purpose#

Provide the prepotential family used near conifold large-complex-structure limits, split into period-coordinate and affine-modulus-coordinate layers.

Main public API#

  • Per-period functions attached to periods: F_coniLCS_bulk_per, F_coniLCS_poly_split_per, F_coni_per, F_inst_per_coni, F_coniLCS_exp_per and F_coniLCS_series_per.

  • First through fourth derivatives of the per-period polynomial part.

  • Per-modulus functions attached to css: F_coniLCS_bulk, F_coniLCS_exp, dF_coniLCS_exp and F_coniLCS_series.

Design notes#

The functions are pure prepotential calculations and have no flux dependence. They are defined as plain functions taking self first so consumer modules can attach them to the relevant classes.

The coniLCS prepotential family. Two layers, both pure-math (no flux dependence):

  1. Per-period (X-coordinate) family — attached to jaxvacua.periods.periods.

  2. Per-modulus (z-coordinate) family — attached to jaxvacua.css.css.

These helpers underpin the dilogarithmic conifold contribution to the LCS prepotential and its Taylor expansion in the conifold modulus \(X^{\rm cf}\) / \(z_{\rm cf}\).

Per-period family (attached to periods)#

F_coniLCS_bulk_per(self, XPer[, conj])

Computes the bulk approximation to the coniLCS prepotential.

F_coniLCS_poly_split_per(self, X0, Xcf, Xbulk)

Dummy function to compute the polynomial part \(F_{\mathrm{poly}}\) of the LCS prepotential \(F_{\mathrm{LCS}}\) in terms of the periods, where the periods are split into conifold and bulk parts.

dF_coniLCS_poly_per(self, X0, Xcf, Xbulk[, conj])

Computes the first derivative of the polynomial part \(F_{\mathrm{poly}}\) of the LCS prepotential \(F_{\mathrm{LCS}}\) in terms of the periods.

ddF_coniLCS_poly_per(self, X0, Xcf, Xbulk[, ...])

Computes the second derivative of the polynomial part \(F_{\mathrm{poly}}\) of the LCS prepotential \(F_{\mathrm{LCS}}\) in terms of the periods.

dddF_coniLCS_poly_per(self, X0, Xcf, Xbulk)

Computes the third derivative of the polynomial part \(F_{\mathrm{poly}}\) of the LCS prepotential \(F_{\mathrm{LCS}}\) in terms of the periods.

ddddF_coniLCS_poly_per(self, X0, Xcf, Xbulk)

Computes the fourth derivative of the polynomial part \(F_{\mathrm{poly}}\) of the LCS prepotential \(F_{\mathrm{LCS}}\) in terms of the periods.

F_inst_per_coni(self, X0, XPerBulk[, conj, n])

Computes the instanton part \(F_{\mathrm{inst}}\) of the LCS prepotential \(F_{\mathrm{LCS}}\) in terms of the periods.

F_coni_per(self, X[, conj])

Computes the conifold part \(F_{\mathrm{conifold}}\) of the LCS prepotential \(F_{\mathrm{LCS}}\) in terms of the periods.

F_coniLCS_exp_per(self, X0, XConi, XPerBulk)

Computes the expansion of the prepotential \(F\) around the conifold point in terms of the periods.

F_coniLCS_series_per(self, XPer[, conj])

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

Per-modulus family (attached to css)#

F_coniLCS_bulk(self, moduli[, conj])

Calculates the value of the LCS prepotential in terms of the complex structure moduli \(z^{i}\).

F_coniLCS_exp(self, bulk_moduli[, conj, n])

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

dF_coniLCS_exp(self, bulk_moduli[, conj, n])

Calculates the derivative of the conifold-LCS prepotential \(F_{\mathrm{coniLCS}}^{(n)}\) with respect to the bulk moduli.

F_coniLCS_series(self, moduli[, conj])

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