jaxvacua.sampling.tadpole_quadratic

jaxvacua.sampling.tadpole_quadratic#

tadpole_quadratic(eft, z, tau, mode)#

Return the closed-form tadpole quadratic for one moduli point and ISD input mode.

For an input-half flux u produced by the corresponding ISD sampling mode, the continuous tadpole is

(2)#\[N_{\rm flux} = \frac{1}{2} u^T M(z,\tau)u .\]

The "F" and "H" modes use the ISD matrix and the symplectic form. The "ISD+" and "ISD-" modes use the gauge-kinetic matrix relation implemented by data_sampler.ISD_sampling.

Parameters:

  • eft (Any) – FluxEFT-like object exposing ISD_matrix, gauge_kinetic_matrix and periods.sigma.

  • z (Array) – Complex-structure moduli of shape (h12,).

  • tau (Array) – Axio-dilaton value.

  • mode (Literal['ISD+', 'ISD-', 'F', 'H']) – One of "ISD+", "ISD-", "F", "H".

Returns:

  • Array – Symmetric real matrix M of shape

  • `` (2*(h12+1), 2*(h12+1))

Raises:

ValueError – If mode is not supported.

Return type:

Array