jaxvacua.conifold.conifold_utils.get_bulk_projection

get_bulk_projection(q)

Bulk projection matrix for the conifold charge \(q\): the bulk columns \((\Lambda^{-1})_{:,1:}\) of the inverse basis change, shape \((h^{1,2}, h^{1,2}-1)\).

Details

Extracts the \((h^{1,2}-1)\) bulk components of a modulus/period vector v via v @ bulk_projection (\(= (\Lambda^{-T} v)_{1:}\)). It is the left inverse of the bulk embedding (get_bulk_embedding()), \(\text{bulk\_embedding}^T\,\text{bulk\_projection} = \mathbb{1}_{h^{1,2}-1}\), so the “extract bulk then re-embed” round-trip is exact. This differs from get_bulk_embedding() in a general basis (projection vs embedding of a vector); the two coincide only in the conifold-aligned basis, where both reduce to \([0;\mathbb{1}]\). \(\Lambda\) is unimodular, so \(\Lambda^{-1}\) is integer.

Parameters:

q (Array) – Integer conifold charge vector of length \(h^{1,2}\).

Returns:

Array – Bulk projection matrix of shape \((h^{1,2}, h^{1,2}-1)\).

See also: get_bulk_embedding(), get_embedding(), get_basis_change()