julia-meets-string-theory / cyaxiverse.jl Goto Github PK

Which of the points this algo finds are actually minima? i.e. implement gradient / hessian

Need to write projection function that accommodates recursive relationship of projections

Currently vacua_full doesn't evaluate due to issue with phases. Go back to example without phases and then compare with vacua_id. Then introduce phases to both functions

Bugfix argument of gradient such that it's really the zeros. Input that to hessian to find minima i.e. eig(H) > 0

Add phases to vacua_id and vacua_full

Need to check how best to construct this matrix (norm over columns or rows and then sum?)

\theta_min is periodic in 2\pi but what is the condition on each component of \theta_min? Should be 0 \leq \theta_{min_i} \cdot e_{q_i} < 2\pi

Fix phases in vacua_projector

Apply projection method to square case to check it outputs abs(det(Qhat))

do we need to use a projected Qhat or use original (saves an h11 * h11 matrix multiplication maybe)?

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Phases at each iteration should also include all previous phases -- can this be done with sums of matrix columns / rows?

Build θ_min vector from min_list and Qsub_list

Include threshold such that some ``degeneracy'' among instantons can be included (would need to then compute hessian for subset of axions à la vacua projectors)

Are the series of projections themselves projectors? i.e. \Pi_1 \cdot \Pi_2 = \Pi_{1,2}? Or should this be orth_basis (but returning an NxN not N-1xN matrix)

Floating point errors are entering projectors -- need to cutoff or write everything as floats (not preferred)

vacua_id returns vacua however currently a dimension mismatch prevents vacua_full running properly -- seems conflict is due to phase inclusion for vacua_full (not yet implemented in vacua_id).

Testing: Write vacua_full without phases initially

When \Omega is not square, make sure sign(L) is considered properly