math-ph — Mathematical Physics

Conjectures of Ashoke Sen: Scope, Exact Tests and Analytic Limits

Contributed by Deep Bhattacharjee

We examine thirty-six selected statements associated with Ashoke Sen's work on duality, tachyon condensation, black hole indices and string field theory. The purpose is to distinguish mathematical results within a specified framework, physical conjectures, and extensions beyond the assumptions used in a derivation. Exact product expansions reproduce known negative dyon indices in toroidal orbifolds; with the charge cone transcribed correctly, a finite scan contains thirty negative-index charge triples. These numbers concern the full index, whose sign need not agree with a horizon index after hair removal. For tachyon dust we give the characteristic flow, the corrected Hessian sign criterion, and precise hypotheses under which the first focusing time is attained. We also separate the D7 divisor on the F-theory base from its singular pullback to the orientifold cover and give a local weak-coupling family with an $I_0^*$ divisor. These calculations delimit claims; they do not disprove the homogeneous rolling solution or Sen's positivity argument under its stated assumptions. The accompanying formal certificates check specified finite computations and algebraic identities, rather than the catalogue's physical interpretations. Established results and later corrections are credited to their sources.