Threshold bound states of D0-branes on D4-branes: the mass-deformed vacuum count, the index, and uniqueness for one D0-brane
We report results on the normalizable zero-energy states of the ADHM quantum mechanics of k D0-branes bound to N_f D4-branes, obtained by carrying over to this system the strategy of the recent, unrefereed proof by OpenAI of the threshold-bound-state conjecture for the BFSS model. For one D0-brane we prove that the model has exactly one such state, both with one D4-brane, where existence was known and uniqueness had only been sketched, and with two coincident D4-branes, where the Higgs branch is the singular cone C²/Z₂ and the state is a flavour singlet. For one D4-brane and every k we…
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