Holography, matrix factorizations and K-stability

Placing D3-branes at conical Calabi-Yau threefold singularities produces many AdS(5)/CFT4 duals. Recent progress in differential geometry has produced a technique (called K-stability) to recognize which singularities admit conical Calabi-Yau metrics. On the other hand, the algebraic technique of non-commutative crepant resolutions, involving matrix factorizations, has been developed to associate a quiver to a singularity. In this paper, we put together these ideas to produce new AdS(5)/CFT4 duals, with special emphasis on non-toric singularities.