Abstract
Placing D3-branes at conical Calabi-Yau threefold singularities produces many AdS5/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 AdS5/CFT4 duals, with special emphasis on non-toric singularities.
Highlights
An important feature of string theory is that it makes sense on spaces with singularities
This plays an important role in holography: placing a stack of D3-branes at a conical singularity and taking a nearhorizon limit, one obtains an AdS5 solution that is dual to a CFT4 described by the quiver
We look for examples where the K-stability test succeeds and an non-commutative crepant resolution (NCCR) can be found
Summary
An important feature of string theory is that it makes sense on spaces with singularities. A criterion was proven [4], called K-stability, that guarantees the existence of a Calabi-Yau metric on a Gorenstein singularity, or equivalently of a Sasaki-Einstein metric on a five-manifold with positive curvature. This was inspired by the recent progress in the existence of Kahler-Einstein metrics [5]. In other cases computations are harder, but in principle still algorithmic Speaking, these two separate developments can be viewed as progress on the complex and Kahler side of non-compact CYs. In this paper we put these two strands together to produce new AdS5/CFT4 duals.
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