Holography, matrix factorizations and K-stability
- PDF / 852,883 Bytes
- 48 Pages / 595.276 x 841.89 pts (A4) Page_size
- 3 Downloads / 191 Views
Springer
Received: January 20, 2020 Accepted: May 3, 2020 Published: May 25, 2020
Marco Fazzia,b and Alessandro Tomasielloc,d a
Department of Physics, Technion, 32000 Haifa, Israel b Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 76100 Rehovot, Israel c Dipartimento di Fisica, Universit` a di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy d INFN, sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
E-mail: [email protected], [email protected] 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. Keywords: AdS-CFT Correspondence, Global Symmetries, Conformal Field Models in String Theory, Supersymmetric Gauge Theory ArXiv ePrint: 1906.08272
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)119
JHEP05(2020)119
Holography, matrix factorizations and K-stability
Contents 1 Introduction
2 3 4 6 7 10 11 12 14 16
3 Quivers from matrix factorizations 3.1 Non-commutative crepant resolutions 3.2 An algorithm for compound Am Du Val threefolds 3.2.1 Algorithm for the quiver 3.2.2 Conifold 3.2.3 Relation to generalized conifolds
17 17 19 19 21 23
4 K-stable cAm singularities 4.1 Yau-Yu classes I–III 4.2 A simple generalization 4.3 Minimally elliptic threefolds
25 25 28 30
5 Additional examples: compound D4 threefolds 5.1 A linear three-node quiver 5.2 Laufer degeneration 5.3 Laufer’s theory
31 32 34 36
6 Conclusions
37
A Maximal modification algebras
38
B NCCRs for orbifolds B.1 The C3 /Z2 × Z2 orbifold B.2 A non-abelian SL(3, C) orbifold
40 41 41
–1–
JHEP05(2020)119
2 Sasaki-Einstein manifolds and K-stability 2.1 Sasaki-Einstein threefolds 2.2 Superconformal models 2.3 K-stability and the Futaki invariant 2.4 Physical interpretation 2.5 Torus actions with complexity one 2.5.1 Fibration and special points 2.5.2 Polytopes 2.6 Examples: Brieskorn-Pham singularities
1
Introduction
–2–
JHEP05(2020)119
An important feature of string theory is that it makes sense on spaces with singularities. In particular, D-branes on such spaces can get stuck at the singular loci, giving rise to intricate algebraic structures that can be described by quiver diagrams. 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. The cleanest example of this procedure is when the conical space is a Calabi-Yau (CY) threefold Y . In the singular case
Data Loading...
