Planar diagrams and Calabi-Yau spaces
| dc.creator | Ferrari, Frank | |
| dc.date | 2003-09-15 | |
| dc.date | 2003-12-23 | |
| dc.date.accessioned | 2026-07-07T04:15:44Z | |
| dc.date.available | 2026-07-07T04:15:44Z | |
| dc.description | Large N geometric transitions and the Dijkgraaf-Vafa conjecture suggest a deep relationship between the sum over planar diagrams and Calabi-Yau threefolds. We explore this correspondence in details, explaining how to construct the Calabi-Yau for a large class of M-matrix models, and how the geometry encodes the correlators. We engineer in particular two-matrix theories with potentials W(X,Y) that reduce to arbitrary functions in the commutative limit. We apply the method to calculate all correlators <tr X^{p}> and <tr Y^{p}> in models of the form W(X,Y)=V(X)+U(Y)-XY and W(X,Y)=V(X)+YU(Y^{2})+XY^{2}. The solution of the latter example was not known, but when U is a constant we are able to solve the loop equations, finding a precise match with the geometric approach. We also discuss special geometry in multi-matrix models, and we derive an important property, the entanglement of eigenvalues, governing the expansion around classical vacua for which the matrices do not commute. | |
| dc.description | 46 pages including 4 figures and 2 appendices | |
| dc.identifier | https://arxiv.org/abs/hep-th/0309151 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0309151 | |
| dc.identifier | Adv.Theor.Math.Phys. 7 (2004) 619-665 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/52123 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Planar diagrams and Calabi-Yau spaces | |
| dc.type | text |