The Geometric dual of a-maximisation for Toric Sasaki-Einstein manifolds

Mar, 2005
33 pages
Published in:
  • Commun.Math.Phys. 268 (2006) 39-65
e-Print:
Report number:
  • CERN-PH-TH-2005-047,
  • HUTP-05-A0012

Citations per year

200420092014201920240510152025
Abstract: (arXiv)
We show that the Reeb vector, and hence in particular the volume, of a Sasaki-Einstein metric on the base of a toric Calabi-Yau cone of complex dimension n may be computed by minimising a function Z on R^n which depends only on the toric data that defines the singularity. In this way one can extract certain geometric information for a toric Sasaki-Einstein manifold without finding the metric explicitly. For complex dimension n=3 the Reeb vector and the volume correspond to the R-symmetry and the a central charge of the AdS/CFT dual superconformal field theory, respectively. We therefore interpret this extremal problem as the geometric dual of a-maximisation. We illustrate our results with some examples, including the Y^{p,q} singularities and the complex cone over the second del Pezzo surface.
  • Einstein equation: solution
  • space: Calabi-Yau
  • geometry: Kaehler
  • geometry: algebra
  • potential: symplectic
  • moduli space
  • duality