The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds View Full Text


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Article Info

DATE

2006-11

AUTHORS

Dario Martelli, James Sparks, Shing-Tung Yau

ABSTRACT

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 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 Yp,q singularities and the complex cone over the second del Pezzo surface. More... »

PAGES

39

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-006-0087-0

DOI

http://dx.doi.org/10.1007/s00220-006-0087-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1031002931


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