Sparks
James
2019-04-11T14:30
2006-11
http://link.springer.com/10.1007%2Fs00220-006-0087-0
https://scigraph.springernature.com/explorer/license/
2006-11-01
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.
The Geometric Dual of a–Maximisation for Toric Sasaki–Einstein Manifolds
en
true
research_article
articles
39
Springer Nature - SN SciGraph project
doi
10.1007/s00220-006-0087-0
dimensions_id
pub.1031002931
Communications in Mathematical Physics
1432-0916
0010-3616
Yau
Shing-Tung
European Organization for Nuclear Research
Department of Physics, CERN Theory Division, 1211, Geneva 23, Switzerland
Dario
Martelli
1
readcube_id
93b2786f0e3b5dc8622f8ba9be7661d8b07552c3b0ee1f1ea06303356862ed66
268
Pure Mathematics
Harvard University
Department of Mathematics, Harvard University, One Oxford Street, 02138, Cambridge, MA, U.S.A
Jefferson Physical Laboratory, Harvard University, 02138, Cambridge, MA, U.S.A
Mathematical Sciences