Einstein manifolds and conformal field theories

Jul, 1998
12 pages
Published in:
  • Phys.Rev.D 59 (1999) 025006
e-Print:
Report number:
  • PUPT-1805

Citations per year

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Abstract:
In light of the AdS/CFT correspondence, it is natural to try to define a conformal field theory in a large N, strong coupling limit via a supergravity compactification on the product of an Einstein manifold and anti-de Sitter space. We consider the five-dimensional manifolds T^{pq} which are coset spaces (SU(2) x SU(2))/U(1). The central charge and a part of the chiral spectrum are calculated, respectively, from the volume of T^{pq} and the spectrum of the scalar laplacian. Of the manifolds considered, only T^{11} admits any supersymmetry: it is this manifold which characterizes the supergravity solution corresponding to a large number of D3-branes at a conifold singularity, discussed recently in hep-th/9807080. Through a field theory analysis of anomalous three point functions we are able to reproduce the central charge predicted for the T^{11} theory by supergravity: it is 27/32 of the central charge of the N=2 Z_2 orbifold theory from which it descends via an RG flow.
Note:
  • 13 pages, latex, no figures, minor changes and references added
  • supergravity
  • compactification
  • field theory: conformal
  • anomaly
  • differential equations
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