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Secrets of the metric in N = 4 and N = 2* geometries

James Babington1, Nick Evans1 and James Hockings1

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The metric of the gravity dual of a field theory should contain precisely the same information as the field theory. We discuss this connection in the Script N = 4 theory where a scalar vev may be introduced at the level of 5d supergravity and the solutions lifted to 10d. We stress the role of brane probing in finding the coordinates appropriate to the field theory. In these coordinates the metric parametrizes the gauge invariant operators of the field theory and either side of the duality is uniquely determined by the other. We follow this same chain of computations for the 10d lift of the Script N = 2* geometry of Pilch and Warner. The brane probe of the metric reveals the 2d moduli space and the functional form of the gauge coupling. In the coordinates appropriate to the field theory the metric on moduli space takes a very simple form and one can read off the gravity predictions for operators in the field theory. Surprisingly there is logarithmic renormalization even in the far UV where the field theory reverts to Script N = 4 super Yang-Mills. We extend the analysis of Buchel et al to find the D3-brane source distribution that generates the supergravity prediction for the gauge coupling for the whole class of solutions corresponding to different points on moduli space. This distribution does not account for the logarithmic behaviour in the rest of the metric though. We discuss possible resolutions of the discrepancy.


Keywords

Renormalization Regularization and Renormalons

AdS-CFT and dS-CFT Correspondence

Brane Dynamics in Gauge Theories

 

E-print Number: hep-th/0105235

Cited: by |

Refers: to

PACS

04.65.+e Supergravity

02.40.-k Geometry, differential geometry, and topology

11.25.Hf Conformal field theory, algebraic structures

11.10.Gh Renormalization

11.25.Uv D branes

11.15.-q Gauge field theories

Subjects

Mathematical physics

Gravitation and cosmology

Particle physics and field theory

Dates

Issue 07 ( 1 July 2001)

Received 14 June 2001, accepted for publication 24 July 2001

Published 8 August 2001



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