Talk page
Title:
Computational Riemannian geometry applied to the physics of the AdS-CFT correspondence
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Abstract:
The AdS-CFT correspondence is a remarkable duality between gravitational systems and certain quantum field theories. One aspect of it is that properties of (Euclidean signature) Einstein metrics, which are perhaps the simplest solutions of these gravitational systems, then become related to properties of strongly coupled field theories, which are interesting and inherently difficult to compute using direct methods. I will review how this correspondence works for these Riemannian geometries. I will then discuss the methods used to explicitly construct Einstein metrics in this context, which involves a ‘harmonic’ formulation of the Einstein condition. I will discuss how to numerically solve this, using both a direct approach and also geometric flows. If time permits I will give some examples of interesting physics that can be extracted from these calculations.
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