Living Reviews in Relativity

"Perturbative Quantum Gravity
and its Relation to Gauge Theory"
by
Zvi Bern  

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Abstract
1 Introduction
2 Outline of the Traditional Approach to Perturbative Quantum Gravity
2.1 Overview of gravity Feynman rules
2.2 Divergences in quantum gravity
2.3 Gravity and gauge theory Feynman rules
3 The Kawai–Lewellen–Tye Relations
3.1 The KLT relations in string theory
3.2 The KLT relations in field theory
3.3 Tree-level applications
3.4 Soft and collinear properties of gravity amplitudes from gauge theory
4 The Einstein–Hilbert Lagrangian and Gauge Theory
5 From Trees to Loops
6 Gravity Loop Amplitudes from Gauge Theory
6.1 One-loop four-point example
6.2 Arbitrary numbers of legs at one loop
7 Divergence Properties of Maximal Supergravity
7.1 One-loop cut construction
7.2 Higher loops
7.3 Divergence properties of N = 8 supergravity
8 Conclusions
9 Acknowledgments
Open References References
Footnotes
Figures