3 The Kawai–Lewellen–Tye Relations

Our starting point for constructing perturbative quantum gravity is the Kawai, Lewellen, and Tye (KLT) relations [86Jump To The Next Citation Point] between closed and open string tree-level amplitudes. Since closed string theories are theories of gravity and open string theories include gauge bosons, in the low energy limit, where string theory reduces to field theory, these relations then necessarily imply relations between gravity and gauge theories. The realization that ordinary gauge and gravity field theories emerge from the low energy limit of string theories has been appreciated for nearly three decades. (See, for example, Refs. [144118117Jump To The Next Citation Point69Jump To The Next Citation Point70Jump To The Next Citation Point110Jump To The Next Citation Point111Jump To The Next Citation Point].)

 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

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