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Approaches to Quantum Gravity

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10Gauge/gravity dualityG. HOROWITZ AND J. POLCHINSKI10.1 IntroductionAssertion: hidden within every non-Abelian gauge theory, even within the weakand strong nuclear interactions, is a theory of <strong>Quantum</strong> <strong>Gravity</strong>.This is one implication of AdS/CFT duality. It was discovered by a circui<strong>to</strong>usroute, involving in particular the relation between black branes and D-branes instring theory. It is an interesting exercise, however, <strong>to</strong> first try <strong>to</strong> find a path fromgauge theory <strong>to</strong> gravity as directly as possible. Thus let us imagine that we know abit about gauge theory and a bit about gravity but nothing about string theory, andask, how are we <strong>to</strong> make sense of the assertion?One possibility that comes <strong>to</strong> mind is that the spin-two gravi<strong>to</strong>n might ariseas a composite of two spin-one gauge bosons. This interesting idea would seem<strong>to</strong> be rigorously excluded by a no-go theorem of Weinberg & Witten [41]. TheWeinberg–Witten theorem appears <strong>to</strong> assume nothing more than the existence ofa Lorentz-covariant energy momentum tensor, which indeed holds in gauge theory.The theorem does forbid a wide range of possibilities, but (as with severalother beautiful and powerful no-go theorems) it has at least one hidden assumptionthat seems so trivial as <strong>to</strong> escape notice, but which later developments show <strong>to</strong> beunnecessary. The crucial assumption here is that the gravi<strong>to</strong>n moves in the samespacetime as the gauge bosons of which it is made!The clue <strong>to</strong> relax this assumption comes from the holographic principle [21; 38],which suggests that a gravitational theory should be related <strong>to</strong> a non-gravitationaltheory in one fewer dimension. In other words, we must find within the gaugetheory not just the gravi<strong>to</strong>n, but a fifth dimension as well: the physics must be localwith respect <strong>to</strong> some additional hidden parameter. Several hints suggest that therole of this fifth dimension is played by the energy scale of the gauge theory. Forexample, the renormalization group equation is local with respect <strong>to</strong> energy: it is<strong>Approaches</strong> <strong>to</strong> <strong>Quantum</strong> <strong>Gravity</strong>: Toward a New Understanding of Space, Time and Matter, ed. Daniele Oriti.Published by Cambridge University Press. c○ Cambridge University Press 2009.

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