Quantum Gravity and String Theory


4D Quantum Gravity via W_infinity Gauge Theories in 2D, Collective Fields and Matrix Models

Authors: Carlos Castro

It is shown how Quantum Gravity in D = 3 can be described by a W_inifnity Matrix Model in D = 1 that can be solved exactly via the Collective Field Theory method. A quantization of 4D Gravity can be attained via a 2D Quantum W_inifnity gauge theory coupled to an infinite-component scalar-multiplet ; i.e. the quantization of Einstein Gravity in 4D admits a reformulation in terms of a 2D Quantum W_inifnity gauge theory coupled to an infinite family of scalar fields. Since higher-spin W_inifnity symmetries are very relevant in the study of 2D W_inifnity Gravity, the Quantum Hall effect, large N QCD, strings, membranes, topological QFT, gravitational instantons, Noncommutative 4D Gravity, Modular Matrix Models and the Monster group, it is warranted to explore further the interplay among all these theories.

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Submission history

[v1] 25 Jul 2007

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