## 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.

**Comments:** recovered from sciprint.org

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### Submission history

[v1] 25 Jul 2007

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