## 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

**Download:** **PDF**

### Submission history

[v1] 25 Jul 2007

**Unique-IP document downloads:** 38 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*