Spacetime Reduction of Large N Flavor Models: A Fundamental Theory of Emergent Local Geometry?

Abstract

We introduce a novel spacetime reduction procedure for the fields of a supergravity-Yang-Mills theory in generic curved spacetime background, and with large N flavor group, to linearized forms on an infinitesimal patch of local tangent space at a point in the spacetime manifold. Our new prescription for spacetime reduction preserves all of the local symmetries of the continuum field theory Lagrangian in the resulting zero-dimensional matrix Lagrangian, thereby obviating difficulties encountered in previous matrix proposals for emergent spacetime in recovering the full nonlinear symmetries of Einstein gravity. We conjecture that the zero-dimensional matrix model obtained by this prescription for spacetime reduction of the circle-compactified type I-I'-mIIA-IIB-heterotic supergravity-Yang-Mills theory with sixteen supercharges and large N flavor group, and inclusive of the full spectrum of Dpbrane charges, offers a potentially complete framework for nonperturbative string/M theory. We explain the relationship of our conjecture for a fundamental theory of emergent local spacetime geometry to recent investigations of the hidden symmetry algebra of M theory, stressing insights that are to be gained from the algebraic perspective. We conclude with a list of open questions and directions for future work.