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. It also obviates the challenges that must be faced by any proposal for a fundamental theory, holographic or topological, where gravity emerges instead as an induced interaction. 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 Dp-brane charges, image, offers a potentially complete framework for nonperturbative String/M theory. We analyze the matrix Lagrangian in detail, comparing with the results of traditional planar reduction, and clarifying the emergence of the spacetime continuum in the large N limit of the zero-dimensional matrix model. 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.
