M-theory 4

The original formulation of M-theory was in terms of a (relatively) low-energy effective field theory, called 11-dimensional Super gravity. Though this formulation provided a key link to the low-energy limits of string theories, it was recognized that a full high-energy formulation (or “UV-completion”) of M-theory was needed.

Analogy with water

For an analogy, the Super gravity description is like treating water as a continuous, incompressible fluid. This is effective for describing long-distance effects such as waves and currents, but inadequate to understand short-distance/high-energy phenomena such as evaporation, for which a description of the underlying molecules is needed. What, then, are the underlying degrees of freedom of M-theory?

BFSS model

Banks, Fischler, Shenker and Susskind (BFSS) conjectured that Matrix theory could provide the answer. They demonstrated that a theory of 9 very large matrices, evolving in time, could reproduce the Super gravity description at low energy, but take over for it as it breaks down at high energy. While the Super gravity description assumes a continuous space-time, Matrix theory predicts that, at short distances, non-commutative geometry takes over, somewhat similar to the way the continuum of water breaks down at short distances in favor of the graininess of molecules.

— Wikipedia on M-theory

2011.01.20 Thursday ACHK