Nomenclature

There are two issues to be dealt with here:

    * When Witten named M-theory, he did not specify what the “M” stood for, presumably because he did not feel he had the right to name a theory which he had not been able to fully describe. According to Witten himself, “‘M’ can stand for either ‘magic’, ‘mystery’, or ‘matrix’, according to taste.” According to the BBC/TLC documentary Parallel Universes, the M stands for “membrane”. Other suggestions by people such as Michio Kaku, Michael Duff and Neil Turok in that documentary are “mother” (as in “mother of all theories”), and “master” theory.

Cynics have noted that the M might be an upside down “W”, standing for Witten. Others have suggested that for now, the “M” in M-theory should stand for Missing or Murky.

2011.01.21 Friday ACHK

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

In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold. Riemann surfaces can be thought of as “deformed versions” of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or a couple of sheets glued together.

The main point of Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm.

— Wikipedia on Riemann surface

2011.01.19 Wednesday ACHK

In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis, hybrid vigour). In string theory, the left-moving and the right-moving excitations almost do not talk to each other, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations “think” that they live on a bosonic string propagating in D = 26 dimensions, while the right-moving (clock-wise) excitations “think” that they belong to a superstring in D = 10 dimensions.

Every heterotic string must be a closed string, not an open string; it is not possible to define any boundary conditions that would relate the left-moving and the right-moving excitations because they have a different character.

— Wikipedia on Heterotic string

2011.01.18 Tuesday ACHK

In physics, the first superstring revolution is a period of important discoveries in string theory roughly between 1984 and 1986. It was realised that string theory was capable of describing all elementary particles as well as the interactions between them. Hundreds of physicists started to work on string theory as the most promising idea to unify physical theories. The revolution was started by a discovery of anomaly cancellation in type I string theory via the Green-Schwarz mechanism in 1984. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985. It was also realised in 1985 that to obtain N = 1 supersymmetry, the six small extra dimensions need to be compactified on a Calabi-Yau manifold.

— Wikipedia on First superstring revolution

2011.01.17 Monday ACHK