## Saturday, August 06, 2005 ... /////

### Non-critical M-theory

Petr Hořava and Cynthia Keeler promote their so-called non-critical M-theory in 2+1 dimensions. It is related to non-critical type 0A in 1+1 dimensions in the same Kaluza-Klein way in which the usual critical 10+1-dimensional M-theory is related to type IIA in 9+1 dimensions: the KK modes of M-theory are represented by some D0-branes in both cases. All dimensionalities are reduced by 8 spatial dimensions; spacetime supersymmetry is sacrificed; the transverse oscillators of the strings and membranes disappear because of the low dimension.

They define the non-critical M-theory as a double scaling limit of non-relativistic fermions in 2+1 dimensions much like the usual M-theory may be defined using the large N limit of a non-relativistic description of D0-branes in type IIA. Petr and Cynthia only have the description in terms of fermions, not the matrix model itself. The off-diagonal elements of such a hypothetical matrix model should be pure gauge anyway, I think. They also show that noncritical type 0A and 0B theories appear as "hydrodynamic" solutions of their noncritical M-theory.

You may think that this work is another variation on the topic of extending the well-known dualities to uncontrollable non-supersymmetric cases. But there's a difference: in two spacetime dimensions, string theory becomes stable and the "tachyon" becomes a misnomer: the stringy "tachyon" actually becomes massless. The same thing morally holds for their non-critical M-theory in 2+1 dimensions. Because of this special feature, the system is actually exactly solvable - unlike the duality between type 0A in 10 dimensions and M-theory on the Scherk-Schwarz circle, for example. A general comment about this situation is that we know two important classes of exactly solvable systems, namely those with

• large enough spacetime supersymmetry algebras
• small enough spacetime dimensionalities
In their case, it seems that my usual objections that non-supersymmetric vacua together with their dualities are uncontrollable no longer apply. What I find worrisome about these new vacua is that they still seem to be disconnected from the usual, semirealistic supersymmetric vacua stemming from the theories in 10 and 11 dimensions. The proposals how the spacetime dimensions may disappear and critical string theories collapse into the low-dimensional non-critical theories remain uncontrollable speculations, as far as I can say. Or am I wrong?

Even if these subcritical vacua are part of the full "generalized string/M-theory", it is less clear how they may be relevant for "the" string/M-theory that should explain the real world.

External links: Jacques Distler has a complementary description of the article with some math in it.