3 ms·
The answer to this question has changed over time. My knowledge of the history is incomplete to say the least. During the first super string revolution, when it
by orbifold 12y ago
The answer to this question has changed over time. My knowledge of the history is incomplete to say the least. During the first super string revolution, when it was understood that perturbative string theory would give a description of perturbative quantum gravity, the goal was to demonstrate that there were only a few choices of compactification manifolds available from consistency arguments (anomaly cancellation and unbroken super symmetry in four dimensions, probably the most well known paper is "Vacuum configurations for superstrings" by Candelas et. al.)
Ignoring heaps of details, the result was that the vacuum manifold (that is a solution to the 10d vacuum Einstein Equations) had to be some 4 dimensional symmetric space (usually taken to be Minkowsky Space) times a Calabi-Yau manifold, those are Kaehler manifolds with vanishing Ricci curvature (those have non-vanishing constant spinors, which you need for unbroken supersymmetry).
Initially it was believed that with additional physical consistency conditions and by relating the geometry of the Calabi-Yau manifold to known physical parameters, like the number of generations of particles, it would be possible to narrow down the number of "stable" vacua to a limited number.
While there were discovered a fair amount of dualities between different string theories, with the discovery of D-Branes and Flux Compactifications (which stabilize the moduli of a huge number of potential vacua, the general idea is that the space of calabi-yau manifolds can locally be paramterized as a finite dimensional manifold and those paramters would show up as massless fields that aren't observed, if there weren't any fluxes they couple to), the number of potentially stable vacua is now sometimes quoted as 10^500.
In itself this is not too concerning, if you think about the fact that there is a infinite number of solutions to the Einstein Field equations and general relativity is still a very predictive theory. In practice this means that you carefully engineer the vacua you study, for example with F-theory techniques in order to relate them to observed phenomena.
You are right that it just reframes the question, the low energy effective field coupling constants turn up as vacuum expectation values of certain fields, but in an interesting way. The idea is then to use relations and identities discovered in string theory (for example AdS-CFT) to study the low energy theories.
- nether 12y agowhat about calabi-yau manifolds and lg orbifolds?
- jerf 12y agoYes, by no means let me be interpreted as claiming that it's not an interesting reformulation. I'm just saying that for example trading 20 arbitrary parameters for 20 differently-inter-related arbitrary parameters is still just a reformulation of the question of where those 20 dimensions of information came from for our universe. (And when I put it that way, in information theoretic terms, one notices that we must also take as parameters the description of the system that consumes those 20-some parameters in the first place. Even if one did come up with an answer for the parameters that question would remain below it. Of course in the end you eventually and inevitably are going to hit some form of "Just Because".)