Friday, September 16, 2005

Entropic principle & asymptotic freedom

The previous blog article about the entropic principle was here.

I would like to draw your attention to the second paper by Sergei Gukov, Kirill Saraikin, and - last but not least :-) - Cumrun Vafa.
They use their (and Ooguri's and Verlinde's) topological edition of the Hartle-Hawking wavefunction to argue that the probability measure is concentrated around the points in the moduli space that
  • lead to asymptotically free low-energy effective field theories
  • and, consequently, for which a maximal number of lines of marginal stability are intersecting in/near a given point
If applied to phenomenology, their first point may explain why low-energy effective field theories and QCD in particular work so well for "probable" stringy backgrounds. The second may be related to the observed fact that various particles prefer to be "just above the threshold mass" for them to become unstable. If neutron were a BPS object on a Calabi-Yau, it would be very close to its line of marginal stability because it barely decays to the proton, electron, and an antineutrino - and it could therefore naturally follow from their new paper. Such facts - and maybe, once in the future, also the hierarchies and the cosmological constant - could have an explanation in terms of the Hartle-Hawking wavefunction. In fact, it seems that some of the solutions to the maximization conditions correspond to points with extra massless particles - which could solve the hierarchy problem(s). Other solutions they find correspond to the existence of quantum-deformed complex multiplication on the Calabi-Yau moduli space.

Even if there is an element of randomness in the vacuum selection in the real world, we must study the rules of this randomness. We must be trying to find the right probability distribution; this tells us not only something about the qualitative properties of the real world, but it is also a guide showing where we should look for the exact right vacuum that describes the real world. The probaility measure has probably nothing to do with the "exact democracy between different vacua" because the latter is completely unjustified (being perhaps related to the infinite temperature) and hard to define; only colleagues with extreme far left wing preconceptions can be convinced that this egalitarianism is necessarily a good zeroth approximation. ;-)

The actual distribution is more likely to be related to the Hartle-Hawking wavefunction, which is why it may be a good idea to follow the path of Sergei, Kirill, and Cumrun.

1 comment:

  1. Lubos:

    This second paper could be a bit more interesting than the first one because now they explicitly use the keyword you suggested "entropic principle". I would like to have a discussion with you and find out exactly what they mean.

    Two keywords in the abstract ring a bell and suggest that it is approaching the truth than I found long ago: The finiteness and conservation of the entropy of the whole universe, the GUITAR theory. Which two words:

    "the entropy is maximized"

    Would you ask Vafa exactly what he meant maximized? Does that mean the entropy reach a maximum peak at a certain point of time, and after that, gradually decrease? Otherwise, if a value, any value, is ever increasing over time, then there is no maximum because there is no peak.

    Do keep in mind that the second law of theormodynamics prevent the entropy from ever decreasing!!! That leaves only one of two possibilities: One, the entropy is ever increasing and it never reach a maximum since it could always increase more. Two: The system entropy is at maximum and remain at that maximum all the time, i.e., entropy conservation at maximum level. That is of course the findamental principle of GUITAR theory.

    So what exactly does Vafa mean the entropy is maximized, in terms of time variation of the entropy?