Sunday, June 18, 2006 ... /////

Top twelve results of string theory

In a discussion, I was asked to enumerate what I considered to be the top ten results in string theory. Of course, it is mostly a matter of convention how you divide the results into groups and their subgroups. Also, the list depends on some personal opinions. Nevertheless, I feel that many people would construct a similar list.

The Reference Frame is grateful to Christine Dantas for having added some of the references. You should be aware that the choice of the references is somewhat random and there are probably better references that could be used as reviews. For a rather extensive list of reading about string theory at all levels, see Donald Marolf's resource letter or my list of textbooks on string theory. Also, there exists a probability that an important group of results has been omitted in the list below, in which case I apologize.

1. Microscopic calculation of entropy of black holes and their other thermodynamical properties [hep-th/0503211][hep-th/9601029]; I finally chose this #1 to agree with Brian Greene. The black holes whose weakly coupled description is known to match the result of GR include seven-parametric families of near-extremal black holes, black rings, and others.
2. The equivalence between conformal field theories (especially gauge theories based on physics of D-branes) and quantum gravity in anti de Sitter space, i.e. AdS/CFT correspondence and other, less rigorous examples of holography (this has a lot of huge subdiscoveries, and it is a matter of convention whether I list them separately or not) [hep-th/0007170][hep-th/0009139][hep-th/9905111]; most colleagues would say that this is #1
3. Unity of all consistent theories of quantum gravity in the maximal dimensions, by dualities [hep-th/9903268][hep-th/0210044]
4. Natural embedding of realistic vacua with all desirable features for phenomenology, SM spectrum gauge groups, SUSY, grand unification, neutrino masses, solutions to numerous particle physics problems within the simplest N=1 vacua of string theory [hep-th/9910042]
5. Matrix models and Matrix theory as alternative descriptions of second-quantized systems without second quantization, including the description of more complicated backgrounds such as 10D type IIA [hep-th/0506186]

6. Mirror symmetry and physical methods to solve difficult questions in algebraic geometry, and geometrization of particle physics processes such as gaugino condensation [hep-th/0601143][math.AG/0405303]; under the general headline "geometrization of particle physics", we may also include the exact description of "N=2" gauge-theoretical and related moduli spaces using SUSY, brane box theories, and other things that MoveOn is thinking about in the comments
7. Detailed proofs that topology can change and description how it precisely occurs [hep-th/0507203][hep-th/0010207]
8. Framework that generates helpful new concepts and ideas that might be relevant in bottom-up phenomenology even without the exact rules of string theory such as large extra dimensions, warped dimensions, application of quiver theories (deconstruction etc.), and others [hep-ph/9803315][hep-th/0605177]; let me include the most intense intellectual thrill of Witten's life - the derivation of Einstein's equations (and GR) from the vanishing beta-functions on the worldsheet - into this group
9. Other mechanisms showing the emergent character of space, other dualities such as K3-heterotic, new transitions, new massless states giving enhanced symmetries and explaining the McKay correspondence, and so forth [hep-th/9605131][hep-th/9709004][hep-th/0601234]
10. Other implications for branches of mathematics such as knot theory, encoded in topological string theory, a subsector of the full string theory [hep-th/0410178][hep-th/0605255][hep-th/0406005]
11. (added by Joe Polchinski) - Absence of free non-dynamical continuous dimensionless parameters in the underlying equations (to the extent that we know these of course, but we know them well enough for this statement to be meaningful) [hep-th/0605264]
12. (added by Joe Polchinski) - The existence of the landscape, a large enough set of metastable solutions that the cosmological constant can adjust to a value small enough as to allow organized structures (which require many bits and many cycles). [hep-th/0603249]

The Reference Frame thinks that the point 12 is not yet supported by sufficiently nontrivial mathematical or observational evidence as an explanation of some features of reality or as an important feature of string theory.

Otherwise, because there are some strange speculations, I am absolutely proud that the human intellect was able to crack the questions #1-11, and if someone happens to find a comparably nontrivial evidence that #12 is correct, I will be proud about it, too. ;-)

I certainly think that the top 11 results belong to the top 100 results in theoretical physics of all times, and the only reason not to think so is to misunderstand the meaning of the discoveries. I am deeply irritated by the vocal ignorants who misunderstand the findings and who would like to shape not only the public perception but even the status of these results within the scientific community.

Twelve is of course far too little. I think that there are roughly 100 remotely comparably important results in string theory that are crucial and can never go away, and any kind of pressure to abandon these results would represent a mathematical inconsistency imposed upon theoretical physics.