Predictions on the symmetry of space-time from string theory
Elementary particle physics is devoted to explaining the basic building blocks (matter particles) and their interactions (forces). Moreover we want to unify all the known forces of Nature---gravity, electromagnetic force, weak and strong nuclear interactions---into one. If we regard the basic element “atom” as not being a point-like particle but a spatially extended “string” we may hope to unify all the known matter and interactions. This is string theory. Like those of a cello, different modes of vibrations of a single string can explain various observed particles such as electrons, quarks and photons (Photons are the particles of light, also responsible for transmitting electromagnetic force).
However, the sizes of the strings are so tiny that we cannot observe them by means of direct experimental observation at the moment. It is therefore of utmost importance to seek a “smoking gun” signal of string theory in other ways.
One of the novel predictions of string theory is the symmetry of the space and time, which are unified into spacetime in Einstein's theory of relativity. For strings to consistently exist, we require ten spacetime dimensions. Among them, however, we can only observe four. The reason is that the extra six dimensions are also so tiny and compact, any of current experiments could not have probed such space. This is because, the motion of particles or waves just neglects the presence of such small space, like a big car does not care much about small pebbles. Interestingly, in such small space, the observed particles can not only be explained by oscillations of freely moving string but also that of winding string in this space. Both behave in the same way. This property, so called T-duality symmetry, is extensively discussed in the context of Double Field Theory, on which the work is based.
In this work, we have found that the above T-duality symmetry naturally predicts the existence of two local Lorentz groups in our four spacetime dimension. In Double Field Theory, this T-duality manifests as a footprint of string theory, therefore we naturally have a double copy of Lorentz groups. Spacetime dependent local Lorentz symmetry is crucial in introducing fermions (a generalized description of particles including electrons and quarks) in gravity. The fact that we have two different Lorentz groups opens a new interesting possibility that electrons and quarks may belong to different Lorentz groups, so that their interactions are restricted than expected. For instance, a direct interaction between electron-electron-quark-quark, which we hope to seek in the near future, may be forbidden. This may initiate challenges on the particle physics.
* Related Article
“Standard Model as a Double Field Theory”
Kang-Sin Choi (Ewha Womans U., Seoul), Jeong-Hyuck Park (Sogang U.). Jun 17, 2015. 5 pp. Published in Phys.Rev.Lett. 115 (2015) 17, 171603