# Does string theory really associate 6 dimensions to electromagnetism & the nuclear forces?

1) I understand string (superstring) theory often ends up with 10 dimensions, 9 space-like and 1 timelike. Typically I read that these are all associated to space-time.

2) So, I was interested when I came across a statement (without reference to source) that string theory also associates four dimensions to space-time (three space-like, one time-like), one to electromagnetism and five to the nuclear forces (these last six also being space-like, and compacted).

Question: is (2) just bad pop-science writing/wrong? If it is right, can someone give a clear & concise summary how this is supposed to work (e.g. why only 1D for electromagnetism etc).

• Yes, (2) is just bad/wrong pop-science writing. Jan 29 '20 at 7:32
• In retrospect, the article conflates KK approach with string theory approach, e.g this answer, due to GR having 4D, then KK using 5D, and then adding in strong+weak nuclear forces supposedly needing another 5D gets to 10D in total. Oct 22 '21 at 5:12

However, there is a technical sense in which 'electromagnetism' is a "1d" force. Quantum electrodynamics follows from 'gauging' (making local) a global phase symmetry $$\psi \to e^{iq\phi}\psi$$ of the wavefunction (a quantum field). The group of phase rotations is called $$U(1)$$, and is a one-dimensional group. More technically, a theory defined in $$d$$-dimensional spacetime with electromagnetism can be considered to have a $$U(1)$$ fibration that describes the EM gauge potential. In string theory, this can come from any number of more complicated geometric internal structures. It is very unlikely that this is what was being referenced, especially since from this point of view you would need 3 + 8 = 11 more 'dimensions' ($$\dim(SU(2)) + \dim(SU(3)) = 11$$) to account for the Standard Model's description of the nuclear forces.