What do the Langland's program and Monstrous Moonshine have in common? The answer lies in M-theory. Stay tuned.
Various and Sundry
3 hours ago
So far, the experiments at the Large Hadron Collider (LHC) have shown no sign of new physics beyond the Standard Model. Assuming the Standard Model is correct at presently available energies, we can accurately extrapolate the theory to higher energies in order to verify its validity. Here we report the results of new high precision calculations which show that absolute stability of the Higgs vacuum state is now excluded. Combining these new results with the recent observation of primordial gravitational waves by the BICEP Collaboration, we find that the Higgs vacuum state would have quickly decayed during cosmic inflation, leading to a catastrophic collapse of the universe into a black hole. Thus, we are driven to the conclusion that there must be some new physics beyond the Standard Model at energies below the instability scaleΛI∼109 GeV, which is responsible for the stabilisation of the Higgs vacuum.
g = E6(6) , II = E6 , II1 = {a1}, g(0) = so(5,5) + R , g(-1) = M1,2(O')
g = E6(-26) , II = A2 , II1 = {a1}, g(0) = so(1,9) + R , g(-1) = M1,2(O)
g = E6C , II = E6 , II1 = {a1}, g(0) = so(10)C + C , g(-1) = M1,2(O)C
g = E7(-25), II = C3, II1 = {y1}, g(0) = so(2,10) + R, dimR g(-1) = 32, dimR g(-2) = 1
where we see a two-time 12-dimensional (2,10) signature arise that reminds us of S-theory constructions with real 32-dimensional Weyl spinor. S-theory proper is 13-dimensional and one expects to see SO(9,1)xSO(2,1) as well, however. Alas, E7 also admits the grading:
g = E7(-25), II = E7, II1 = {y2}, g(0) = so(1,9) + sl(2,R) + R, dimR g(-1) = 32, dimR g(-2) = 10
where the real 32-dimensional Weyl spinor is still present and SO(9,1)xSO(2,1) can be recovered from SO(9,1) and SL(2,R)~Spin(2,1).
g = E8(-24), II = F4, II1 = {y4}, g(0) = so(3,11) + R, dimR g(-1) = 64, dimR g(-2) = 14.
g = E8(8), II = E8, II1 = {y1}, g(0) = so(7,7) + R, dimR g(-1) = 64, dimR g(-2) = 14
g = E8C, II = E8, II1 = {y1}, g(0) = so(14,C) + C, dimC g(-1) = 64, dimC g(-2) = 14
There seems to be hints of a 14-dimensional theory lurking in the gradings with a 64-dimensional real or complex spinor. Viewed from the viewpoint of octonions, E8(8) corresponds to a split-octonion (would be) theory with 14-dimensional (7,7) signature. E8(-24) arises from the octonions, where the 14-dimensional (3,11) three-time signature is recovered. The complexified octonion construction gives the E8(C) case with 14-dimensional SO(14,C) symmetry and complex 64-dimensional spinor.