AdAMP recently proposed a string-reminiscent E8 GUT (digest, full) where 6 extra dimensions are compactified on a $\mathbb T^6/(\mathbb Z_3\times\mathbb Z_3)$ orbifold to yield the 4d Standard Model.

Orbifolding avoids the usual E8 issues, and the model has many desirable qualities (chiral fermions, no mirror matter, 3 generations, CKM values, light neutrinos, one light Higgs, suppressed proton decay, etc).

Is such an E8 GUT part of the string landscape, or swampland?


While AdAMP's analysis is pure QFT, they briefly contrast their model to string theory. Some differences are recognized as out of scope for a GUT without gravity (from full §I.C)

in the heterotic string theory case, the gauge group $E_8\times E_8'$ plays a key role in the cancellation of anomalies in supergravity2. For the GUT proposed in this article, a single E8 is chosen since it unifies all the representations of the SM into a single one, while gravity lies beyond the scope of the current analysis.

… Notice also that gravity lies at the core of any ST-based framework and the gravitational anomaly cancellation between the gravitino, dilatino and gauginos defines the gauge group. However, there is no known consistent QFT of gravity at present.

The model presented in this work has a Lorentz anomaly since there is a single 10d chiral – left by definition – fermion in the 248 E8 representation3. Since it is a global symmetry, that is not viewed as a problem as the 10d Lorentz symmetry is broken by the orbifold compactification anyway. However, it would be a problem if one includes gravity. In this case, gravity would be added by upgrading the global Poincaré symmetry to a local one, which is equivalent to full coordinate invariance, i.e. General Relativity. The simplest, but not unique, way to cancel the anomaly realised in ST is to add an extra E′8 248 10d right chiral supermultiplet or 248 E8 singlets.

If SUSY becomes local then there is also a spin-3/2 10d chiral gravitino. The minimal way to cancel the anomaly is to add 247 singlet 10d left chiral superfields, although it is a more symmetric approach to add a single 10d right chiral superfield E8 singlet, usually called dilaton, and an E8 248 10d left chiral supermultiplet [67]. As in ST an adjoint chiral multiplet can not be added by itself, one must add a second gauge symmetry E′8.

But they speculate some things are impossible in ST,

the considered model is free from gauge anomalies which would not be the case in a ST based framework. First, the decomposition in Eq. (1.21) would be incomplete in ST due to the presence of winding modes around each of the circles of each of the torus. Thus, since they do not add up to a complete 248 irrep, this typically leads to emergence of gauge anomalies. ST also contains twisted states which are inherently localized at the fixed branes and equally lie in incomplete E8 representations, also contributing to the gauge anomaly problem. Furthermore, there can be strings localized in a brane or connecting two of them. These would only “feel” a fraction of the Wilson line, or none at all, while the ST must be kept anomaly free for all values of the continuous Wilson line [66]. In QFT with only bulk states the continuous Wilson lines do alleviate the gauge anomaly problem [65]. So, the gauge anomaly cancellation is a particularly important feature of this model as it is a QFT with no localized fields, which would not be possible in ST.

and instead suggest an emergent gravity theory (which de Anda has proposed),

it is worth mentioning that if one sticks to a QFT approach as realised in this work, gravity can in principle be an emergent phenomenon instead of treating it as a fundamental one as in the ST-based framework [68–70]. In this case, the 10d super-Poincaré symmetry stays global and its anomaly would not be a problem, while it is broken by the orbifold compactification anyway. If an emergent local symmetry arises after compactification one would end up with an effective 4d theory of gravity.

That aside, is this GUT a valid low-energy limit / effective QFT of string theory? (Mutatis mutandis for E′8 effects above the unification scale?) Or is it in the swampland?


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