Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy

Abstract

A recent work [1] suggests that a 4d nonperturbative global anomaly of mod 16 class hinting a possible new hidden gapped topological sector beyond the Standard Model (SM) and Georgi-Glashow su(5) Grand Unified Theory (GUT) with 15n chiral Weyl fermions and a discrete Z 4,X symmetry of X = 5(B − L) − 4Y . This Z 16 class global anomaly is a mixed gauge-gravitational anomaly between the discrete X and spacetime backgrounds. The new topological sector has a GUT scale high energy gap, below its low energy encodes either a 4d noninvertible topological quantum field theory (TQFT), or a 5d short-range entangled invertible TQFT, or their combinations. This hidden topological sector provides the 't Hooft anomaly matching of the missing sterile right-handed neutrinos (3 generations of 16th Weyl fermions), and possibly also accounts for the Dark Matter sector. In the SM and su(5) GUT, the discrete X can be either a global symmetry or gauged. In the so(10) GUT, the X must become gauged, the 5d TQFT becomes noninvertible and long-range entangled (which can couple to dynamical gravity). In this work, we further examine the anomaly and cobordism constraints at higher energy scales above the su(5) GUT to so(10) GUT and so(18) GUT (with Spin(10) and Spin(18) gauge groups precisely). We also find the [1]'s proposal on new hidden gapped topological sectors can be consistent with anomaly matching under the energy/mass hierarchy. Novel ingredients along tuning the energy include various energy scales of anomaly-free symmetric mass generation (i.e., Kitaev-Wen mechanism), the Topological Mass/Energy Gap from anomalous symmetric topological order (attachable to a 5d Z 4,X -symmetric topological superconductor), possible topological quantum phase transitions, and Ultra Unification that includes GUT with new topological sectors.

Gauge Enhanced Quantum Criticality Beyond the Standard Model

“…In contrast, Ref. [29][30][31] considers the SM or GUT with 15n Weyl fermions and with a discrete variant of baryon minus lepton number B − L symmetry preserved. Ref.…”

“…Ref. [29][30][31] then suggests the consequences that the missing 16th Weyl fermions can be substituted by additional 4d or 5d gapped topological quantum field theories (TQFTs), or by 4d gapless interacting conformal field theories (CFTs) to saturate a certain Z16 global anomaly. On the other hand, our present work does not introduce these Z16-class anomalous sectors, because we already have implemented the 16n Weyl fermion models that already make the Z16 global anomaly fully cancelled.…”

“…Inspired by highly-entangled interacting quantum matter recent developments (see reviews in [63,64]), Ref. [29][30][31] proposed additional new sectors to cancel the anomalies, for example, 3. Symmetry-preserving anomalous gapped 4d TQFT.…”

Cobordism and Deformation Class of the Standard Model

“…[23][24][25][26][27][28][29] consider highly relevant systematic anomaly classifications include several SM-like or Grand Unification (GUT)-like groups. To determine the 4d 't Hooft anomaly and hence the iTFT Z 5 , we gather the cobordism group data from [26,[28][29][30][31][32] to obtain…”

“…7. Ultra Unification (UU) [30][31][32] replaces some of "right-handed sterile neutrinos" (sterile only to G SMq gauge force, but not sterile to GUT or X forces) by new exotic gapped/gapless sectors (e.g., topological or conformal field theory) or by gravitational sectors with topological origins, via nonperturbative global anomaly cancellation and cobordism constraints. Namely (−3 + n νe,R + n νµ,R + n ντ,R + .…”