Discussion Overview
The discussion revolves around the concept of extending the Standard Model (SM) symmetry group by proposing a sequence of gauge groups, specifically U(1)XSU(2)XSU(3)XSU(4)XSU(5)...XSU(N) as N approaches infinity. Participants explore the implications of this idea for grand unified theories (GUTs) and gauge theories, questioning the feasibility and consequences of such an extension.
Discussion Character
- Exploratory
- Debate/contested
- Technical explanation
Main Points Raised
- Some participants propose extending the SM symmetry group indefinitely, questioning if this has been previously attempted.
- Others suggest that such an extension may be homomorphic to SU(N) as N approaches infinity, relating it to planar gauge theory.
- A participant mentions having derived a "sillier" GUT theory and inquires about the behavior of planar gauge theory as a particle gauge theory.
- It is noted that planar gauge theory behaves more like string theory and has simplifications at the quantum level, potentially leading to exact solvability.
- One participant argues that as energy increases, the best description of particles would be a new direct product with the next SU(j), suggesting an almost exact approximation at each energy level.
- Another participant counters that for finite j, leading order groups would only allow self-conjugate irreducible representations (irreps) and would be non-chiral, complicating effective theories.
- Some participants express that non-chirality is acceptable, as the Standard Model remains a subgroup of the proposed sequence.
- Concerns are raised about the necessity of chiral gauge groups, citing implications for fermion masses and the constraints in GUT model building.
- One participant asserts that N cannot approach infinity due to physical limitations on particle mass relative to the universe's total energy.
- Discussions include the complexities of SU(N) with finite N, emphasizing the need for complex representations and anomaly cancellation for viable candidates.
- A participant expresses confusion about the implications of fermions having large masses and seeks clarification on unifying an infinite sequence of forces.
Areas of Agreement / Disagreement
Participants express multiple competing views regarding the feasibility and implications of extending the gauge groups indefinitely. There is no consensus on whether this approach is viable or how it would function in practice.
Contextual Notes
Participants highlight limitations related to the assumptions of chiral gauge groups, the implications of finite versus infinite N, and the necessity of anomaly cancellation in constructing viable GUTs.
