Renormalizability via extensions of the basis-vector framework

Establish whether the theory becomes renormalizable by either extending the basis-vector description in 2(2n+1)-dimensional spaces to string-based basis vectors or by extending those basis vectors to odd-dimensional spaces of the form 2(2n+1)+1.

Background

The paper proposes a new formulation of internal spaces using Clifford-odd (fermionic) and Clifford-even (bosonic) basis vectors. The authors raise the question of renormalizability within this framework and suggest two possible routes—string-like extensions or dimensional extensions to odd-dimensional spaces—as potential resolutions.

Determining renormalizability is crucial for quantum consistency and predictive power of the framework beyond perturbative toy examples provided in the text.

References

There remain questions to be answered: iv.a. Can the theory achieve renormalizability by extending the “basis vectors” in 2(2n+1)-dimensional spaces with the ”basis vectors” of strings, or by extending the “basis vectors” in 2(2n+1)-dimensional spaces to odd-dimensional, 2(2n + 1) + 1, spaces?

— Can the "basis vectors", describing the internal spaces of fermion and boson fields with the Clifford odd (for fermion) and Clifford even (for boson) objects, explain interactions among fields, with gravitons included?  (2407.09482 - Borštnik, 2024) in Section 4 (Conclusions), iv.a

Nevertheless, in other cases one should enlarge the structural constraints in order to reabsorb all the infinities and it is not known if this procedure can generally be done [6].

— Chiral Symmetries in the Standard Model of Particle Physics and its Extensions  (2610.13332 - Solera, 9 Oct 2026) in Page 32, Section 1.7, “Renormalizability of Gauge Theories”