Fermion interactions, cosmological constant and spacetime dimensionality in an unified approach based on affine geometry

TL;DR

This paper explores how affine geometry-based unified models naturally generate interactions, focusing on torsion-induced fermion interactions and their influence on the cosmological constant, with implications for spacetime dimensionality.

Contribution

It provides an analysis of torsion-induced fermion interactions within affine geometry models and discusses their effects on the cosmological constant and spacetime dimensions.

Findings

Torsion induces 4-fermion interactions affecting the cosmological constant.

No parity-violating pseudo-scalar density arises from the curvature tensor.

Spacetime dimensionality cannot be constrained from these models.

Abstract

One of the main features of unified models, based on affine geometries, is that all possible interactions and fields naturally arise under the same standard. Here, we consider, from the effective Lagrangian of the theory, the torsion induced 4-fermion interaction. In particular, how this interaction affects the cosmological term, supposing that a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early universe. We explicitly show that there is no parity-violating pseudo-scalar density, dual to the curvature tensor (Holst term) and the spinor-bilinear scalar density has no mixed couplings of A-V form. On the other hand, the space-time dimensionality cannot be constrained from multidimensional phenomenological models admitting torsion.