Fixing the spin-connection ambiguity

Characterize the spin-connection coefficient $c_1$ in the affine-group coset construction and determine whether the effective theory dynamically fixes the value $c_1=-1$ rather than imposing it through the torsion-free assumption.

Background

The coset construction does not uniquely determine the spin connection: a covariantly transforming term proportional to the coefficient c1c_1 may be added while preserving the required Lorentz-index antisymmetry. The choice c1=−1c_1=-1 makes the torsion vanish identically and reproduces the usual torsion-free geometric formulation.

The authors state that their current approach does not resolve this arbitrariness. They suggest that constructing the most general quadratic effective action and analyzing its dynamics—particularly its stability and possible ghost content—could determine whether the torsion-free value is physically selected or whether c1c_1 remains a free parameter.

References

While our current approach cannot fix this arbitrariness, one can always make an assumption involving the absence of torsion as in Ref., which leads to the result $c_1 = -1$ described in the main text.

— General relativity and its modifications as effective field theories of $GL(4)$ breaking  (2610.13323 - Viacava et al., 9 Oct 2026) in Section 3, “Discussion”