Generality of curvature response in link-based causal-set propagators

Determine whether particular classes of causal-set propagators constructed directly from links exhibit a characteristic curvature response, rather than the nonuniversal responses found across different causal-set discretizations.

Background

The paper derives an effective curvature coupling of ξeff=1/6\xi_{\rm eff}=1/6 for the normalized link-exponential propagator in $1+1$-dimensional constant-curvature spacetimes. The authors contrast this value with curvature coefficients obtained from causal-set d'Alembertian operators, emphasizing that curvature response is not universal across discretization schemes.

The unresolved issue is whether the value or form of the curvature response is a distinctive feature of broad classes of link-based propagators or merely an artifact of the particular link-exponential construction studied here.

References

Whether particular classes of constructions, such as propagators built directly from links, exhibit a characteristic curvature response remains an open question.

— Effective curvature coupling of link-based causal set propagators in $1+1$ dimensions  (2608.18753 - Kastrati, 19 Aug 2026) in Section 1, Introduction

The regular-region approximation used here does not analyze possible curvature sources from the singular region T-r\sim q. In flat spacetime that region is responsible for the logarithmic contribution in Eq.~eq:flat-conv-result-main. The present calculation extracts the leading curvature source; a full treatment of singular-region curvature corrections remains an open technical point.

— Effective curvature coupling of link-based causal set propagators in $1+1$ dimensions  (2608.18753 - Kastrati, 19 Aug 2026) in Appendix, Section "Curvature-flow matching" (Appendix \ref{subsec:appendix-curv-flow})