Gravitational backreaction to resolve worldsheet degeneration divergences

Develop a consistent treatment of gravitational backreaction within the emergent non‑critical string theory constructed by mapping Schwinger‑parametrized Feynman diagrams to Riemann surfaces via Strebel differentials, in order to cancel divergences arising from worldsheet degeneration limits and determine the resulting background (e.g., AdS) for the string amplitudes.

Background

The paper reorganizes perturbative QFT amplitudes into string‑like sums over two‑dimensional geometries using Schwinger parameters and Strebel differentials, then builds a worldsheet CFT whose correlators reproduce the QFT Feynman rules. This construction produces a non‑critical string with a Liouville mode and matches loop divergences to standard string‑theoretic degeneration limits.

Because renormalization of genus‑g graphs requires counterterms at different genera, divergences persist even after resummation over the order of diagrams. The authors state that these divergences align with worldsheet degeneration limits and that including gravitational backreaction is the way to fix them. They explicitly leave the resolution of these issues for future work, noting that their current construction does not include the necessary backreaction and therefore does not produce an AdS background.

References

We will find that these divergence match the well known divergences from degeneration limits of the worldsheet and the way to fix them is to include the backreaction of gravity on the background. We leave addressing such issues to future work, so the string theory we obtain will not be in an AdS background given that no gravitational backreactions will be included.

— Emergent Strings from Quantum Field Theory (2512.07928 - Planas, 8 Dec 2025) in Introduction (Section 1)