Polyakov backreaction in large D discretely self-similar collapse

Abstract

We study anomaly-induced semiclassical backreaction on an analytic family of discretely self-similar solutions of Einstein--Klein--Gordon theory at large spacetime dimension. Horizon regularity fixes a null-coordinate Floquet exponent and selects a unique regular quantum state. The Polyakov auxiliary field is affine-periodic rather than periodic, with a monodromy that is determined independently by a global zero-mode condition and by the conformal-coordinate scaling. Spherical reduction introduces a quantum coupling that grows toward the center, so the periodic first-order expansion is nonuniform. We construct the resulting nonlinear inner problem and find a critical dilaton surface. Generic crossings of this surface are singular, whereas matching to the regular zero-mass exterior selects a narrow, high-curvature throat. The anomaly also separates the effective null-energy boundaries from the classical matter flux and zero-curvature curves. These results show that the minimally coupled Polyakov model does not yield a generic smooth, exactly self-similar completion of the classical center.

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BibTeX RIS

BibTeX

@misc{lai2026polyakov,
  title = {{Polyakov backreaction in large D discretely self-similar collapse}},
  author = {Sheng-Hong Lai and Wen-Yu Wen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04960},
  eprint = {2610.04960},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04960},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Polyakov backreaction in large D discretely self-similar collapse
AU  - Sheng-Hong Lai
AU  - Wen-Yu Wen
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.04960
UR  - https://arxiv.org/abs/2610.04960
AB  - We study anomaly-induced semiclassical backreaction on an analytic family of discretely self-similar solutions of Einstein--Klein--Gordon theory at large spacetime dimension. Horizon regularity fixes a null-coordinate Floquet exponent and selects a unique regular quantum state. The Polyakov auxiliary field is affine-periodic rather than periodic, with a monodromy that is determined independently by a global zero-mode condition and by the conformal-coordinate scaling. Spherical reduction introduces a quantum coupling that grows toward the center, so the periodic first-order expansion is nonuniform. We construct the resulting nonlinear inner problem and find a critical dilaton surface. Generic crossings of this surface are singular, whereas matching to the regular zero-mass exterior selects a narrow, high-curvature throat. The anomaly also separates the effective null-energy boundaries from the classical matter flux and zero-curvature curves. These results show that the minimally coupled Polyakov model does not yield a generic smooth, exactly self-similar completion of the classical center.
ER  -

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