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PreprintCC BY 4.0arXiv

Critical Lin-Lunin-Maldacena geometries

  • Prokopii Anempodistov
  • Vladimir Kazakov
  • Lev Senchukov
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Abstract

We study the critical behavior of the Lin-Lunin-Maldacena (LLM) geometry in the case when a droplet in the LLM base space develops a cusp. This cusp is a generic feature of the density of complex eigenvalues in the dual complex matrix model (CMM) computing the correlation functions of huge 1/2-BPS operators in 𝒩=4 SYM theory. It is also related to the criticality in CMM describing the pure 2D quantum gravity behavior. The supergravity dual -- LLM metric in the vicinity of the tip of the cusp -- acquires a universal ISO(1,3)× SO(5) symmetric form, with a naked singularity along a half-infinite line. Both massless and massive particles get trapped by this line singularity for almost any impact parameter. Generic trajectories ending on the singular line reach it in finite affine time, while the corresponding observer time diverges. An explicit analytic solution for a large class of massless trajectories together with the absence of stochastic behavior in the vicinity of the cusp hint on a certain integrability of the problem.

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Cite

BibTeXRIS
BibTeX
@misc{anempodistov2026critical,
  title = {{Critical Lin-Lunin-Maldacena geometries}},
  author = {Prokopii Anempodistov and Vladimir Kazakov and Lev Senchukov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.31424},
  eprint = {2606.31424},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.31424},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Critical Lin-Lunin-Maldacena geometries
AU  - Prokopii Anempodistov
AU  - Vladimir Kazakov
AU  - Lev Senchukov
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2606.31424
UR  - https://arxiv.org/abs/2606.31424
AB  - We study the critical behavior of the Lin-Lunin-Maldacena (LLM) geometry in the case when a droplet in the LLM base space develops a cusp. This cusp is a generic feature of the density of complex eigenvalues in the dual complex matrix model (CMM) computing the correlation functions of huge 1/2-BPS operators in 𝒩=4 SYM theory. It is also related to the criticality in CMM describing the pure 2D quantum gravity behavior. The supergravity dual -- LLM metric in the vicinity of the tip of the cusp -- acquires a universal ISO(1,3)× SO(5) symmetric form, with a naked singularity along a half-infinite line. Both massless and massive particles get trapped by this line singularity for almost any impact parameter. Generic trajectories ending on the singular line reach it in finite affine time, while the corresponding observer time diverges. An explicit analytic solution for a large class of massless trajectories together with the absence of stochastic behavior in the vicinity of the cusp hint on a certain integrability of the problem.
ER  -