Exploring thermal order in conformal theories with multiple scalars coupled to an O(N) vector field

Abstract

We study thermal order in conformal field theories (CFTs) in d=4−ε and d=3 dimensions where several scalars are coupled to an O(N) vector field. In (4−ε) dimensions, we consider models coupling a cubic model of M scalars with ℤ₂^Mrtimes S_M symmetry (corresponding to sign flips and permutations of the scalars) to an O(N) vector model. For any M, we find a window of N in which two Wilson-Fisher-like fixed points exist. We show that the ℤ₂^Mrtimes S_M symmetry is spontaneously broken at arbitrary nonzero temperatures for M=2 and sufficiently large N within this window, but it remains unbroken for M>2. Using the functional renormalisation group to continue these fixed points towards three dimensions, we find that they collide and move into the complex plane well before reaching d=3, suggesting that their continuation to d=3 does not yield unitary CFTs. We then work directly in three dimensions at large but finite N, with M≪ N, initially without assuming any permutation symmetry among the M scalars. By studying the RG flow, we show that these models possess a conformal manifold up to the leading nontrivial order in the 1/N expansion of the beta functions (which is 𝒪(1/N)). At each point on this manifold, the scalars split into two classes that are distinguished by how they couple to the O(N) vector field. We then restrict to a subspace of the conformal manifold where there is an additional symmetry under permutations of the scalars within each class. We prove that in a domain of this subspace, all M scalars acquire thermal expectation values such that the symmetry under sign flips of the scalars is spontaneously broken at all nonzero temperatures. This provides a novel class of large N CFTs that exhibit a rich pattern of persistent symmetry breaking at nonzero temperatures.

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BibTeX RIS

BibTeX

@misc{chaudhuri2026exploring,
  title = {{Exploring thermal order in conformal theories with multiple scalars coupled to an $O(N)$ vector field}},
  author = {Soumyadeep Chaudhuri and Bilal Hawashin and Eliezer Rabinovici and Michael M. Scherer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00160},
  eprint = {2609.00160},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00160},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Exploring thermal order in conformal theories with multiple scalars coupled to an O(N) vector field
AU  - Soumyadeep Chaudhuri
AU  - Bilal Hawashin
AU  - Eliezer Rabinovici
AU  - Michael M. Scherer
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00160
UR  - https://arxiv.org/abs/2609.00160
AB  - We study thermal order in conformal field theories (CFTs) in d=4−ε and d=3 dimensions where several scalars are coupled to an O(N) vector field. In (4−ε) dimensions, we consider models coupling a cubic model of M scalars with ℤ_2^Mrtimes S_M symmetry (corresponding to sign flips and permutations of the scalars) to an O(N) vector model. For any M, we find a window of N in which two Wilson-Fisher-like fixed points exist. We show that the ℤ_2^Mrtimes S_M symmetry is spontaneously broken at arbitrary nonzero temperatures for M=2 and sufficiently large N within this window, but it remains unbroken for M>2. Using the functional renormalisation group to continue these fixed points towards three dimensions, we find that they collide and move into the complex plane well before reaching d=3, suggesting that their continuation to d=3 does not yield unitary CFTs. We then work directly in three dimensions at large but finite N, with M≪ N, initially without assuming any permutation symmetry among the M scalars. By studying the RG flow, we show that these models possess a conformal manifold up to the leading nontrivial order in the 1/N expansion of the beta functions (which is 𝒪(1/N)). At each point on this manifold, the scalars split into two classes that are distinguished by how they couple to the O(N) vector field. We then restrict to a subspace of the conformal manifold where there is an additional symmetry under permutations of the scalars within each class. We prove that in a domain of this subspace, all M scalars acquire thermal expectation values such that the symmetry under sign flips of the scalars is spontaneously broken at all nonzero temperatures. This provides a novel class of large N CFTs that exhibit a rich pattern of persistent symmetry breaking at nonzero temperatures.
ER  -

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