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Dimensional Reduction by Conformal Bootstrap

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arxiv 1801.09052 v3 pith:KFFJP533 submitted 2018-01-27 cond-mat.dis-nn hep-thmath-phmath.MP

Shinobu Hikami This is my paper · ORCID
classification cond-mat.dis-nnhep-thmath-phmath.MP
keywords dimensionalreductionbootstrapcaseconformaldimensionsisingmodel
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abstract

The dimensional reductions in the branched polymer and the random field Ising model (RFIM) are discussed by a conformal bootstrap method. The small size minors are applied for the evaluations of the scale dimensions of these two models and the results are compared to D'=D-2 dimensional Yang-Lee edge singularity and to pure D'=D-2 dimensional Ising model, respectively. For the former case, the dimensional reduction is shown to be valid for $3 \le D \le 8$, and for the latter case, the deviation from the dimensional reduction can be seen below five dimensions.

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  1. Parisi-Sourlas Supertranslation and Scale without Conformal symmetry

    hep-th 2024-11 accept novelty 7.0 of 10

    Supertranslation symmetry protects the virial current's scaling dimension, giving eight perturbative scale-invariant but non-conformal fixed points in a quartic superfield model.

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