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<p>We consider a composite defect system where a lower-dimensional defect (sub-defect) is embedded to a higher-dimensional one, and examine renormalization group (RG) flows localized on the defect. A composite defect is constructed in the (3 − <i>ϵ</i>)-dimensional free O(<i>N</i>) vector model with line and surface interactions by triggering localized RG flows to non-trivial IR fixed points. Focusing on the case where the symmetry group O(<i>N</i>) is broken to a subgroup O(<i>m</i>) × O(<i>N</i> − <i>m</i>) on the line defect, there is an O(<i>N</i>) symmetric fixed point for all <i>N</i>, while two additional O(<i>N</i>) symmetry breaking ones appear for <i>N</i> ≥ 23. We also examine a <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25453_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">C</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{C} \)</EquationSource> </InlineEquation>-theorem for localized RG flows along the sub-defect and show that the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25453_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">C</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{C} \)</EquationSource> </InlineEquation>-theorem holds in our model by perturbative calculations.</p>

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Localized RG flows on composite defects and \( \mathcal{C} \)-theorem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月4日

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  • Dongsheng Ge,
  • Tatsuma Nishioka,
  • Soichiro Shimamori

摘要

We consider a composite defect system where a lower-dimensional defect (sub-defect) is embedded to a higher-dimensional one, and examine renormalization group (RG) flows localized on the defect. A composite defect is constructed in the (3 − ϵ)-dimensional free O(N) vector model with line and surface interactions by triggering localized RG flows to non-trivial IR fixed points. Focusing on the case where the symmetry group O(N) is broken to a subgroup O(m) × O(N − m) on the line defect, there is an O(N) symmetric fixed point for all N, while two additional O(N) symmetry breaking ones appear for N ≥ 23. We also examine a C \( \mathcal{C} \) -theorem for localized RG flows along the sub-defect and show that the C \( \mathcal{C} \) -theorem holds in our model by perturbative calculations.