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<p>This note introduces a novel paradigm for conformal defects with continuously adjustable dimensions. Just as the standard <i>ε</i> expansion interpolates between integer spacetime dimensions, a new parameter, <i>δ</i>, is used to interpolate between different integer-dimensional defects. This framework is explored in detail for defects of dimension <i>p</i> = 2 + <i>δ</i> in both free and interacting <i>O</i>(<i>N</i>) bulk conformal field theories (CFTs) in <i>d</i> = 4 – <i>ε</i>. Comprehensive calculations are performed to first and second order in <i>ε</i> and to high or all orders in <i>δ</i>. Additionally, in the large-<i>N</i> limit, the interpolation between defects of dimensions <i>p</i> = 1 and <i>p</i> = 2 is analysed for spacetime dimensions 4 ⩽ <i>d</i> ⩽ 6. The new parameter <i>δ</i> provides a natural enrichment of the space of defect CFTs and allows to find new integer dimension or co-dimension defects.</p>

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Transdimensional defects

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年8月25日

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  • Elia de Sabbata,
  • Nadav Drukker,
  • Andreas Stergiou

摘要

This note introduces a novel paradigm for conformal defects with continuously adjustable dimensions. Just as the standard ε expansion interpolates between integer spacetime dimensions, a new parameter, δ, is used to interpolate between different integer-dimensional defects. This framework is explored in detail for defects of dimension p = 2 + δ in both free and interacting O(N) bulk conformal field theories (CFTs) in d = 4 – ε. Comprehensive calculations are performed to first and second order in ε and to high or all orders in δ. Additionally, in the large-N limit, the interpolation between defects of dimensions p = 1 and p = 2 is analysed for spacetime dimensions 4 ⩽ d ⩽ 6. The new parameter δ provides a natural enrichment of the space of defect CFTs and allows to find new integer dimension or co-dimension defects.