<p>We discuss how to obtain the symmetric orbifold fusion rule/OPE from the dual string theory. We consider two explicit examples: <i>k</i><sub><i>b</i></sub> = 3 bosonic strings in AdS<sub>3</sub> × <i>X</i> in the near-boundary limit and <i>k</i> = 1 hybrid strings in AdS<sub>3</sub> × S<sup>3</sup> × <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27018_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi mathvariant="double-struck">T</mi> <mn>4</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">\( {\mathbbm{T}}^4 \)</EquationSource> </InlineEquation>. The main advantage of these two examples is that they have explicit expressions for the vertex operators in the <i>x</i>-basis. We show that the OPE of such vertex operators explicitly captures the longest cycle contribution in the symmetric orbifold fusion rule/OPE. We then argue how one can obtain the shorter-cycle contributions using the screening operators existing in the theories. We also discuss how our general result reduces to the earlier results in the literature.</p>

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Symmetric orbifold OPE from string theory

  • Vit Sriprachyakul

摘要

We discuss how to obtain the symmetric orbifold fusion rule/OPE from the dual string theory. We consider two explicit examples: kb = 3 bosonic strings in AdS3 × X in the near-boundary limit and k = 1 hybrid strings in AdS3 × S3 × T 4 \( {\mathbbm{T}}^4 \) . The main advantage of these two examples is that they have explicit expressions for the vertex operators in the x-basis. We show that the OPE of such vertex operators explicitly captures the longest cycle contribution in the symmetric orbifold fusion rule/OPE. We then argue how one can obtain the shorter-cycle contributions using the screening operators existing in the theories. We also discuss how our general result reduces to the earlier results in the literature.