<p>It has been suggested that a <i>dS</i><sub><i>d</i>+1</sub> spacetime of radius <i>R</i><sub><i>ds</i></sub> has a holographic dual, living at future space-like infinity <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26243_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">I</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{I} \)</EquationSource> </InlineEquation><sup>+</sup>, with the bulk wave function being dual to the partition function of the boundary theory, [<CitationRef CitationID="CR1">1</CitationRef>]. We consider some aspects of this correspondence. For under damped scalars with mass <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26243_Article_IEq2.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi>M</mi> <mn>2</mn> </msup> <msubsup> <mi>R</mi> <mi mathvariant="italic">ds</mi> <mn>2</mn> </msubsup> <mo>&gt;</mo> <mfrac> <msup> <mi>d</mi> <mn>2</mn> </msup> <mn>4</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( {M}^2{R}_{ds}^2&gt;\frac{d^2}{4} \)</EquationSource> </InlineEquation>, belonging to the principal series, we show that for the Bunch Davies vacuum a suitable source in the boundary theory can be identified in terms of the coherent state representation of the wave function. We argue that terms in the resulting correlation functions, which are independent of the late time cut-off, satisfy the Ward identities of a conformal field theory. We also discuss other ways to identify sources, both in the under damped and the over damped case, where <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26243_Article_IEq3.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msup> <mi>M</mi> <mn>2</mn> </msup> <msubsup> <mi>R</mi> <mi mathvariant="italic">ds</mi> <mn>2</mn> </msubsup> <mo>&lt;</mo> <mfrac> <msup> <mi>d</mi> <mn>2</mn> </msup> <mn>4</mn> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( {M}^2{R}_{ds}^2&lt;\frac{d^2}{4} \)</EquationSource> </InlineEquation>, and argue that these too can lead to correlators satisfying the Ward identities of a CFT. Some comments on the violation of reflection positivity, and the cut-off dependent terms, along with some explicit checks and sample calculations, are also included.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Aspects of dS/CFT holography

  • Indranil Dey,
  • Kanhu Kishore Nanda,
  • Akashdeep Roy,
  • Sandip P. Trivedi

摘要

It has been suggested that a dSd+1 spacetime of radius Rds has a holographic dual, living at future space-like infinity I \( \mathcal{I} \) +, with the bulk wave function being dual to the partition function of the boundary theory, [1]. We consider some aspects of this correspondence. For under damped scalars with mass M 2 R ds 2 > d 2 4 \( {M}^2{R}_{ds}^2>\frac{d^2}{4} \) , belonging to the principal series, we show that for the Bunch Davies vacuum a suitable source in the boundary theory can be identified in terms of the coherent state representation of the wave function. We argue that terms in the resulting correlation functions, which are independent of the late time cut-off, satisfy the Ward identities of a conformal field theory. We also discuss other ways to identify sources, both in the under damped and the over damped case, where M 2 R ds 2 < d 2 4 \( {M}^2{R}_{ds}^2<\frac{d^2}{4} \) , and argue that these too can lead to correlators satisfying the Ward identities of a CFT. Some comments on the violation of reflection positivity, and the cut-off dependent terms, along with some explicit checks and sample calculations, are also included.