<p>We present a holographic set up that computes timelike Entanglement Entropy (tEE) in (0 + 1)d QFTs preserving some amount of SUSY. The first example we consider is that of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26319_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 2 matrix models with massive deformations. These are dual to non-Abelian T-dual of <i>AdS</i><sub>5</sub> × <i>S</i><sup>5</sup> that asymptotes to <i>smeared</i> D0 branes. The second example, that we consider is of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26319_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 4 superconformal quantum mechanical quivers in (0 + 1)d that are dual to a class of type IIB backgrounds with an <i>AdS</i><sub>2</sub> factor. In both of these examples, tEE reveals a remarkable similarity with holographic <i>c</i> function pertaining to a RG flow. We further compute the complexity in these models, which also reveals an identical behaviour indicating the fact that tEE is a measure of number of degrees of freedom for these (0 + 1)d SQFTs in a RG flow from UV to deep IR.</p>

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Holographic timelike entanglement and c theorem for supersymmetric QFTs in (0 + 1)d

  • Dibakar Roychowdhury

摘要

We present a holographic set up that computes timelike Entanglement Entropy (tEE) in (0 + 1)d QFTs preserving some amount of SUSY. The first example we consider is that of N \( \mathcal{N} \) = 2 matrix models with massive deformations. These are dual to non-Abelian T-dual of AdS5 × S5 that asymptotes to smeared D0 branes. The second example, that we consider is of N \( \mathcal{N} \) = 4 superconformal quantum mechanical quivers in (0 + 1)d that are dual to a class of type IIB backgrounds with an AdS2 factor. In both of these examples, tEE reveals a remarkable similarity with holographic c function pertaining to a RG flow. We further compute the complexity in these models, which also reveals an identical behaviour indicating the fact that tEE is a measure of number of degrees of freedom for these (0 + 1)d SQFTs in a RG flow from UV to deep IR.