<p>Over the past quarter century, considerable effort has been invested in the study of nonrelativistic (NR) string theory, its U-dual NR brane theories, and their geometric foundations in (generalized) Newton-Cartan geometry. Many interesting results have been obtained, both for their intrinsic value and in the hope that they hold useful lessons for relativistic string/M theory. By synthesizing two strands of recent developments (especially, arXiv:2312.13243 and arXiv:2410.03591), we argue that this hope has already come to fruition, because standard, <i>relativistic</i> holography can now be recognized as a statement within a corresponding <i>nonrelativistic</i> brane theory. Our main conclusions are general, but in the familiar example of D3-brane based holography, they read as follows: (i) <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26998_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 SYM is exactly the worldvolume theory of D3-branes within ‘NR D3-brane theory’; (ii) AdS<sub>5</sub> × S<sup>5</sup> is exactly the corresponding RR black 3-brane, and includes an asymptotically flat-Newton- Cartan region; (iii) AdS/CFT duality is precisely synonymous with black-brane/D-brane (i.e., closed-string/open-string) duality within NR D3-brane theory; (iv) Newton-Cartan geometry is the underlying structure upon which entanglement of the D3-brane degrees of freedom builds relativistic spacetime.</p>

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On the underlying nonrelativistic nature of relativistic holography

  • Alberto Güijosa

摘要

Over the past quarter century, considerable effort has been invested in the study of nonrelativistic (NR) string theory, its U-dual NR brane theories, and their geometric foundations in (generalized) Newton-Cartan geometry. Many interesting results have been obtained, both for their intrinsic value and in the hope that they hold useful lessons for relativistic string/M theory. By synthesizing two strands of recent developments (especially, arXiv:2312.13243 and arXiv:2410.03591), we argue that this hope has already come to fruition, because standard, relativistic holography can now be recognized as a statement within a corresponding nonrelativistic brane theory. Our main conclusions are general, but in the familiar example of D3-brane based holography, they read as follows: (i) N \( \mathcal{N} \) = 4 SYM is exactly the worldvolume theory of D3-branes within ‘NR D3-brane theory’; (ii) AdS5 × S5 is exactly the corresponding RR black 3-brane, and includes an asymptotically flat-Newton- Cartan region; (iii) AdS/CFT duality is precisely synonymous with black-brane/D-brane (i.e., closed-string/open-string) duality within NR D3-brane theory; (iv) Newton-Cartan geometry is the underlying structure upon which entanglement of the D3-brane degrees of freedom builds relativistic spacetime.