We revisit the decoupling limits that lead to matrix theories on D-branes. We highlight the BPS nature of these limits, in which the target space geometry becomes non-Lorentzian and wrapped D-branes experience instantaneous gravitational forces. Applied to curved D-brane geometries, we show that a single BPS decoupling limit induces the bulk near-horizon limit leading to AdS/CFT. By consecutively applying two such limits, we systematically generate further examples of holography, including novel versions with non-Lorentzian bulk geometry. Uplifted to M-theory, we are led to a unified framework where each BPS decoupling limit corresponds to a Discrete Light Cone Quantisation (DLCQ). We conjecture that a DLCQn/DLCQm correspondence, with m > n, captures the notion of holography in string theory. In particular, AdS5/CFT4 can be viewed as an example of DLCQ0/DLCQ1, with the extra DLCQ on the field theory side corresponding to the near-horizon limit in the bulk geometry. We further show that undoing these BPS decoupling limits can be viewed as deformations of matrix theories. We explain how these deformations are related to the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25465_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ T\overline{T} $</EquationSource> </InlineEquation> deformation in two dimensions. In the context of holography, this allows us to view the ten-dimensional near-horizon brane geometry as an intrinsic deformation of the flat non-Lorentzian geometry that arises asymptotically. In field theoretic terms, these generalisations lead to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25465_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi>T</mi> <mover accent="true"> <mi>T</mi> <mo stretchy="true">¯</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ T\overline{T} $</EquationSource> </InlineEquation>-like flow equations for the Dp-brane DBI action.

Matrix theory reloaded: a BPS road to holography

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2025年2月5日

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Chris D. A. Blair,
Johannes Lahnsteiner,
Niels A. Obers,
Ziqi Yan

摘要

We revisit the decoupling limits that lead to matrix theories on D-branes. We highlight the BPS nature of these limits, in which the target space geometry becomes non-Lorentzian and wrapped D-branes experience instantaneous gravitational forces. Applied to curved D-brane geometries, we show that a single BPS decoupling limit induces the bulk near-horizon limit leading to AdS/CFT. By consecutively applying two such limits, we systematically generate further examples of holography, including novel versions with non-Lorentzian bulk geometry. Uplifted to M-theory, we are led to a unified framework where each BPS decoupling limit corresponds to a Discrete Light Cone Quantisation (DLCQ). We conjecture that a DLCQⁿ/DLCQ^m correspondence, with m > n, captures the notion of holography in string theory. In particular, AdS₅/CFT₄ can be viewed as an example of DLCQ⁰/DLCQ¹, with the extra DLCQ on the field theory side corresponding to the near-horizon limit in the bulk geometry. We further show that undoing these BPS decoupling limits can be viewed as deformations of matrix theories. We explain how these deformations are related to the $T \bar{T}$ $ T\overline{T} $ deformation in two dimensions. In the context of holography, this allows us to view the ten-dimensional near-horizon brane geometry as an intrinsic deformation of the flat non-Lorentzian geometry that arises asymptotically. In field theoretic terms, these generalisations lead to $T \bar{T}$ $ T\overline{T} $ -like flow equations for the Dp-brane DBI action.