<p>In this work we analyze the asymptotic symmetries of the three-dimensional Chern-Simons (CS) gravity theory for a higher spin extension of the so-called Maxwell algebra. We propose a generalized set of asymptotic boundary conditions for the aforementioned flat gravity theory and we show that the corresponding charge algebra defines a higher-spin extension of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25589_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mo mathvariant="fraktur">max</mo> </math></EquationSource> <EquationSource Format="TEX">$ \mathfrak{\max}$</EquationSource> </InlineEquation>-<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25589_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="fraktur">bm</mi> <msub> <mi mathvariant="fraktur">s</mi> <mn>3</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$ \mathfrak{bm}{\mathfrak{s}}_3 $</EquationSource> </InlineEquation> algebra, which in turn corresponds the asymptotic symmetries of the Maxwell CS gravity. We also show that the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25589_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="fraktur">h</mi> <msub> <mi mathvariant="fraktur">s</mi> <mn>3</mn> </msub> <mo mathvariant="fraktur">max</mo> </math></EquationSource> <EquationSource Format="TEX">$ \mathfrak{h}{\mathfrak{s}}_3\mathfrak{\max} $</EquationSource> </InlineEquation>-<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25589_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="fraktur">bm</mi> <msub> <mi mathvariant="fraktur">s</mi> <mn>3</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$ \mathfrak{bm}{\mathfrak{s}}_3 $</EquationSource> </InlineEquation> algebra can alternatively be obtained as a vanishing cosmological constant limit of three copies of the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25589_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi mathvariant="script">W</mi> <mn>3</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$ {\mathcal{W}}_3 $</EquationSource> </InlineEquation> algebra, with three independent central charges.</p>

Asymptotic structure of three-dimensional Maxwell Chern-Simons gravity coupled to spin-3 fields

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2025年2月21日

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Patrick Concha,
Javier Matulich,
Daniel Pino,
Evelyn Rodríguez

摘要

In this work we analyze the asymptotic symmetries of the three-dimensional Chern-Simons (CS) gravity theory for a higher spin extension of the so-called Maxwell algebra. We propose a generalized set of asymptotic boundary conditions for the aforementioned flat gravity theory and we show that the corresponding charge algebra defines a higher-spin extension of the $max$ $ \mathfrak{\max}$ - $bm s_{3}$ $ \mathfrak{bm}{\mathfrak{s}}_3 $ algebra, which in turn corresponds the asymptotic symmetries of the Maxwell CS gravity. We also show that the $h s_{3} max$ $ \mathfrak{h}{\mathfrak{s}}_3\mathfrak{\max} $ - $bm s_{3}$ $ \mathfrak{bm}{\mathfrak{s}}_3 $ algebra can alternatively be obtained as a vanishing cosmological constant limit of three copies of the $W_{3}$ $ {\mathcal{W}}_3 $ algebra, with three independent central charges.