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<p>We investigate several possible generalisations of <InlineEquation ID="IEq2"> <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> deformations to three- and higher-dimensional field theories. Starting from the two-dimensional <InlineEquation ID="IEq3"> <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> flow, we work out its higher-dimensional uplift, which results in a non-local and non-isotropic three-dimensional theory. Starting instead from the relation between the Nambu-Goto action and <InlineEquation ID="IEq4"> <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> in <i>d</i> = 2, we study the flow equation obeyed by the Dirac-Nambu-Goto actions in <i>d &gt;</i> 2 dimensions, written in terms of the stress-energy tensor only. Similarly, we derive the stress-tensor flow obeyed by the Born-Infeld actions in <i>d</i> dimensions and by the Dirac-Born-Infeld actions in <i>d</i> = 2 and <i>d</i> = 3.</p>

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More on \( T\overline{T} \)-like deformations in higher dimensions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月25日

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  • Nicolò Brizio,
  • Moritz Kade,
  • Alessandro Sfondrini,
  • Dmitri P. Sorokin

摘要

We investigate several possible generalisations of T T ¯ \( T\overline{T} \) deformations to three- and higher-dimensional field theories. Starting from the two-dimensional T T ¯ \( T\overline{T} \) flow, we work out its higher-dimensional uplift, which results in a non-local and non-isotropic three-dimensional theory. Starting instead from the relation between the Nambu-Goto action and T T ¯ \( T\overline{T} \) in d = 2, we study the flow equation obeyed by the Dirac-Nambu-Goto actions in d > 2 dimensions, written in terms of the stress-energy tensor only. Similarly, we derive the stress-tensor flow obeyed by the Born-Infeld actions in d dimensions and by the Dirac-Born-Infeld actions in d = 2 and d = 3.