<p>Effective string theory describes the physics of long confining strings in theories, like Yang-Mills theory, where the mass gap <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25799_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>M</mi> <mi>gap</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {M}_{\textrm{gap}}^2 \)</EquationSource> </InlineEquation> is of the same order as the string tension <i>T</i>. In 2 + 1 dimensions, there is a class of confining theories, including massive QED<sub>3</sub> as first analyzed by Polyakov, for which <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25799_Article_IEq2.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>M</mi> <mi>gap</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {M}_{\textrm{gap}}^2 \)</EquationSource> </InlineEquation> ≪ <i>T</i>. These theories are weakly coupled at low energies of order <i>M</i><sub>gap</sub>, and may be analyzed perturbatively. In this paper, we analyze the physics of strings in such theories, focusing on QED<sub>3</sub>, at energies of order <i>M</i><sub>gap</sub> (but still well below <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25799_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msqrt> <mi>T</mi> </msqrt> </math></EquationSource> <EquationSource Format="TEX">\( \sqrt{T} \)</EquationSource> </InlineEquation>). We argue that the width of the string in these theories should be of order 1/<i>M</i><sub>gap</sub> independently of its length, as long as the string is not exponentially long. We also compute at leading order in perturbation theory the ground state energy of a confining string on a circle, and the scattering of Nambu-Goldstone bosons on the string worldsheet.</p>

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Effective strings in QED3

  • Ofer Aharony,
  • Netanel Barel,
  • Tal Sheaffer

摘要

Effective string theory describes the physics of long confining strings in theories, like Yang-Mills theory, where the mass gap M gap 2 \( {M}_{\textrm{gap}}^2 \) is of the same order as the string tension T. In 2 + 1 dimensions, there is a class of confining theories, including massive QED3 as first analyzed by Polyakov, for which M gap 2 \( {M}_{\textrm{gap}}^2 \) T. These theories are weakly coupled at low energies of order Mgap, and may be analyzed perturbatively. In this paper, we analyze the physics of strings in such theories, focusing on QED3, at energies of order Mgap (but still well below T \( \sqrt{T} \) ). We argue that the width of the string in these theories should be of order 1/Mgap independently of its length, as long as the string is not exponentially long. We also compute at leading order in perturbation theory the ground state energy of a confining string on a circle, and the scattering of Nambu-Goldstone bosons on the string worldsheet.