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<p>We consider the supersymmetric Wess-Zumino model at large <i>N</i> in (2 + 1) dimension. We introduce a chemical potential(<i>μ</i>) at finite temperature(<i>T</i>). The non-trivial fixed point of this model is described by a pair of coupled gap equations. This fixed point behaves as a thermal CFT for all values of the coupling. We find that at large chemical potential these coupled equations simplify and solutions become analytically tractable. We solve them analytically for all values of the coupling at this limit. The solutions admit a systematic series expansion in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27007_Article_IEq1.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mi>T</mi> <mi>μ</mi> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( \frac{T}{\mu } \)</EquationSource> </InlineEquation>. Thus, using the solutions of the gap equation at large chemical potential we can evaluate the analytic form of the partition function, stress tensor and spin-1 current as a perturbative expansion in orders of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27007_Article_IEq1.gif" Format="GIF" Height="25" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mfrac> <mi>T</mi> <mi>μ</mi> </mfrac> </math></EquationSource> <EquationSource Format="TEX">\( \frac{T}{\mu } \)</EquationSource> </InlineEquation>. Applying the OPE inversion formula on the scalar and fermion two point functions of the theory, we compute higher spin currents at large <i>μ</i>.</p>

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Large N Wess-Zumino model at finite temperature and large chemical potential in 3d

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  • 发表日期：

    2025年8月19日

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  • Srijan Kumar

摘要

We consider the supersymmetric Wess-Zumino model at large N in (2 + 1) dimension. We introduce a chemical potential(μ) at finite temperature(T). The non-trivial fixed point of this model is described by a pair of coupled gap equations. This fixed point behaves as a thermal CFT for all values of the coupling. We find that at large chemical potential these coupled equations simplify and solutions become analytically tractable. We solve them analytically for all values of the coupling at this limit. The solutions admit a systematic series expansion in T μ \( \frac{T}{\mu } \) . Thus, using the solutions of the gap equation at large chemical potential we can evaluate the analytic form of the partition function, stress tensor and spin-1 current as a perturbative expansion in orders of T μ \( \frac{T}{\mu } \) . Applying the OPE inversion formula on the scalar and fermion two point functions of the theory, we compute higher spin currents at large μ.