We study the (type 0B) <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = 1 supersymmetric complex Liouville string (SℂLS), a supersymmetric extension of the bosonic complex Liouville string (ℂLS). We compute the sphere three-point amplitudes (including NS-NS-NS and NS-R-R types) and find they share the same form as the sphere three-point amplitude of the bosonic ℂLS. Analysis of the analytic structure of the NS-NS-NS-NS four-point amplitude and the higher equations of motion also yields results identical to the bosonic case. Based on these findings, we propose that the dual matrix model for the SℂLS is the same as that for the bosonic ℂLS. We also investigate a related theory <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mrow> <mi mathvariant="normal">S</mi> <mi>ℂ</mi> <mi>LS</mi> </mrow> <mo stretchy="true">̂</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $</EquationSource> </InlineEquation>, which differs in the gauged worldsheet supersymmetry. A parallel analysis is performed for <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mrow> <mi mathvariant="normal">S</mi> <mi>ℂ</mi> <mi>LS</mi> </mrow> <mo stretchy="true">̂</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $</EquationSource> </InlineEquation>, and a candidate for its dual matrix model is proposed. We then carry out a partial numerical evaluation of the moduli space integral, which provides further evidence for both the proposals of the dual matrix model regarding SℂLS and <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mrow> <mi mathvariant="normal">S</mi> <mi>ℂ</mi> <mi>LS</mi> </mrow> <mo stretchy="true">̂</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">$ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $</EquationSource> </InlineEquation>.

$ \mathcal{N} $ = 1 super complex Liouville string

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2026年7月8日

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Zhengyuan Du,
Kangning Liu,
Zhe-fei Yu

摘要

We study the (type 0B) $N$ $ \mathcal{N} $ = 1 supersymmetric complex Liouville string (SℂLS), a supersymmetric extension of the bosonic complex Liouville string (ℂLS). We compute the sphere three-point amplitudes (including NS-NS-NS and NS-R-R types) and find they share the same form as the sphere three-point amplitude of the bosonic ℂLS. Analysis of the analytic structure of the NS-NS-NS-NS four-point amplitude and the higher equations of motion also yields results identical to the bosonic case. Based on these findings, we propose that the dual matrix model for the SℂLS is the same as that for the bosonic ℂLS. We also investigate a related theory $\hat{S ℂ LS}$ $ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $ , which differs in the gauged worldsheet supersymmetry. A parallel analysis is performed for $\hat{S ℂ LS}$ $ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $ , and a candidate for its dual matrix model is proposed. We then carry out a partial numerical evaluation of the moduli space integral, which provides further evidence for both the proposals of the dual matrix model regarding SℂLS and $\hat{S ℂ LS}$ $ \hat{\mathrm{S}\mathbb{C}\mathrm{LS}} $ .

\( \mathcal{N} \) = 1 super complex Liouville string

摘要