Abstract
In the \( \mathcal{N} \) = 1 supersymmetric coset minimal model based on \( \left( {B_N^{(1)}\oplus D_N^{(1) },\ D_N^{(1) }} \right) \) at level (k, 1) studied recently, the standard \( \mathcal{N} \) = 1 super stress tensor of spins \( \left( {\frac{3}{2},2} \right) \) is reviewed. By considering the stress tensor in the coset \( \left( {B_N^{(1) },\ D_N^{(1) }} \right) \) at level k, the higher spin-2′ Casimir current was obtained previously. By acting the above spin- \( \frac{2}{3} \) current on the higher spin-2′ Casimir current, its superpartner, the higher spin- \( \frac{5}{2} \) current, can be generated and combined as the first higher spin supercurrent with spins \( \left( {{2^{\prime }},\frac{5}{2}} \right) \). By calculating the operator product expansions (OPE) between the higher spin supercurrent and itself, the next higher spin supercurrent can be generated with spins \( \left( {\frac{7}{2},4} \right) \). Moreover, the other higher spin supercurrent with spins \( \left( {{4^{\prime }},\frac{9}{2}} \right) \) can be generated by calculating the OPE between the first higher spin supercurrent with spins \( \left( {{2^{\prime }},\frac{5}{2}} \right) \) and the second higher spin supercurrent with spins \( \left( {\frac{7}{2},\ 4} \right) \). Finally, the higher spin supercurrent, \( \left( {\frac{11 }{2},6} \right) \), can be extracted from the right hand side of OPE between the higher spin supercurrents, \( \left( {{2^{\prime }},\frac{5}{2}} \right) \) and \( \left( {{4^{\prime }},\frac{9}{2}} \right) \).
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Ahn, C., Paeng, J. Higher spin currents in the holographic \( \mathcal{N} \) = 1 coset minimal model. J. High Energ. Phys. 2014, 7 (2014). https://doi.org/10.1007/JHEP01(2014)007
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DOI: https://doi.org/10.1007/JHEP01(2014)007