Supersymmetric soliton \(\sigma\)-models from non-Lorentzian field theories

DOI10.1007/JHEP04(2020)129zbMATH Open1436.81139arXiv1911.11504MaRDI QIDQ780807

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Publication date: 15 July 2020

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Abstract: Recently, a class of non-Lorentzian supersymmetric Lagrangian field theories was considered, in some cases describing M-theory brane configurations, but more generally found as fixed points of non-Lorentzian RG flows induced upon Lorentzian theories. In this paper, we demonstrate how the dynamics of such theories can be reduced to motion on the supersymmetric moduli space of BPS solitons of the parent theory. We focus first on the $mathcalN=(1,1)$ $sigma$-model in $(1+1)$-dimensions with potential, where we produce a supersymmetric extension to the standard geodesic approximation for slow kink motion. We then revisit the $(4+1)$-dimensional Yang-Mills-like theory with 24 supercharges describing a null compactification of M5-branes. We show that the theory reduces to a $sigma$-model on instanton moduli space, extended by couplings to additional fields from the parent theory, and possessing (8+8) super(conformal) symmetries along with 8 further fermionic shift symmetries. We derive this model explicitly for the single $SU(2)$ instanton.

Full work available at URL: https://arxiv.org/abs/1911.11504

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