Preservation of epsilon-minus supersymmetry under renormalizing deformations

Determine whether any marginal deformation of three-dimensional supersymmetric Galilean Yang–Mills that is compatible with renormalizability and the intended gravitational dual preserves the epsilon-minus supersymmetry.

Background

The proposed deformations needed to address the one-loop divergences may modify the supersymmetry algebra and are expected, from the associated non-relativistic D2-brane and M2-brane solutions, potentially to break part of the original supersymmetry.

The paper specifically leaves unresolved whether a suitable deformation can preserve the epsilon-minus supercharges, noting that the relevant backreacting M2-brane solution preserves only eight Killing spinors.

References

A related question is whether any deformation also preserves the $\epsilon_-$-supersymmetry. In it was shown that the backreacting M2-brane solution eq: m2-brane solution of eleven-dimensional supergravity's M2-brane limit only preserves 8 Killing spinors; as the D2-brane solution eq: NH NL D2 Solution of type IIA supergravity's non-relativistic string limit is obtained from this via reduction on a circle, one would imagine its supersymmetry structure is the same. One may therefore imagine that the deformation of the QFT required to relate the theory to the non-Lorentzian gravitational dual solution must break the $\epsilon_-$-supersymmetry. More work should be done on both sides of this problem to investigate this further.

— Quantum Effects in Supersymmetric Galilean Yang-Mills  (2608.18843 - Lambert et al., 19 Aug 2026) in Section 6, “Conclusion and Outlook”