Non-relativistic supersymmetry on curved three-manifolds

Abstract

We construct explicit examples of non-relativistic supersymmetric field theories on curved Newton-Cartan three-manifolds. These results are obtained by performing a null reduction of four-dimensional supersymmetric field theories on Lorentzian manifolds and the Killing spinor equations that their supersymmetry parameters obey. This gives rise to a set of algebraic and differential Killing spinor equations that are obeyed by the supersymmetry parameters of the resulting three-dimensional non-relativistic field theories. We derive necessary and sufficient conditions that determine whether a Newton-Cartan background admits non-trivial solutions of these Killing spinor equations. Two classes of examples of Newton-Cartan backgrounds that obey these conditions are discussed. The first class is characterised by an integrable foliation, corresponding to so-called twistless torsional geometries, and includes manifolds whose spatial slices are isomorphic to the Poincaré disc. The second class of examples has a non-integrable foliation structure and corresponds to contact manifolds.

Null reductions of the M5-brane

“…In contrast, the field theories we obtain do not have higher derivatives but involve Lagrange multiplier constraints that reduce the dynamics to motion on a moduli space of anti-selfdual gauge fields [9,10], in line with the DLCQ description of the M5-brane [11,12]. Other classes of theories without Lorentz invariance but related to String/M-Theory have recently received attention in works such as [13][14][15][16][17][18].…”

Non-Lorentzian avatars of (1,0) theories

“…Let us start with the 32 × 32 Γ-matrices of Spin (1,10). In this appendix we use a hat to denote elements associated to Spin (1,10) and M = 0, 1, 2, . .…”

“…There is a growing interest in non-Lorentzian field theories from a variety of view points and applications, for some recent studies see [8][9][10][11][12][13][14][15][16]. Our own interest stems from a novel form of conformal compactification, which appears to be able to reproduce aspects of the original non-compact six-dimensional SCFT from a five-dimensional Lagrangian theory with a Kaluza-Klein-like tower [17][18][19].…”

Non-Lorentzian Avatars of (1,0) Theories

“…There is a growing interest in non-Lorentzian field theories from a variety of view points and applications, for some recent studies see [8,9,10,11,12,13,14,15,16]. Our own interest stems from a novel form of conformal compactification, which appears to be able to reproduce aspects of the original non-compact six-dimensional SCFT from a fivedimensional Lagrangian theory with a Kaluza-Klein-like tower [17,18,19].…”