Non-Relativistic Supersymmetry on Curved Three-Manifolds
arXiv:2005.09001 · doi:10.1007/JHEP07(2020)175
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.
arXiv comment43 pages
References in corpus (50)
- Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
- Gravity Duals of Lifshitz-like Fixed Points
- Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- Gravity duals for non-relativistic CFTs
- Rigid Supersymmetric Theories in Curved Superspace
- General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
- Localization techniques in quantum field theories
- Hall Viscosity and Electromagnetic Response
- Non-Relativistic Closed String Theory
- Torsional Newton-Cartan Geometry and Lifshitz Holography
- Supersymmetric Field Theories on Three-Manifolds
- Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
- Lifshitz holography
- Supersymmetry on Curved Spaces and Holography
- Spacetime Symmetries of the Quantum Hall Effect
- Exploring Curved Superspace
- `Stringy' Newton-Cartan Gravity
- Null Killing Vector Dimensional Reduction and Galilean Geometrodynamics
- Thermal Hall Effect and Geometry with Torsion
- Nonrelativistic String Theory and T-Duality
- String Theory and String Newton-Cartan Geometry
- Newton-Cartan Supergravity
- Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
- Supersymmetry in Lorentzian Curved Spaces and Holography
- Boundary effective action for quantum Hall states
- On the supersymmetries of anti de Sitter vacua
- Newton-Cartan (super)gravity as a non-relativistic limit
- Fields and fluids on curved non-relativistic spacetimes
- Exploring Curved Superspace (II)
- Newton-Cartan Gravity and Torsion
- Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity
- On the effective hydrodynamics of FQHE
- Anomalies for Galilean fields
- Non-Relativistic Scale Anomalies
- Homogeneous Nonrelativistic Geometries as Coset Spaces
- On the Heat Kernel and Weyl Anomaly of Schrödinger invariant theory
- Killing superalgebras for Lorentzian four-manifolds
- Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory
- On Supersymmetric Lifshitz Field Theories
- On Newton-Cartan local renormalization group and anomalies
- Renormalization properties of a Galilean Wess-Zumino model
- Heat kernel for Newton-Cartan trace anomalies
- Bosonic Symmetries of DLCQ Field Theories
- Spencer cohomology and eleven-dimensional supergravity
- Non-Lorentzian Field Theories with Maximal Supersymmetry and Moduli Space Dynamics
- Holomorphic Structure and Quantum Critical Points in Supersymmetric Lifshitz Field Theories
- Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity
- Killing superalgebras for Lorentzian six-manifolds
- Covariant effective action for a Galilean invariant quantum Hall system
Cited by in corpus (6)
- Aspects of Non-Relativistic Quantum Field Theories
- The Supersymmetric Neveu-Schwarz Branes of Non-Relativistic String Theory
- Null Reductions of M5-Branes
- Non-Lorentzian Avatars of (1,0) Theories
- Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
- Kaluza-Klein reductions of maximally supersymmetric five-dimensional lorentzian spacetimes