Superfield Formulation for Non-Relativistic Chern–Simons-Matter Theory

We construct a non-relativistic limit of ten-dimensional $$ \mathcal{N} $$ N = 1 supergravity from the point of view of the symmetries, the action, and the equations of motion. This limit can only be realized in a supersymmetric way provided we impose by hand a set of geometric constraints, invariant under all the symmetries of the non-relativistic theory, that define a so-called ‘self-dual’ Dilatation-invariant String Newton-Cartan geometry. The non-relativistic action exhibits three emerging symmetries: one local scale symmetry and two local conformal supersymmetries. Due to these emerging symmetries the Poisson equation for the Newton potential and two partner fermionic equations do not follow from a variation of the non-relativistic action but, instead, are obtained by a supersymmetry variation of the other equations of motion that do follow from a variation of the non-relativistic action. We shortly discuss the inclusion of the Yang-Mills sector that would lead to a non-relativistic heterotic supergravity action.

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“…For earlier discussions of such a non-relativistic superspace and superfields in lower dimensions, see e.g. [28][29][30][31][32].…”

Section: Discussionmentioning

confidence: 99%

Non-relativistic ten-dimensional minimal supergravity

Bergshoeff

Lahnsteiner

Romanò

et al. 2021

J. High Energ. Phys.

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“…Having in mind to apply the same techniques to non-relativistic SUSY systems, we first construct the N = 2 non-relativistic superspace by applying null reduction to the four-dimensional one. The non-relativistic superspace was first introduced in four dimensions [22,23], whereas previous constructions in three dimensions based on different techniques can be found in [26,34]. We start with the relativistic N = 1 superspace in (3+1) described by superspace coordinates (x µ , θ α ,θα).…”

Section: Non-relativistic Superspacementioning

confidence: 99%

Renormalization properties of a Galilean Wess-Zumino model

Auzzi

Baiguera

Nardelli

et al. 2019

J. High Energ. Phys.

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We consider a Galilean N = 2 supersymmetric theory with F-term couplings in 2 + 1 dimensions, obtained by null reduction of a relativistic Wess-Zumino model. We compute quantum corrections and we check that, as for the relativistic parent theory, the F-term does not receive quantum corrections. Even more, we find evidence that the causal structure of the non-relativistic dynamics together with particle number conservation constrain the theory to be one-loop exact. arXiv:1904.08404v2 [hep-th]

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“…The non-relativistic ABJM theory with fourteen supercharges was first derived in [12] by taking non-relativistic limit of the mass deformed ABJM theory 1 (see also [13]). Subsequently, a superfield formulation with manifest dynamical supersymmetry (SUSY) was developed in [14].…”

Section: Non-relativistic Abjm Theorymentioning

confidence: 99%

Observables and correlators in non-relativistic ABJM theory

Nakayama

Rey

2009

J. High Energy Phys.

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Non-relativistic ABJM theory is defined by Galilean limit of mass-deformed N = 6 Chern-Simons theory. Holographic string theory dual to the theory is not known yet. To understand features candidate gravity dual might exhibit, we examine local and nonlocal physical observables and their correlations in the non-relativistic ABJM theory. We show that gauge invariant local observables correspond to zero-norm states and that correlation functions among them are trivial. We also show that a particular class of nonlocal observables, Wilson loops, are topological in the sense that their correlation functions coincide with those of pure Chern-Simons theory. We argue that the theory is nevertheless physical and illustrate several physical observables whose correlation functions are nontrivial. We also study quantum aspects. We show that Chern-Simons level is finitely renormalized and that dilatation operator is trivial at planar limit.These results all point to string scale geometry of gravity dual and to intriguing topological and tensionless nature of dual string or M theory defined on it.

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Superfield Formulation for Non-Relativistic Chern–Simons-Matter Theory

Cited by 9 publications

References 32 publications

Non-relativistic ten-dimensional minimal supergravity

Non-relativistic ten-dimensional minimal supergravity

Renormalization properties of a Galilean Wess-Zumino model

Observables and correlators in non-relativistic ABJM theory

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