A geometric approach to scalar field theories on the supersphere

Schunck, A. F.; Wainwright, Chris

doi:10.1063/1.1850363

Cited by 13 publications

(32 citation statements)

References 15 publications

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“…In globally curved space an example of the use of graded Majorana spinors is obtained by considering field theories on the supersphere S 2|2 = UOSp(1|2)/U(1), as investigated in [11]. Graded Majorana spinors could also play an important role in the construction of supergravity theories.…”

Section: Discussionmentioning

confidence: 99%

Graded Majorana spinors

Kleppe¹,

Wainwright²

2006

J. Phys. A: Math. Gen.

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In many mathematical and physical contexts spinors are treated as Grassmann odd valued fields. We show that it is possible to extend the classification of reality conditions on such spinors by a new type of Majorana condition. In order to define this graded Majorana condition we make use of pseudo-conjugation, a rather unfamiliar extension of complex conjugation to supernumbers. Like the symplectic Majorana condition, the graded Majorana condition may be imposed, for example, in spacetimes in which the standard Majorana condition is inconsistent. However, in contrast to the symplectic condition, which requires duplicating the number of spinor fields, the graded condition can be imposed on a single Dirac spinor. We illustrate how graded Majorana spinors can be applied to supersymmetry by constructing a globally supersymmetric field theory in three-dimensional Euclidean space, an example of a spacetime where standard Majorana spinors do not exist.

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Section: Discussionmentioning

confidence: 99%

Graded Majorana spinors

Kleppe¹,

Wainwright²

2006

J. Phys. A: Math. Gen.

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“…6 It is reported that in scalar field theories on supersphere effective potentials are not generally bounded below, so the groundstates are not stable [20]. However, such problem cannot be applied to SUSY QHE, since the pseudo-potential Hamiltonian (3.15) has the lowest eigenvalue and the energies are bounded.…”

Section: The Spherical Susy Laughlin Wavefunction and Excitations [35]mentioning

confidence: 99%

“…Algebraic and topological structures of the fuzzy supersphere are well examined in [17,18]. Field theory models on supersphere have already been proposed; a non-linear sigma model and a scalar field model were explored in [19] and [20], respectively. Numerical calculations on fuzzy spaces have also been carried out (see [21] as a review).…”

Section: Introductionmentioning

confidence: 99%

SUSY Quantum Hall Effect on Non-Anti-Commutative Geometry

Hasebe¹

2008

SIGMA

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Abstract. We review the recent developments of the SUSY quantum Hall effect [hep-th/0409230, hep-th/0411137, hep-th/0503162, hep-th/0606007, arXiv:0705.4527]. We introduce a SUSY formulation of the quantum Hall effect on supermanifolds. On each of supersphere and superplane, we investigate SUSY Landau problem and explicitly construct SUSY extensions of Laughlin wavefunction and topological excitations. The non-anticommutative geometry naturally emerges in the lowest Landau level and brings particular physics to the SUSY quantum Hall effect. It is shown that SUSY provides a unified picture of the original Laughlin and Moore-Read states. Based on the charge-flux duality, we also develop a Chern-Simons effective field theory for the SUSY quantum Hall effect.

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“…This generalization is obtained in the course of developing a homological theory for supermanifolds. There are different supergeometric generalizations of the two-sphere S 2 , all of which are called superspheres [1][2][3]. These are useful models to study supersymmetry.…”

Section: Introductionmentioning

confidence: 99%