Symmetries and conservation laws of a nonlinear sigma model with gravitino

Jost, Jürgen; Keßler, Enno; Tolksdorf, Jürgen; Wu, Ruijun; Zhu, Miaomiao

doi:10.1016/j.geomphys.2018.01.019

Cited by 13 publications

(21 citation statements)

References 21 publications

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“…They are useful when dealing with the solution space of the Euler-Lagrange equations. A detailed discussion of the symmetries of A and the corresponding conservation laws can be found in [22]. As already mentioned in the introduction the functional (5) is essentially the action functional of the two-dimensional nonlinear supersymmetric sigma model, see [7,13,20].…”

Section: The Action Functionalmentioning

confidence: 99%

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Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

Jost

Keßler

Tolksdorf

et al. 2017

Commun. Math. Phys.

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Abstract:We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler-Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calculated explicitly. The gravitino terms pose additional analytic difficulties to show smoothness of its weak solutions which are overcome using Rivière's regularity theory and Riesz potential theory.

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Section: The Action Functionalmentioning

confidence: 99%

“…In contrast to what is discussed there, we deal with commuting spinors. For that matter the action functional (5) does in general not possess supersymmetry, except in special cases, see [22]. Furthermore, a term which vanishes identically at critical points is omitted here.…”

Section: The Action Functionalmentioning

confidence: 99%

Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

Jost

Keßler

Tolksdorf

et al. 2017

Commun. Math. Phys.

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“…in general dimensions in a manner similar to the two dimensional case considered in [16]. Also in this local Euclidean chart, g αβ = δ αβ and…”

Section: Partial Regularity For Stationary Solutionsmentioning

confidence: 81%

Partial regularity for a nonlinear sigma model with gravitino in higher dimensions

Jost

Zhu

2018

Calc. Var.

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We study the regularity problem of the nonlinear sigma model with gravitino fields in higher dimensions. After setting up the geometric model, we derive the Euler-Lagrange equations and consider the regularity of weak solutions defined in suitable Sobolev spaces. We show that any weak solution is actually smooth under some smallness assumption for certain Morrey norms. By assuming some higher integrability of the vector spinor, we can show a partial regularity result for stationary solutions, provided the gravitino is critical, which means that the corresponding supercurrent vanishes. Moreover, in dimension less than 6, partial regularity holds for stationary solutions with respect to general gravitino fields.

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“…Recently, in [36], we have constructed and investigated a version of this model that involves only commuting variables, analogous to and generalizing the Dirac-harmonic action function (32). For some further results on this model, see [52,51,37]. We shall now describe that model.…”

Section: The Gravitinomentioning

confidence: 99%

From Harmonic Maps to the Nonlinear Supersymmetric Sigma Model of Quantum Field Theory: at the Interface of Theoretical Physics, Riemannian Geometry, and Nonlinear Analysis

et al. 2018

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Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is noncompact, constitute a prototype for the formation of singularities, the so-called bubbles, in geometric analysis. In theoretical physics, they arise from the nonlinear σ -model of quantum field theory. That model possesses a supersymmetric extension, coupling a harmonic map like field with a nonlinear spinor field. In the physical model, that spinor field is anticommuting. In this contribution, we analyze both a mathematical version with a commuting spinor field and the original supersymmetric version. Moreover, this model gives rise to a further field, a gravitino, that can be seen as the supersymmetric partner of a Riemann surface metric. Altogether, this leads to a beautiful combination of concepts from quantum field theory, structures from Riemannian geometry and Riemann surface theory, and methods of nonlinear geometric analysis.

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Symmetries and conservation laws of a nonlinear sigma model with gravitino

Cited by 13 publications

References 21 publications

Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

Regularity of Solutions of the Nonlinear Sigma Model with Gravitino

Partial regularity for a nonlinear sigma model with gravitino in higher dimensions

From Harmonic Maps to the Nonlinear Supersymmetric Sigma Model of Quantum Field Theory: at the Interface of Theoretical Physics, Riemannian Geometry, and Nonlinear Analysis

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