The paper examines the regularity of solutions to a nonlinear sigma model with gravitino in higher dimensions.
problem The study focuses on the regularity of weak solutions to a nonlinear sigma model with gravitino fields in higher dimensions.
method The authors derive the Euler--Lagrange equations and consider the regularity of weak solutions in Sobolev spaces. They show smoothness under smallness assumptions for certain Morrey norms and partial regularity for stationary solutions with higher integrability of the vector spinor.
result The paper demonstrates that weak solutions are smooth under certain conditions and shows partial regularity for stationary solutions in higher dimensions.
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 calc…
The regularity of weak solutions of a two-dimensional nonlinear sigma model with coarse gravitino is shown. Here the gravitino is only assumed to be in Lp for some p>4. The precise regularity results depend on the value of p.
The nonlinear sigma model with gravitino exhibits symmetries and conservation laws.
problem Exploring symmetries and conservation laws in a nonlinear sigma model with gravitino.
method Geometric analysis of rescaled conformal transformations, super Weyl transformations, and diffeomorphisms.
result The model possesses degenerate super symmetry leading to geometric interpretations of energy-momentum tensor and supercurrent.
We study some analytical and geometric properties of a two-dimensional nonlinear sigma model with gravitino which comes from supersymmetric string theory. When the action is critical w.r.t. variations of the various fields including the gravitino, there is a symmetric, traceless and divergence-free energy-momentum tens…
The underlying even manifold of a super Riemann surface is a Riemann surface with a spinor valued differential form called gravitino. Consequently infinitesimal deformations of super Riemann surfaces are certain infinitesimal deformations of the Riemann surface and the gravitino. Furthermore the action functional of no…
We consider type II string theory in space-time backgrounds which admit eight supercharges and can be characterized by the existence of an SU(3) x SU(3) structure. We show that the couplings of such backgrounds strongly resemble the couplings of four-dimensional N=2 supergravities and precisely coincide with the N=2 co…
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an analogue of Riemann surfaces in the world of super geometry. After a short intro…
We recover the classification of the maximally supersymmetric bosonic backgrounds of eleven-dimensional supergravity by Lie algebraic means. We classify all filtered deformations of the Z-graded subalgebras h=h−2⊕h−1⊕h0 of the Poincaré superalge…
T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E_8 and also using S-duality. We present known and new examples including NS5-branes, nilmanifolds, Lens spaces, both circle bundles over RP^n, and the AdS^5 x S^5 to AdS^5 x CP^2 x S^1 w…
Harmonic maps connect physics, geometry, and analysis.
problem Understanding singularities in geometric analysis.
method Analysis of harmonic maps and their supersymmetric extensions.
result Formation of bubbles in geometric analysis.
We study 4-dimensional higher-derivative conformal higher spin (CHS) fields generalising Weyl graviton and conformal gravitino. They appear, in particular, as "induced" theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. …