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Ulf Lindström

Publications and source records attributed to Ulf Lindström.

At least 37 records · Page 2Linked to original sources
arXiv2023

New currents with Killing-Yano tensors

New relations involving the Riemann, Ricci and Einstein tensors that have to hold for a given geometry to admit Killing-Yano tensors are described. These relations are then used to introduce novel conserved "currents" involving such Killing-Yano tensors. For a particular current based on the Einstein tensor, we discuss the issue of conserved charges and consider implications for matter coupled to gravity. The condition on the background geometry to allow asymptotic conserved charges for a current introduced by Kastor and Traschen is found and a number of other new aspects of this current are commented on. In particular we show that it vanishes for rank $(D-1)$ Killing-Yano tensors in $D$ dimensions.

hep-th↗
arXiv2023

Killing-Yano charges of asymptotically maximally symmetric black holes

We construct an asymptotic conserved charge for a current that has been defined using Killing-Yano tensors. We then calculate the corresponding conserved charges of of the Kerr and AdS-Kerr black holes, and their higher-dimensional generalizations, Myers-Perry and Gibbons-Lü-Page-Pope black holes. The new charges all turn out to be proportional to the angular momenta of their parent black holes.

gr-qc↗
arXiv2022

A comment on Metric vs Metric-Affine Gravity

We consider the sum of the Einstein-Hilbert action and a Pontryagin density (PD) in arbitrary even dimension $D$. All curvatures are functions of independent affine (torsionless) connections only. In arbitrary dimension, not only in $D=4n$, these first order PD terms are shown to be covariant divergences of "Chern-Simons" currents. The field equation for the connection leads to it being Levi-Civita, and to the metric and affine field equations being equivalent to the second order metric theory. This result is a counterexample to the theorem stating that purely metric and metric-affine models can only be equivalent for Lovelock theories.

gr-qc↗
arXiv2022

Yano F structures and extended Supersymmetry

It is shown how extended supersymmetry realised directly on the (2,2) semichiral superfields of a symplectic sigma model gives rise to a geometry on the doubled tangent bundle consisting of two Yano F structures on an almost para-hermitian manifold. Closure of the algebra and invariance of the action is discussed in this framework and integrability of the F structures is defined and shown to hold. The reduction to the usual (1, 1) sigma model description and identification with the bi-quaternionic set of complex structures and their properties is elucidated. The F structure formulation should be applicable to many other models and will have an equivalent formulation in Generalised Geometry.

hep-th↗
arXiv2022

$2d$ Sigma Models and Geometry

Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since they allow for torsionful geometries. In this review I describe and exemplify the relation of $2d$ supersymmetry to Riemannian, complex, bihermitian, $(p,q)$ Hermitean, Kähler, hyperkähler, generalised geometry and more

hep-th↗
arXiv2022

Killing-Yano Cotton Currents

We discuss conserved currents constructed from the Cotton tensor and (conformal) Killing-Yano tensors (KYTs). We consider the corresponding charges generally and then exemplify with the four-dimensional Plebański-Demiański metric where they are proportional to the sum of the squares of the electric and the magnetic charges. As part of the derivation, we also find the two conformal Killing-Yano tensors of the Plebański-Demiański metric in the recently introduced coordinates of Podolsky and Vratny. The construction of asymptotic charges for the Cotton current is elucidated and compared to the three-dimensional construction in Topologically Massive Gravity. For the three-dimensional case, we also give a conformal superspace multiplet that contains the Cotton current in the bosonic sector. In a mathematical section, we derive potentials for the currents, find identities for conformal KYTs and for KYTs in torsionful backgrounds.

hep-th↗
arXiv2022

Uses of Killing and Killing-Yano Tensors

In this contribution we have collected some facts about Killing and Killing-Yano tensors that we feel are of general interest for researchers working on problems that rely on differential geometry. We also include some of our recent studies pertaining to currents, charges and (super)invariants for particles and tensionless strings.

hep-th↗
arXiv2022

Tensionless Strings and Killing(-Yano) Tensors

We construct invariants for bosonic and spinning tensionless (null) strings in backgrounds that carry Killing tensors or Killing-Yano tensors of mixed type. This is facilitated by the close relation of these strings to point particles. We apply the construction to the Minkowski and to the Kerr-Newman backgrounds.

hep-th↗
arXiv2020

Symmetries of $\mathcal{N} = (1,0)$ supergravity backgrounds in six dimensions

General $\mathcal{N}=(1,0)$ supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) $\mathsf{SU}(2)$ superspace; and (ii) conformal superspace. With motivation to develop rigid supersymmetric field theories in curved space, this paper is devoted to the study of the geometric symmetries of supergravity backgrounds. In particular, we introduce the notion of a conformal Killing spinor superfield $ε^α$, which proves to generate extended superconformal transformations. Among its cousins are the conformal Killing vector $ξ^a$ and tensor $ζ^{a(n)}$ superfields. The former parametrise conformal isometries of supergravity backgrounds, which in turn yield symmetries of every superconformal field theory. Meanwhile, the conformal Killing tensors of a given background are associated with higher symmetries of the hypermultiplet. By studying the higher symmetries of a non-conformal vector multiplet we introduce the concept of a Killing tensor superfield. We also analyse the problem of computing higher symmetries for the conformal d'Alembertian in curved space and demonstrate that, beyond the first-order case, these operators are defined only on conformally flat backgrounds.

hep-th↗
arXiv2020

Covariant Hamiltonians, sigma models and supersymmetry

We introduce a phase space with spinorial momenta, corresponding to fermionic derivatives, for a 2d supersymmetric (1, 1) sigma model. We show that there is a generalisation of the covariant De Donder-Weyl Hamiltonian formulation on this phase space with canonical equations equivalent to the Lagrangian formulation, find the corresponding multisymplectic form and Hamiltonian multivectors. The covariance of the formulation makes it possible to see how additional non-manifest supersymmetries arise in analogy to those of the Lagrangian formulation. We then observe that an intermediate phase space Lagrangian defined on the sum of the tangent and cotanget spaces is a first order Lagrangian for the sigma model and derive additional supersymmetries for this.

hep-th↗
arXiv2019

Strong Kähler with Torsion as Generalised Geometry

Strong Kähler with Torsion is the target space geometry of $(2,1)$ and $(2,0)$ supersymmetric nonlinear sigma models. We discuss how it can be represented in terms of Generalised Complex Geometry in analogy to the Gualtieri map from the geometry of $(2,2)$ supersymmetric nonlinear sigma models to Generalised Kähler Geometry.

hep-th↗
arXiv2018

The Generalised Complex Geometry of $(p,q)$ Hermitian Geometries

We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised Kähler geometry for $(2,2)$, generalised hyperkähler geometry for $(4,2)$, strong Kähler with torsion geometry for $(2,1)$ and strong hyperkähler with torsion geometry for $(4,1)$. We provide a generalised complex geometry formulation of hermitian geometry, generalising Gualtieri's formulation of the $(2,2)$ case. Our formulation involves a chiral version of generalised complex structure and we provide explicit formulae for the map to generalised geometry.

hep-th↗
arXiv2018

Uses of Sigma Models

This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries. The relation of supersymmetric non-linear sigma models to Kähler, hyperkähler, hyperkähler with torsion and generalised Kähler geometries is described.

hep-th↗
arXiv2017

All $(4,0)$: Sigma Models with $(4,0)$ Off-Shell Supersymmetry

Off-shell $(4,0)$ supermultiplets in 2-dimensions are formulated. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperkähler with torsion. The off-shell supersymmetry implies that the complex structures are simultaneously integrable and allows us to write actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.

hep-th↗
arXiv2017

All $(4,1)$: Sigma Models with $(4,q)$ Off-Shell Supersymmetry

Off-shell $(4,q)$ supermultiplets in 2-dimensions are constructed for $q=1,2,4$. These are used to construct sigma models whose target spaces are hyperkähler with torsion. The off-shell supersymmetry implies the three complex structures are simultaneously integrable and allows us to construct actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.

hep-th↗
arXiv2015

Semichirals and Four Dimensional Geometry

Semichiral $(2,2)$ sigma models with $4d$ target space are discussed. A novel description in $(1,1)$ superspace allows an analysis of possible extended supersymmetries. It is argued that a manifest semichiral realization of an extra supersymmetry is only possible for hyperkähler target geometry. A semichiral formulation of the $SU(2)\otimes U(1)$ WZW model is seemingly a counterexample to this. After deriving the extra supersymmetries of this model in $(1,1)$ superspace it is shown that they cannot be lifted to transformations of semichirals in $(2,2)$ superspace.

hep-th↗
arXiv2012

Semichiral Sigma Models with 4D Hyperkaehler Geometry

Semichiral sigma models with a four-dimensional target space do not support extended N=(4,4) supersymmetries off-shell arXiv:0903.2376, arXiv:0912.4724. We contribute towards the understanding of the non-manifest on-shell transformations in (2,2) superspace by analyzing the extended on-shell supersymmetry of such models and find that a rather general ansatz for the additional supersymmetry (not involving central charge transformations) leads to hyperkähler geometry. We give non-trivial examples of these models.

hep-th↗