arXiv subjects

Olaf Lechtenfeld

Publications and source records attributed to Olaf Lechtenfeld.

At least 127 records · Page 7Linked to original sources

arXiv2011

Yang-Mills instantons on cones and sine-cones over nearly Kähler manifolds

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly Kähler manifold. The cone over the sine-cone on a nearly Kähler manifold has holonomy group Spin(7) and can be foliated by submanifolds with either holonomy group G_2, a nearly parallel G_2-structure or a cocalibrated G_2-structure. We show that there is a G_2-instanton on each of these seven-dimensional manifolds which gives rise to a Spin(7)-instanton in eight dimensions. The well-known octonionic instantons on R^7 and R^8 are contained in our construction as the special cases of an instanton on the cone and on the cone over the sine-cone, both over the six-sphere, respectively.

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arXiv2011

An N=8 superconformal particle in the half-plane

By imposing global supersymmetry and scale invariance we construct an N=8 superconformal mechanical system based on the inhomogeneous (2,8,6) linear multiplet. The unique action describes a special K"ahler sigma model with a Calogero-type potential and Fayet-Iliopoulos terms. The classical dynamics of the two propagating bosons is restricted to a (warped) half-plane and bounded. We numerically inspect typical trajectories of this special particle.

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arXiv2011

Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons

Due to their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G_2-structures and admit the G_2-instanton equations, which are natural BPS equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons-type functional. We consider the Chern-Simons flow between different G_2-instantons on Aloff-Wallach spaces, which is equivalent to Spin(7)-instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C^3 x R^2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape.

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arXiv2011

N=4 Multi-Particle Mechanics, WDVV Equation and Roots

We review the relation of N=4 superconformal multi-particle models on the real line to the WDVV equation and an associated linear equation for two prepotentials, F and U. The superspace treatment gives another variant of the integrability problem, which we also reformulate as a search for closed flat Yang-Mills connections. Three- and four-particle solutions are presented. The covector ansatz turns the WDVV equation into an algebraic condition, for which we give a formulation in terms of partial isometries. Three ideas for classifying WDVV solutions are developed: ortho-polytopes, hypergraphs, and matroids. Various examples and counterexamples are displayed.

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arXiv2010

Action-angle variables for dihedral systems on the circle

A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi) potential is related to the two-dimensional (dihedral) Coxeter system I_2(k), for k in N. For such `dihedral systems' we construct the action-angle variables and establish a local equivalence with a free particle on the circle. We perform the quantization of these systems in the action-angle variables and discuss the supersymmetric extension of this procedure. By allowing radial motion one obtains related two-dimensional systems, including A_2, BC_2 and G_2 three-particle rational Calogero models on R, which we also analyze.

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arXiv2010

Invariants of the spherical sector in conformal mechanics

A direct relation is established between the constants of motion for conformal mechanics and those for its spherical part. In this way we find the complete set of functionally independent constants of motion for the so-called cuboctahedric Higgs oscillator, which is just the spherical part of the rational A_3 Calogero model (describing four Calogero particles after decoupling their center of mass).

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arXiv2010

Heterotic compactifications on nearly Kähler manifolds

We consider compactifications of heterotic supergravity on anti-de Sitter space, with a six-dimensional nearly K"ahler manifold as the internal space. Completing the model proposed by Frey and Lippert with the particular choice of SU(3)/U(1)xU(1) for the internal manifold, we show that it satisfies not only the supersymmetry constraints but also the equations of motion with string corrections of order alpha'. Furthermore, we present a non-supersymmetric model. In both solutions we find confirmed a recent result of Ivanov on the connection used for anomaly cancellation. Interestingly, the volume of the internal space is fixed by the supersymmetry constraints and/or the equations of motion.

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arXiv2010

Yang-Mills instantons and dyons on homogeneous G_2-manifolds

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of a particle moving in R^6, R^4 or R^2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)xU(1), Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink- and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S^1 x G/H and dyons on iR x G/H are also given.

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arXiv2010

The Noncommutative Ward Metric

We analyze the moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP^1 sigma model in 1+2 dimensions. After carefully reviewing the commutative results of Ward and Ruback, the noncommutative K"ahler potential is expanded in powers of dimensionless moduli. In two special cases we sum the perturbative series to analytic expressions. For any nonzero value of the noncommutativity parameter, the logarithmic singularity of the commutative metric is expelled from the origin of the moduli space and possibly altogether.

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arXiv2010

New D(2,1;alpha) Mechanics with Spin Variables

We elaborate on a novel superconformal mechanics model possessing D(2,1;alpha) symmetry and involving extra U(2) spin variables. It is the one-particle case of the N=4 superconformal matrix model recently proposed in arXiv:0812.4276 [hep-th], and it generalizes to arbitrary alpha\neq0 the OSp(4|2) superconformal mechanics of arXiv:0905.4951 [hep-th]. As in the latter case, the U(2) spin variables are described by a Wess-Zumino action and define the first Hopf map S^3 -> S^2 in the target space. Upon quantization, they represent a fuzzy sphere. We find the classical and quantum generators of the D(2,1;alpha) superalgebra and their realization on the physical states. The super wavefunction encompasses various multiplets of the SU(2)_R and SU(2)_L subgroups of D(2,1;alpha), with fixed isospins. The conformal potential is determined by the external magnetic field in the Wess-Zumino term, whose amplitude is quantized like in the OSp(4|2) case. As a byproduct, we reveal new invariant subspaces in the enveloping algebra of D(2,1;alpha) for our quantum realization.

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arXiv2010

N=4 Supersymmetry and the BPST Instanton

In this paper we construct the Lagrangian and Hamiltonian formulations of N=4 supersymmetric systems describing the motion of an isospin particle on a conformally flat four-manifold with SO(4) isometry carrying the non-Abelian field of a BPST instanton. The conformal factor can be specified to yield various particular systems, such as superconformally invariant mechanics as well as a particle on the four-sphere, the pseudosphere or on R x S^3. The isospin degrees of freedom arise as bosonic components of an additional fermionic N=4 supermultiplet, whose other components are rendered auxiliary by a nonlocal redefinition. Our on-shell component action coincides with the one recently proposed in arXiv:0912.3289.

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arXiv2010

Yang-Mills flows on nearly Kaehler manifolds and G_2-instantons

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, RxG/H and R^2xG/H, where G/H is a compact nearly Kaehler six-dimensional homogeneous space, and the manifolds RxG/H and R^2xG/H carry G_2- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on RxG/H is reduced to Newtonian mechanics of a particle moving in a plane with a quartic potential. For particular values of the torsion, we find explicit particle trajectories, which obey first-order gradient or hamiltonian flow equations. In two cases, these solutions correspond to anti-self-dual instantons associated with one of two G_2-structures on RxG/H. It is shown that both G_2-instanton equations can be obtained from a single Spin(7)-instanton equation on R^2xG/H.

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arXiv2010

New Super Calogero Models and OSp(4|2) Superconformal Mechanics

We report on the new approach to constructing superconformal extensions of the Calogero-type systems with an arbitrary number of involved particles. It is based upon the superfield gauging of non-abelian isometries of some supersymmetric matrix models. Among its applications, we focus on the new N=4 superconformal system yielding the U(2) spin Calogero model in the bosonic sector, and the one-particle case of this system, which is a new OSp(4|2) superconformal mechanics with non-dynamical U(2) spin variables. The characteristic feature of these models is that the strength of the conformal inverse-square potential is quantized.

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arXiv2009

Hidden symmetries of integrable conformal mechanical systems

We split the generic conformal mechanical system into a "radial" and an "angular" part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We reduce the analysis of the constants of motion of the full system to the study of certain differential equations on this orbit. For integrable mechanical systems, the conformal invariance renders them superintegrable, yielding an additional series of conserved quantities originally found by Wojciechowski in the rational Calogero model. Finally, we show that, starting from any N=4 supersymmetric "angular" Hamiltonian system one may construct a new system with full N=4 superconformal D(1,2;α) symmetry.

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arXiv2009

OSp(4|2) Superconformal Mechanics

A new superconformal mechanics with OSp(4|2) symmetry is obtained by gauging the U(1) isometry of a superfield model. It is the one-particle case of the new N=4 super Calogero model recently proposed in arXiv:0812.4276 [hep-th]. Classical and quantum generators of the osp(4|2) superalgebra are constructed on physical states. As opposed to other realizations of N=4 superconformal algebras, all supertranslation generators are linear in the odd variables, similarly to the N=2 case. The bosonic sector of the component action is standard one-particle (dilatonic) conformal mechanics accompanied by an SU(2)/U(1) Wess-Zumino term, which gives rise to a fuzzy sphere upon quantization. The strength of the conformal potential is quantized.

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arXiv2009

A new class of solutions to the WDVV equation

The known prepotential solutions F to the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation are parametrized by a set {alpha} of covectors. This set may be taken to be indecomposable, since F_{alpha oplus beta}=F_{alpha}+F_{beta}. We couple mutually orthogonal covector sets by adding so-called radial terms to the standard form of F. The resulting reducible covector set yields a new type of irreducible solution to the WDVV equation.

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arXiv2009

Harmonic N=2 Mechanics

N=2 superconformal many-body quantum mechanics in arbitrary dimensions is governed by a single scalar prepotential which determines the bosonic potential and the boson-fermion couplings. We present a special class of such models, for which the bosonic potential is absent. They are classified by homogeneous harmonic functions subject to physical symmetry requirements, such as translation, rotation and permutation invariance. The central charge is naturally quantized. We provide some examples for systems of identical particles in any dimension.

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arXiv2009

Noncommutative Baby Skyrmions

We subject the baby Skyrme model to a Moyal deformation, for unitary or Grassmannian target spaces and without a potential term. In the abelian case, the radial BPS configurations of the ordinary noncommutative sigma model also solve the baby Skyrme equation of motion. This gives a class of exact analytic noncommutative baby Skyrmions, which have a singular commutative limit but are stable against scaling due to the noncommutativity. We compute their energies, investigate their stability and determine the asymptotic two-Skyrmion interaction.

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