arXiv subjects

Olaf Lechtenfeld

Publications and source records attributed to Olaf Lechtenfeld.

At least 91 records · Page 5Linked to original sources

arXiv2015

Yang-Mills moduli space in the adiabatic limit

We consider the Yang-Mills equations for a matrix gauge group $G$ inside the future light cone of 4-dimensional Minkowski space, which can be viewed as a Lorentzian cone $C(H^3)$ over the 3-dimensional hyperbolic space $H^3$. Using the conformal equivalence of $C(H^3)$ and the cylinder $R\times H^3$, we show that, in the adiabatic limit when the metric on $H^3$ is scaled down, classical Yang-Mills dynamics is described by geodesic motion in the infinite-dimensional group manifold $C^\infty (S^2_\infty,G)$ of smooth maps from the boundary 2-sphere $S^2_\infty=\partial H^3$ into the gauge group $G$.

hep-th↗

arXiv2015

Supermembrane limit of Yang-Mills theory

We consider Yang-Mills theory with $N{=}1$ super translation group in eleven auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $Σ_3\times S^1$, where $Σ_3$ is a three-dimensional Lorentzian manifold and $S^1$ is a circle. We show that in the infrared limit, when the metric on $S^1$ is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term reduces to the action of an M2-brane.

hep-th↗

arXiv2015

Sigma-model limit of Yang-Mills instantons in higher dimensions

We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional Kähler manifold X which is a product Y x Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that in the adiabatic limit, when the metric in the Z direction is scaled down, the gauge instanton equations on Y x Z become sigma-model instanton equations for maps from Y to the moduli space M (target space) of gauge instantons on Z if q>= 4. For q<4 we get maps from Y to the moduli space M of flat connections on Z. Thus, the Yang-Mills instantons on Y x Z converge to sigma-model instantons on Y while Z shrinks to a point. Put differently, for small volume of Z, sigma-model instantons on Y with target space M approximate Yang-Mills instantons on Y x Z.

hep-th↗

arXiv2015

Instantons on conical half-flat 6-manifolds

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kahler in the special case of sine-cones over Sasaki-Einstein 5-manifolds. Both half-flat and nearly Kahler 6-manifolds are prominent in flux compactifications of string theory. Subsequently, we investigate instanton equations for connections on vector bundles over these half-flat manifolds. A suitable ansatz for gauge fields on these 6-manifolds reduces the instanton equation to a set of matrix equations. We finally present some of its solutions and discuss the instanton configurations obtained this way.

hep-th↗

arXiv2014

Auxiliary tensor fields for Sp(2,R) self-duality

The coset Sp(2,R)/U(1) is parametrized by two real scalar fields. We generalize the formalism of auxiliary tensor (bispinor) fields in U(1) self-dual nonlinear models of abelian gauge fields to the case of Sp(2,R) self-duality. In this new formulation, Sp(2,R) duality of the nonlinear scalar-gauge equations of motion is equivalent to an Sp(2,R) invariance of the auxiliary interaction. We derive this result in two different ways, aiming at its further application to supersymmetric theories. We also consider an extension to interactions with higher derivatives.

hep-th↗

arXiv2014

Order $α'$ heterotic domain walls with warped nearly Kähler geometry

We consider 1+3-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kähler manifold $X_6$ in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [arXiv:1109.3552]. We include first order $α'$ corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present a variety of solutions, depending on the choice of instantons, for the special case in which the SU(3) structure on $X_6$ satisfies $W_1^-=0$. The solutions preserve two real supercharges, which corresponds to $\mathcal{N}{=}1/2$ supersymmetry from the four-dimensional point of view. Besides serving as a useful framework for collecting existing solutions, the formulation in terms of dynamic SU(3) structures utilized here allows us to obtain new solutions in as yet unexplored corners of the instanton configuration space. Our approach thus offers a unified description of the embedding of tanh-kink-type instantons into half-BPS solutions of heterotic supergravity where the internal six-dimensional manifold has a warped nearly Kähler geometry

hep-th↗

arXiv2014

Superintegrability of (generalized) Calogero models with oscillator or Coulomb potential

We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb systems, replacing their angular degrees of freedom by those of a generalized rational Calogero model. Using the action-angle description, it is established that maximal superintegrability is retained. For the rational Calogero model with Coulomb potential, we present all constants of motion via matrix model reduction. In particular, we construct the analog of the Runge-Lenz vector.

hep-th↗

arXiv2014

Instantons on sine-cones over Sasakian manifolds

We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric torsion. Furthermore, a deformation of the metric on the sine-cone over 3-Sasakian manifolds allows one to introduce a hyper-K"ahler with torsion (HKT) structure. In the large-volume limit these KT and HKT spaces become Calabi-Yau and hyper-K"ahler conifolds, respectively. We construct gauge connections on complex vector bundles over conical KT and HKT manifolds which solve the instanton equations for Yang-Mills fields in higher dimensions.

hep-th↗

arXiv2014

Nonlinear supersymmetry in the quantum Calogero model

It is long known that the rational Calogero model describing n identical particles on a line with inverse-square mutual interaction potential is quantum superintegrable. We review the (nonlinear) algebra of the conserved quantum charges and the intertwiners which relate the Liouville charges at couplings g and g+1. For integer values of g, these intertwiners give rise to additional conserved charges commuting with all Liouville charges and known since the 1990s. We give a direct construction of such a charge, the unique one being totally antisymmetric under particle permutations. It is of order n(n-1)(2g-1)/2 in the momenta and squares to a polynomial in the Liouville charges. With a natural Z_2 grading, this charge extends the algebra of conserved charges to a nonlinear supersymmetric one. We provide explicit expressions for intertwiners, charges and their algebra in the cases of two, three and four particles.

hep-th↗

arXiv2014

Dirac structures on nilmanifolds and coexistence of fluxes

We study some aspects of the generalized geometry of nilmanifolds and examine to which extent different types of fluxes can coexist on them. Nilmanifolds constitute a class of homogeneous spaces which are interesting in string compactifications with fluxes since they carry geometric flux by construction. They are generalized Calabi-Yau spaces and therefore simple examples of generalized geometry at work. We identify and classify Dirac structures on nilmanifolds, which are maximally isotropic subbundles closed under the Courant bracket. In the presence of non-vanishing fluxes, these structures are twisted and closed under appropriate extensions of the Courant bracket. Twisted Dirac structures on a nilmanifold may carry multiple coexistent fluxes of any type. We also show how dual Dirac structures combine to Courant algebroids and work out an explicit example where all types of generalized fluxes coexist. These results may be useful in the context of general flux compactifications in string theory.

hep-th↗

arXiv2014

Instantons in six dimensions and twistors

Recently, conformal field theories in six dimensions were discussed from the twistorial point of view. In particular, it was demonstrated that the twistor transform between chiral zero-rest-mass fields and cohomology classes on twistor space can be generalized from four to six dimensions. On the other hand, the possibility of generalizing the correspondence between instanton gauge fields and holomorphic bundles over twistor space is questionable. It was shown by Saemann and Wolf that holomorphic line bundles over the canonical twistor space Tw(X) (defined as a bundle of almost complex structures over the six-dimensional manifold X) correspond to pure-gauge Maxwell potentials, i.e. the twistor transform fails. On the example of X=CP^3 we show that there exists a twistor correspondence between Abelian or non-Abelian Yang-Mills instantons on CP^3 and holomorphic bundles over complex submanifolds of Tw(CP^3), but it is not so efficient as in the four-dimensional case because the twistor transform does not parametrize instantons by unconstrained holomorphic data as it does in four dimensions.

hep-th↗

arXiv2014

The structure of invariants in conformal mechanics

We investigate the integrals of motion of general conformal mechanical systems with and without confining harmonic potential as well as of the related angular subsystems, by employing the SL(2,R) algebra and its representations. In particular, via the tensor product of two representations we construct new integrals of motion from old ones. Furthermore, the temporally periodic observables (including the integrals) of the angular subsystem are explicitly related to those of the full system in a confining harmonic potential. The techniques are illustrated for the rational Calogero models and their angular subsystems, where they generalize known methods for obtaining conserved charges beyond the Liouville ones.

hep-th↗

arXiv2013

On the Gribov problem in Yang-Mills theory

I briefly review the Gribov ambiguity of Yang-Mills theory, some of its features and attempts to control it, in particular the Gribov-Zwanziger proposal to restrict the functional integration in the Landau gauge to the Gribov region. This proposal is extended to an arbitrary gauge in such a way as to guarantee BRST invariance. The key insight is that any gauge change in the generating functional can be effected by a suitable field-dependent BRST transformation. I derive a simple analytic formula for the Jacobian of such a transformation, which yields an explicit recipe for the required transformation-parameter functional and allows for the computation of the Gribov horizon functional in any gauge, as I illustrate for the class of R_xi gauges.

hep-th↗

arXiv2013

Higher-derivative N=4 superparticle in three-dimensional spacetime

Using the coset approach (nonlinear realization) we construct component actions for a superparticle in three-dimensional spacetime with N=4 supersymmetry partially broken to N=2. These actions may contain an anyonic term and the square of the first extrinsic worldline curvature. We present the supercharges for the unbroken and broken supersymmetries as well as the Hamiltonian for the supersymmetric anyon. In terms of the nonlinear realization superfields, the superspace actions take a simple form in all cases.

hep-th↗

arXiv2013

New Approach to Duality-Invariant Nonlinear Electrodynamics

We survey a new approach to the duality-invariant systems of nonlinear electrodynamics, based on introducing auxiliary bi-spinor fields. In this approach, the entire information about the given self-dual system is encoded in the U(1) invariant interaction of the auxiliary fields, while the standard self-dual Lagrangians appear on shell as a result of eliminating auxiliary fields by their equations of motion. Starting from the simplest U(1) duality, we show how this approach can be generalized to the U(N) duality (with N independent Maxwell field strengths), as well as to self-dual systems of {\cal N}=1 supersymmetric electrodynamics. Also, it works perfectly for self-dual systems with higher derivatives in the action.

hep-th↗

arXiv2013

Orbifold instantons, moment maps and Yang-Mills theory with sources

We revisit the problem of constructing instantons on ADE orbifolds R^4/Γand point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R^4/Γwhich are BPS equations for the Yang-Mills equations with an external current. The relation between level sets of the moment maps in the hyper-Kaehler quotient construction of the instanton moduli space and sources in the Yang-Mills equations is discussed. We describe two types of spherically-symmetric Γ-equivariant connections on complex V-bundles over R^4/Γwhich are tailored to the way in which the orbifold group acts on the fibres. Some explicit abelian and nonabelian SU(2)-invariant solutions to the nstanton equations on the orbifold are worked out.

hep-th↗

arXiv2013

Auxiliary superfields in N=1 supersymmetric self-dual electrodynamics

We construct the general formulation of N=1 supersymmetric self-dual abelian gauge theory involving auxiliary chiral spinor superfields. Self-duality in this context is just U(N) invariance of the nonlinear interaction of the auxiliary superfields. Focusing on the U(1) case, we present the most general form of the U(1) invariant auxiliary interaction, consider a few instructive examples and show how to generate self-dual N=1 models with higher derivatives in this approach.

hep-th↗

arXiv2013

On two-dimensional integrable models with a cubic or quartic integral of motion

Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance under continuous rescalings and a dihedral symmetry, we construct new integrable models with a cubic or quartic integral, each of which involves either one or two continuous parameters. A reducible case related to the two-dimensional wave equation is discussed as well. We conjecture a hidden D_{2n} dihedral symmetry for models with an integral of n-th order in the velocities.

math-ph↗