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Olaf Lechtenfeld

Publications and source records attributed to Olaf Lechtenfeld.

At least 181 records · Page 10Linked to original sources
arXiv2004

Nilpotent deformations of N=2 superspace

We investigate deformations of four-dimensional N=(1,1) euclidean superspace induced by nonanticommuting fermionic coordinates. We essentially use the harmonic superspace approach and consider nilpotent bi-differential Poisson operators only. One variant of such deformations (termed chiral nilpotent) directly generalizes the recently studied chiral deformation of N=(1/2,1/2) superspace. It preserves chirality and harmonic analyticity but generically breaks N=(1,1) to N=(1,0) supersymmetry. Yet, for degenerate choices of the constant deformation matrix N=(1,1/2) supersymmetry can be retained, i.e. a fraction of 3/4. An alternative version (termed analytic nilpotent) imposes minimal nonanticommutativity on the analytic coordinates of harmonic superspace. It does not affect the analytic subspace and respects all supersymmetries, at the expense of chirality however. For a chiral nilpotent deformation, we present non(anti)commutative euclidean analogs of N=2 Maxwell and hypermultiplet off-shell actions.

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arXiv2004

Noncommutative Monopoles and Riemann-Hilbert Problems

The Bogomolny equations for Yang-Mills-Higgs monopoles follow from a system of linear equations which may be solved through a parametric Riemann-Hilbert problem. We extend this approach to noncommutative R^3 and use it to (re)construct noncommutative Dirac, Wu-Yang, and BPS monopole configurations in a unified manner. In all cases we write down the underlying matrix-valued functions for multi-monopoles and solve the corresponding Riemann-Hilbert problems for charge one.

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arXiv2004

Noncommutative Instantons and Solitons

I explain how to construct noncommutative BPS configurations in four and lower dimensions by solving linear matrix equations. Examples are instantons in D=4 Yang-Mills, monopoles in D=3 Yang-Mills-Higgs, and (moving) solitons in D=2+1 Yang-Mills-Higgs. Some emphasis is on the latter as a showcase for the dressing method.

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arXiv2003

N=4, d=1 supermultiplets from nonlinear realizations of D(2,1;α)

Proceeding from nonlinear realizations of the most general N=4, d=1 superconformal symmetry associated with the supergroup D(2,1;α), we construct all known and two new off-shell N=4, d=1 supermultiplets as properly constrained N=4 superfields. We find plenty of nonlinear interrelations between the multiplets constructed and present a few examples of invariant superfield actions for them. The superconformal transformation properties of these multiplets are explicit within our method.

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arXiv2003

Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles

We construct explicit BPS and non-BPS solutions of the U(2k) Yang-Mills equations on the noncommutative space R^{2n}_θx S^2 with finite energy and topological charge. By twisting with a Dirac multi-monopole bundle over S^2, we reduce the Donaldson-Uhlenbeck-Yau equations on R^{2n}_θx S^2 to vortex-type equations for a pair of U(k) gauge fields and a bi-fundamental scalar field on R^{2n}_θ. In the SO(3)-invariant case the vortices on R^{2n}_θdetermine multi-instantons on R^{2n}_θx S^2. We show that these solutions give natural physical realizations of Bott periodicity and vector bundle modification in topological K-homology, and can be interpreted as a blowing-up of D0-branes on R^{2n}_θinto spherical D2-branes on R^{2n}_θx S^2. In the generic case with broken rotational symmetry, we argue that the D0-brane charges on R^{2n}_θx S^2 provide a physical interpretation of the Adams operations in K-theory.

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arXiv2003

Hidden Symmetries of the Open N=2 String

It is known for ten years that self-dual Yang-Mills theory is the effective field theory of the open N=2 string in 2+2 dimensional spacetime. We uncover an infinite set of abelian rigid string symmetries, corresponding to the symmetries and integrable hierarchy of the self-dual Yang-Mills equations. The twistor description of the latter naturally connects with the BRST approach to string quantization, providing an interpretation of the picture phenomenon in terms of the moduli space of string backgrounds.

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arXiv2003

Noncommutative Multi-Solitons in 2+1 Dimensions

The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing method to construct explicit multi-soliton configurations on noncommutative R^{2,1}. These solutions, abelian and nonabelian, feature exact time-dependence for any value of the noncommutativity parameter theta and describe various lumps of finite energy in relative motion. We discuss their scattering properties and prove asymptotic factorization for large times.

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arXiv2003

Noncommutative Instantons via Dressing and Splitting Approaches

Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative Euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavin's and Zakharov's work to the noncommutative setup. Secondly, we relate the dressing approach with Ward's splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques.

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arXiv2003

Noncommutative Multi-Instantons on R^{2n} x S^2

Generalizing self-duality on R^2 x S^2 to higher dimensions, we consider the Donaldson-Uhlenbeck-Yau equations on R^{2n} x S^2 and their noncommutative deformation for the gauge group U(2). Imposing SO(3) invariance (up to gauge transformations) reduces these equations to vortex-type equations for an abelian gauge field and a complex scalar on R^{2n}_θ. For a special S^2-radius R depending on the noncommutativity θwe find explicit solutions in terms of shift operators. These vortex-like configurations on R^{2n}_θdetermine SO(3)-invariant multi-instantons on R^{2n}_θx S^2_R for R=R(θ). The latter may be interpreted as sub-branes of codimension 2n inside a coincident pair of noncommutative Dp-branes with an S^2 factor of suitable size.

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arXiv2003

Solving String Field Equations: New Uses for Old Tools

It is argued that the (NS-sector) superstring field equations are integrable, i.e. their solutions are obtainable from linear equations. We adapt the 25-year-old solution-generating "dressing" method and reduce the construction of nonperturbative superstring configurations to a specific cohomology problem. The application to vacuum superstring field theory is outlined.

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arXiv2002

On Nonperturbative Solutions of Superstring Field Theory

Nonperturbative solutions to the nonlinear field equations in the NS sector of cubic as well as nonpolynomial superstring field theory can be obtained from a linear equation which includes a "spectral" parameter λand a coboundary operator Q(λ). We borrow a simple ansatz from the dressing method (for generating solitons in integrable field theories) and show that classical superstring fields can be constructed from any string field T subject merely to Q(λ)T=0. Following the decay of the non-BPS D9 brane in IIA theory and shifting the background to the tachyon vacuum, we repeat the arguments in vacuum superstring field theory and outline how to compute classical solutions explicitly.

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arXiv2002

Exact Solutions of Berkovits' String Field Theory

The equation of motion for Berkovits' WZW-like open (super)string field theory is shown to be integrable in the sense that it can be written as the compatibility condition ("zero-curvature condition") of some linear equations. Employing a generalization of solution-generating techniques (the splitting and the dressing methods), we demonstrate how to construct nonperturbative classical configurations of both N=1 superstring and N=2 fermionic string field theories. With and without u(n) Chan-Paton factors, various solutions of the string field equation are presented explicitly.

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arXiv2002

Scattering of Noncommutative Solitons in 2+1 Dimensions

Interactions of noncommutative solitons in a modified U(n) sigma model in 2+1 dimensions can be analyzed exactly. Using an extension of the dressing method, we construct explicit time-dependent solutions of its noncommutative field equation by iteratively solving linear equations. The approach is illustrated by presenting bound states and right-angle scattering configurations for two noncommutative solitons.

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arXiv2002

Light-Cone Gauge for N=2 Strings

Covariant quantization of self-dual strings in 2+2 flat dimensions reduces them to their zero modes, a consequence of extended world-sheet supersymmetry. We demonstrate how to arrive at the same result more directly by employing a `double' light-cone gauge. An unconventional feature of this gauge is the removal of anticommuting degrees of freedom by commuting symmetries and vice versa. The reducibility of the N=4 string and its equivalence with the N=2 string become apparent.

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arXiv2002

A Heterotic N=2 String with Space-Time Supersymmetry

We reconsider the issue of embedding space-time fermions into the four-dimensional N=2 world-sheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.

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arXiv2002

Noncommutative 't Hooft Instantons

We employ the twistor approach to the construction of U(2) multi-instantons `a la 't Hooft on noncommutative R^4. The noncommutative deformation of the Corrigan-Fairlie-'t Hooft-Wilczek ansatz is derived. However, naively substituting into it the 't Hooft-type solution is unsatisfactory because the resulting gauge field fails to be self-dual on a finite-dimensional subspace of the Fock space. We repair this deficiency by a suitable Murray-von Neumann transformation after a specific projection of the gauge potential. The proper noncommutative 't Hooft multi-instanton field strength is given explicitly, in a singular as well as in a regular gauge.

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arXiv2001

Noncommutative Solitons in Open N=2 String Theory

Coincident D2-branes in open N=2 fermionic string theory with a B-field background yield an integrable modified U(n) sigma model on noncommutative R^{2,1}. This model provides a showcase for an established method (the `dressing approach') to generate solutions for integrable field equations, even in the noncommutative case. We demonstrate the technique by constructing moving U(1) and U(2) solitons and by computing their energies. It is outlined how to derive multi-soliton configurations with arbitrary relative motion; they correspond to D0-branes moving inside the D2-branes.

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