arXiv subjects

Martin Wolf

Publications and source records attributed to Martin Wolf.

154 records · Page 9Linked to original sources

arXiv2005

The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations

In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three dimensions. Without the D1-branes, this topological B-model is equivalent to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the latter with a holomorphic BF-type theory, we describe a twistor correspondence between this theory and a supersymmetric Bogomolny model on R^3. The connecting link in this correspondence is a partially holomorphic Chern-Simons theory on a Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the mini-supertwistor space. Along the way of proving this twistor correspondence, we review the necessary basic geometric notions and construct action functionals for the involved theories. Furthermore, we discuss the geometric aspect of a recently proposed deformation of the mini-supertwistor space, which gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually, we present solution generating techniques based on the developed twistorial description together with some examples and comment briefly on a twistor correspondence for super Yang-Mills theory in three dimensions.

hep-th↗

arXiv2005

Twistors and Aspects of Integrability of self-dual SYM Theory

With the help of the Penrose-Ward transform, which relates certain holomorphic vector bundles over the supertwistor space to the equations of motion of self-dual SYM theory in four dimensions, we construct hidden infinite-dimensional symmetries of the theory. We also present a new and shorter proof (cf. hep-th/0412163) of the relation between certain deformation algebras and hidden symmetry algebras. This article is based on a talk given by the author at the Workshop on Supersymmetries and Quantum Symmetries 2005 at the BLTP in Dubna, Russia.

hep-th↗

arXiv2005

On Hidden Symmetries of a Super Gauge Theory and Twistor String Theory

We discuss infinite-dimensional hidden symmetry algebras (and hence an infinite number of conserved nonlocal charges) of the N-extented self-dual super Yang-Mills equations for general N\leq4 by using the supertwistor correspondence. Furthermore, by enhancing the supertwistor space, we construct the N-extended self-dual super Yang-Mills hierarchies, which describe infinite sets of graded Abelian symmetries. We also show that the open topological B-model with the enhanced supertwistor space as target manifold will describe the hierarchies. Furthermore, these hierarchies will in turn -- by a supersymmetric extension of Ward's conjecture -- reduce to the super hierarchies of integrable models in D<4 dimensions.

hep-th↗

arXiv2004

Topological B-Model on Weighted Projective Spaces and Self-Dual Models in Four Dimensions

It was recently shown by Witten on the basis of several examples that the topological B-model whose target space is a Calabi-Yau (CY) supermanifold is equivalent to holomorphic Chern-Simons (hCS) theory on the same supermanifold. Moreover, for the supertwistor space CP^{3|4} as target space, it has been demonstrated that hCS theory on CP^{3|4} is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four dimensions. We consider as target spaces for the B-model the weighted projective spaces WCP^{3|2}(1,1,1,1|p,q) with two fermionic coordinates of weight p and q, respectively - which are CY supermanifolds for p+q=4 - and discuss hCS theory on them. By using twistor techniques, we obtain certain field theories in four dimensions which are equivalent to hCS theory. These theories turn out to be self-dual truncations of N=4 SYM theory or of its twisted (topological) version.

hep-th↗

arXiv2004

Constraint and Super Yang-Mills Equations on the Deformed Superspace R^(4|16)_\hbar

It has been known for quite some time that the N=4 super Yang-Mills equations defined on four-dimensional Euclidean space are equivalent to certain constraint equations on the Euclidean superspace R^(4|16). In this paper we consider the constraint equations on a deformed superspace R^(4|16)_\hbar a la Seiberg and derive the deformed super Yang-Mills equations. In showing this, we propose a super Seiberg-Witten map.

hep-th↗

arXiv2003

Seiberg-Witten Monopole Equations on Noncommutative R^4

It is well known that, due to vanishing theorems, there are no nontrivial finite action solutions to the Abelian Seiberg-Witten (SW) monopole equations on Euclidean four-dimensional space R^4. We show that this is no longer true for the noncommutative version of these equations, i.e., on a noncommutative deformation R^4_θof R^4 there exist smooth solutions to the SW equations having nonzero topological charge. We introduce action functionals for the noncommutative SW equations and construct explicit regular solutions. All our solutions have finite energy. We also suggest a possible interpretation of the obtained solutions as codimension four vortex-like solitons representing D(p-4)- and anti-D(p-4)-branes in a Dp-anti-Dp brane system in type II superstring theory.

hep-th↗

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.

hep-th↗

arXiv2002

Soliton-Antisoliton Scattering Configurations in a Noncommutative Sigma Model in 2+1 Dimensions

In this paper we study the noncommutative extension of a modified U(n) sigma model in 2+1 dimensions. Using the method of dressing transformations, an iterative approach for the construction of solutions from a given seed solution, we demonstrate the construction of multi-soliton and soliton-antisoliton configurations for general n. As illustrative examples we discuss U(3) solitons and consider the head-on collision of a U(2) soliton and an antisoliton explicitly, which will result in a 90^{\text{o}} angle scattering. Further we discuss the head-on collision of one U(2) soliton with two antisolitons. This results in a 60^{\text{o}} angle scattering.

hep-th↗

arXiv2001

Anisotropy of Quasiparticle Lifetimes and the Role of Disorder for Ultrafast Electron Dynamics in Graphite

Femtosecond time-resolved photoemission of photoexcited electrons in highly oriented pyrolytic graphite (HOPG) provides strong evidence for anisotropies of quasiparticle (QP) lifetimes. Indicative of such anisotropies is a pronounced anomaly in the energy dependence of QP lifetimes between 1.1 eV and 1.5 eV - the vicinity of a saddle point in the graphite bandstructure. This is supported by recent ab initio calculations and a comparison with experiments on defect-enriched HOPG which reveal that disorder, e.g. defects or phonons, increases electron energy relaxation rates.

cond-mat↗

arXiv1999

Artificiality of multifractal phase transitions

A multifractal phase transition is associated to a nonanalyticity in the generalised dimensions. We show that its occurrence is an artifact of the asymptotic scaling behaviour of integral moments and that it is not observed in an analysis based on differential n-point correlation densities.

chao-dyn↗