620,171 research outputs found

    Seiberg-Witten Monopole Equations on Noncommutative R^4

    Full text link
    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_\theta of 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.Comment: 33 pages, v2: typos corrected, to appear in J.Math.Phy

    Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds

    Get PDF
    An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finite-energy solutions are necessarily BPS. In this paper we present a study of this basic question in the context of the domain wall equations whose potential is induced from a superpotential so that the ground states are the critical points of the superpotential. We prove that the definiteness of the Hessian of the superpotential suffices to ensure that all finite-energy domain-wall solutions are BPS. We give several examples to show that such a BPS property may fail such that non-BPS solutions exist when the Hessian of the superpotential is indefinite.Comment: 25 page

    Polynomial solutions to the WDVV equations in four dimensions

    Get PDF
    All polynomial solutions of the WDVV equations for the case n = 4 are determined. We find all five solutions predicted by Dubrovin, namely those corresponding to Frobenius structures on orbit spaces of finite Coxeter groups. Moreover we find two additional series of polynomial solutions of which one series is of semi-simple type (massive). This result supports Dubrovin's conjecture if modified appropriately

    The Role of Boundary Conditions in Solving Finite-Energy, Two-Body, Bound-State Bethe-Salpeter Equations

    Full text link
    The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary conditions. The method discussed here for solving the Bethe-Salpeter equation requires only that the equation can be Wick rotated and that the two angular variables associated with rotations in three-dimensional space can be separated, properties that are possessed by many Bethe-Salpeter equations including all two-body, bound-state Bethe-Salpeter equations in the ladder approximation. The efficacy of the method is demonstrated by calculating finite-energy solutions to the partially-separated Bethe-Salpeter equation describing the Wick-Cutkosky model when the constituents do not have equal masses.Comment: 18 page

    Chern-Simons Solitons, Toda Theories and the Chiral Model

    Full text link
    The two-dimensional self-dual Chern--Simons equations are equivalent to the conditions for static, zero-energy solutions of the (2+1)(2+1)-dimensional gauged nonlinear Schr\"odinger equation with Chern--Simons matter-gauge dynamics. In this paper we classify all finite charge SU(N)SU(N) solutions by first transforming the self-dual Chern--Simons equations into the two-dimensional chiral model (or harmonic map) equations, and then using the Uhlenbeck--Wood classification of harmonic maps into the unitary groups. This construction also leads to a new relationship between the SU(N)SU(N) Toda and SU(N)SU(N) chiral model solutions
    corecore