15,567 research outputs found

    Three Dimensional Topological Field Theory induced from Generalized Complex Structure

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    We construct a three-dimensional topological sigma model which is induced from a generalized complex structure on a target generalized complex manifold. This model is constructed from maps from a three-dimensional manifold XX to an arbitrary generalized complex manifold MM. The theory is invariant under the diffeomorphism on the world volume and the bb-transformation on the generalized complex structure. Moreover the model is manifestly invariant under the mirror symmetry. We derive from this model the Zucchini's two dimensional topological sigma model with a generalized complex structure as a boundary action on X\partial X. As a special case, we obtain three dimensional realization of a WZ-Poisson manifold.Comment: 18 page

    Couplings between a collection of BF models and a set of three-form gauge fields

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    Consistent interactions that can be added to a free, Abelian gauge theory comprising a collection of BF models and a set of three-form gauge fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smooth, local, PT invariant, Lorentz covariant, and Poincare invariant interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra.Comment: 17 page

    AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories

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    We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz- Zaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a three-dimensional topological sigma-model. Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action for the model.Comment: 13 pages, based on lectures at Rencontres mathematiques de Glanon 200

    QP-Structures of Degree 3 and 4D Topological Field Theory

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    A A BV algebra and a QP-structure of degree 3 is formulated. A QP-structure of degree 3 gives rise to Lie algebroids up to homotopy and its algebraic and geometric structure is analyzed. A new algebroid is constructed, which derives a new topological field theory in 4 dimensions by the AKSZ construction.Comment: 17 pages, Some errors and typos have been correcte

    The Functional Integral for a Free Particle on a Half-Plane

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    A free non-relativistic particle moving in two dimensions on a half-plane can be described by self-adjoint Hamiltonians characterized by boundary conditions imposed on the systems. The most general boundary condition is parameterized in terms of the elements of an infinite-dimensional matrix. We construct the Brownian functional integral for each of these self-adjoint Hamiltonians. Non-local boundary conditions are implemented by allowing the paths striking the boundary to jump to other locations on the boundary. Analytic continuation in time results in the Green's functions of the Schrodinger equation satisfying the boundary condition characterizing the self-adjoint Hamiltonian.Comment: 16 page

    An Alternative Topological Field Theory of Generalized Complex Geometry

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    We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is AA model in the case that the generalized complex structuredepends on only a symplectic structure. Our new model is BB model in the case that the generalized complex structure depends on only a complex structure.Comment: 29 pages, typos and references correcte

    Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras

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    The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in three dimensions induces the Courant algebroid structure on the target space as a sigma model. Deformations of BF theories in nn dimensions are also analyzed. Two dimensional deformed BF theory induces the Poisson structure and three dimensional deformed BF theory induces the Courant algebroid structure on the target space as a sigma model. The deformations of BF theories in nn dimensions induce the structures of Batalin-Vilkovisky algebras on the target space.Comment: 25 page

    High field superconducting phase diagrams including Fulde-Ferrell-Larkin-Ovchinnikov vortex states

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    Motivated by a striking observation of a Fulde-Ferell-Larkin-Ovchinnikov (FFLO) vortex state in the heavy fermion material CeCoIn5 in fields {\it perpendicular} to the superconducting planes (Hc{\bf H} \parallel c), superconducting phase diagrams including an FFLO state of quasi two-dimensional (Q2D) superconductors are systematically studied. In the clean {\it limit}, the high field superconducting state in the low temperature limit should be not the FFLO state modulating along H{\bf H}, appeared in CeCoIn5 in both Hc{\bf H} \parallel c and Hc{\bf H} \perp c, but a different vortex state with a modulation, induced by the paramagnetism, perpendicular to the field. It is found that the presence of weak impurities is the origin of the absence in CeCoIn5 of the latter state and leads to the Hc{\bf H} \parallel c phase diagram, as seen in CeCoIn5, {\it apparently} different in character from that in Hc{\bf H} \perp c.Comment: A reference was updated. To appear in Phys. Rev.
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