On open-closed extension of boundary string field theory

We investigate a classical open-closed string field theory whose open string sector is given by boundary string field theory. The open-closed interaction is introduced by the overlap of a boundary state with a closed string field. With the help of the Batalin-Vilkovisky formalism, the closed string sector is determined to be the HIKKO closed string field theory. We also discuss the gauge invariance of this theory in both open and closed string sides.Comment: 25 pages, 2 figures, comments and a reference added, typos correcte

Boundary states, matrix factorisations and correlation functions for the E-models

The open string spectra of the B-type D-branes of the N=2 E-models are calculated. Using these results we match the boundary states to the matrix factorisations of the corresponding Landau-Ginzburg models. The identification allows us to calculate specific terms in the effective brane superpotential of E_6 using conformal field theory methods, thereby enabling us to test results recently obtained in this context.Comment: 20 pages, no figure

Rigidity and defect actions in Landau-Ginzburg models

Studying two-dimensional field theories in the presence of defect lines naturally gives rise to monoidal categories: their objects are the different (topological) defect conditions, their morphisms are junction fields, and their tensor product describes the fusion of defects. These categories should be equipped with a duality operation corresponding to reversing the orientation of the defect line, providing a rigid and pivotal structure. We make this structure explicit in topological Landau-Ginzburg models with potential x^d, where defects are described by matrix factorisations of x^d-y^d. The duality allows to compute an action of defects on bulk fields, which we compare to the corresponding N=2 conformal field theories. We find that the two actions differ by phases.Comment: 53 pages; v2: clarified exposition of pivotal structures, corrected proof of theorem 2.13, added remark 3.9; version to appear in CM

Matrix Factorizations, Minimal Models and Massey Products

We present a method to compute the full non-linear deformations of matrix factorizations for ADE minimal models. This method is based on the calculation of higher products in the cohomology, called Massey products. The algorithm yields a polynomial ring whose vanishing relations encode the obstructions of the deformations of the D-branes characterized by these matrix factorizations. This coincides with the critical locus of the effective superpotential which can be computed by integrating these relations. Our results for the effective superpotential are in agreement with those obtained from solving the A-infinity relations. We point out a relation to the superpotentials of Kazama-Suzuki models. We will illustrate our findings by various examples, putting emphasis on the E_6 minimal model.Comment: 32 pages, v2: typos corrected, v3: additional comments concerning the bulk-boundary crossing constraint, some small clarifications, typo

Triangle-generation in topological D-brane categories

Tachyon condensation in topological Landau-Ginzburg models can generally be studied using methods of commutative algebra and properties of triangulated categories. The efficiency of this approach is demonstrated by explicitly proving that every D-brane system in all minimal models of type ADE can be generated from only one or two fundamental branes.Comment: 34 page

L∞L_\infty-Algebras, the BV Formalism, and Classical Fields

We summarise some of our recent works on $L_\infty$-algebras and quasi-groups with regard to higher principal bundles and their applications in twistor theory and gauge theory. In particular, after a lightning review of $L_\infty$-algebras, we discuss their Maurer-Cartan theory and explain that any classical field theory admitting an action can be reformulated in this context with the help of the Batalin-Vilkovisky formalism. As examples, we explore higher Chern-Simons theory and Yang-Mills theory. We also explain how these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of $L_\infty$-quasi-isomorphisms, and we propose a twistor space action.Comment: 19 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 201

Solitons on Noncommutative Torus as Elliptic Calogero Gaudin Models, Branes and Laughlin Wave Functions

For the noncommutative torus ${\cal T}$, in case of the N.C. parameter $\theta = \frac{Z}{n}$, we construct the basis of Hilbert space {\caH}_n$in terms of$\theta$functions of the positions$z_i$of$n$solitons. The wrapping around the torus generates the algebra${\cal A}_n$, which is the$Z_n \times Z_n$Heisenberg group on$\theta$functions. We find the generators$g$of an local elliptic$su(n)$, w$transform covariantly by the global gauge transformation of ${\cal A}$By acting on ${\cal H}_n$ we establish the isomorphism of ${\cal A}_n$$g$. We embed this $g$ into the $L$-matrix of the elliptic Gaudin and$models to give the dynamics. The moment map of this twisted cotangent$su_n({\cal T})$bundle is matched to the$D$-equation with Fayet-Illiopoulos source term, so the dynamics of the N.C. solitons becomes that of the brane. The geometric configuration$(k, u)$of th$spectral curve ${\rm det}|L(u) - k| = 0$ describes the brane configuration, with the dynamical variables $z_i$ of N.C. solitons as$moduli$T^{\otimes n} / S_n$. Furthermore, in the N.C. Chern-Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map eqaution$the N.C. $su_n({\cal T})$ cotangent bundle with marked points. The eigenfunction of the Gaudin differential $L$-operators as the Laughli$wavefunction is solved by Bethe ansatz.Comment: 25 pages, plain latex, no figure

On the contribution of the horizontal sea-bed displacements into the tsunami generation process

The main reason for the generation of tsunamis is the deformation of the bottom of the ocean caused by an underwater earthquake. Usually, only the vertical bottom motion is taken into account while the horizontal co-seismic displacements are neglected in the absence of landslides. In the present study we propose a methodology based on the well-known Okada solution to reconstruct in more details all components of the bottom coseismic displacements. Then, the sea-bed motion is coupled with a three-dimensional weakly nonlinear water wave solver which allows us to simulate a tsunami wave generation. We pay special attention to the evolution of kinetic and potential energies of the resulting wave while the contribution of the horizontal displacements into wave energy balance is also quantified. Such contribution of horizontal displacements to the tsunami generation has not been discussed before, and it is different from the existing approaches. The methods proposed in this study are illustrated on the July 17, 2006 Java tsunami and some more recent events.Comment: 30 pages; 14 figures. Accepted to Ocean Modelling. Other authors papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Tachyon Condensation on Noncommutative Torus

We discuss noncommutative solitons on a noncommutative torus and their application to tachyon condensation. In the large B limit, they can be exactly described by the Powers-Rieffel projection operators known in the mathematical literature. The resulting soliton spectrum is consistent with T-duality and is surprisingly interesting. It is shown that an instability arises for any D-branes, leading to the decay into many smaller D-branes. This phenomenon is the consequence of the fact that K-homology for type II von Neumann factor is labeled by R.Comment: LaTeX, 17 pages, 1 figur

Mirror duality and noncommutative tori

In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find a mirror correspondence on generalized complex tori and generalize the mirror duality on complex tori to the case of noncommutative complex tori.Comment: 22pages, no figure