Related papers: The role of string topology in symplectic field th…

In this paper we derive the symplectic framework for field theories defined by higher-order Lagrangians. The construction is based on the symplectic reduction of suitable spaces of iterated jets. The possibility of reducing a higher-order…

In this thesis we investigate topological aspects and arithmetic structures in quantum field theory and string theory. Particular focus is put on consistent truncations of supergravity and compactifications of F-theory.

Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…

The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex triples and holomorphic symplectic 2-forms on manifolds…

Generalizing local Gromov-Witten theory, in this paper we define a local version of symplectic field theory. When the symplectic manifold with cylindrical ends is four-dimensional and the underlying simple curve is regular by automatic…

Homotopy algebra and its involutive generalisation plays an important role in the construction of string field theory. I will review recent progress in these applications of homotopy algebra and its relation to moduli spaces.

We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…

We equip the whole space of fields of the triplectic formalism of Lagrangian quantization with an even supersymplectic structure and clarify its geometric meaning. We also discuss its relation to a closed two-form arising naturally in the…

In the symplectic Lagrangian framework we newly embed an irreducible massive vector-tensor theory into a gauge invariant system, which has become reducible, by extending the configuration space to include an additional pair of scalar and…

This is an expository account of some applications of string topology to the study of Lagrangian embeddings into symplectic manifolds, originally due to Fukaya, which was written as a contribution to a book on free loop spaces.

In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.

We define a symplectic structure on the space of non parametrized loops in $G_2$ manifold. We also develop some basics of intersection theory of Lagrangian submanifolds.

String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend…

This thesis is based on some selected topics in open topological string theory which I have worked on during my Ph.D. It comprises an introductory part where I have focused on the points most needed for the later chapters, trading…

I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for…

We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended…

We introduce the notion of a symplectic Lie affgebroid and their Lagrangian submanifolds in order to describe the Lagrangian (Hamiltonian) dynamics on a Lie affgebroid in terms of this type of structures. Several examples are discussed.

We discuss general properties of classical string field theories with symmetric vertices in the context of deformation theory. For a given conformal background there are many string field theories corresponding to different decomposition of…

We provide some constructions using Lagrangian cobordisms which improve known examples for some symplectic squeezing problems. Additionally, we prove a flexibility result that Lagrangian submanifolds which are Lagrangian isotopic are also…

We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity…