Related papers: Double Field Theory and Geometric Quantisation
The zero modes of closed strings on a torus --the torus coordinates plus dual coordinates conjugate to winding number-- parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be…
Consider a fiber bundle in which the total space, the base space and the fiber are all symplectic manifolds. We study the relations between the quantization of these spaces. In particular, we discuss the geometric quantization of a vector…
Duality covariant curvature and torsion tensors in double field theory/generalized geometry are central in analyzing consistent truncations, generalized dualities, and related integrable $\sigma$-models. They are constructed systematically…
We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…
We consider the linear space of composite fields as an infinite dimensional vector bundle over the theory space whose coordinates are simply the parameters of a renormalized field theory. We discuss a geometrical expression for the short…
We formulate a kinematical extension of Double Field Theory on a $2d$-dimensional para-Hermitian manifold $(\mathcal{P},\eta,\omega)$ where the $O(d,d)$ metric $\eta$ is supplemented by an almost symplectic two-form $\omega$. Together…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
Reconsideration of the T-duality of the open string allows us to introduce some geometric features in non-geometric theories. First, we have found what symmetry is T-dual to the local gauge transformations. It includes transformations of…
We investigate $\alpha'$ corrections of bosonic strings in the framework of double field theory. The previously introduced "doubled $\alpha'$-geometry" gives $\alpha'$-deformed gauge transformations arising in the Green-Schwarz anomaly…
T-Duality is a poorly understood symmetry of the space-time fields of string theory that interchanges long and short distances. It is best understood in the context of toroidal compactification where, loosely speaking, radii of the torus…
Quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of…
In this article we offer the new interpretation of T-dualization procedure of type II superstring theory in double space framework. We use the ghost free action of type II superstring in pure spinor formulation in approximation of constant…
Poisson-Lie (PL) T-duality has received much attention over the last five years in connection with integrable string worldsheet theories. At the level of the worldsheet, the algebraic structure underpinning these connections is made…
Classical target space duality transformations are studied for the non-linear sigma model with a dilaton field. Working within the framework of the Hamiltonian formalism we require the duality transformation to be a property only of the…
Complex geometry and symplectic geometry are mirrors in string theory. The recently developed generalised complex geometry interpolates between the two of them. On the other hand, the classical and quantum mechanics of a finite number of…
By doubling the target space of a canonical Courant algebroid and subsequently projecting down to a specific subbundle, we identify the data of double field theory (DFT) and hence define its algebroid structure. We specify the properties of…
We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We…
We construct an action for double field theory using a metric connection that is compatible with both the generalised metric and the O_{D,D} structure. The connection is simultaneously torsionful and flat. Using this connection one may…
The main principles of two-dimensional quantum field theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of…
Toroidal backgrounds for bosonic strings are used to understand target space duality as a symmetry of string field theory and to study explicitly issues in background independence. Our starting point is the notion that the string field…