arXiv research

QP perspective on Poisson-Lie T-duality topology changes.

For a particular class of backgrounds, equations of motion for string sigma models targeted in mutually dual Poisson-Lie groups are equivalent. This phenomenon is called the Poisson-Lie T-duality. On the level of the corresponding string effective actions, the situation becomes more complicated due to the presence of t…

We use a generalized Ricci tensor, defined for generalized metrics in Courant algebroids, to show that Poisson-Lie T-duality is compatible with the 1-loop renormalization group.

We reexamine the notions of generalized Ricci tensor and scalar curvature on a general Courant algebroid, reformulate them using objects natural w.r.t. pull-backs and reductions, and obtain them from the variation of a natural action functional. This allows us to prove, in a very general setup, the compatibility of the…

Extending our reduction construction in \cite{Hu} to the Hamiltonian action of a Poisson Lie group, we show that generalized Kähler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show that the constructions in string theory of the (geometrical) $T$-dua…

These letters, written in 1998-2000, contain various basic results about Courant algebroids (CAs), such as classification of exact and transitive CAs, reduction of CAs, description in terms of symplectic dg manifolds, a canonical generating Dirac operator, and a relation with Poisson-Lie T-duality.

This thesis proposes a global geometric formulation of Extended Field Theories.

A new, simplified form of 10D supergravity action is derived up to all fermion orders.

Courant algebroids provide a useful mathematical tool (not only) in string theory. It is thus important to define and examine their morphisms. To some extent, this was done before using an analogue of canonical relations known from symplectic geometry. However, it turns out that applications in physics require a more g…

The paper explores the connection between Poisson-Lie structures and invariant volume forms in Hamiltonian dynamics.

We show that for any coboundary Poisson Lie group G, the Poisson structure on G^* is linearizable at the group unit. This strengthens a result of Enriquez-Etingof-Marshall, who had established formal linearizability of G^* for quasi-triangular Poisson Lie groups G. We also prove linearizability properties for the group…

The paper proves T-duality and Hori formulae for winding loop spaces.

Equivariant T-duality connects bundles with twists.

New structure on unitary group of Hilbert space.

The paper establishes T-duality for 2D σ-models with H-flux.

Unified framework for T-duality in both trivial and non-trivial topologies.

This dissertation explores T-duality between hyperkähler structures and branes on algebraic integrable systems.

We study generalized complex structures and $T$-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called "Infinitesimal $T$-duality". As an application we deal with the problem of finding symplectic stru…

Let $(G,Π_{G},\tilde{g})$ be a Poisson-Lie group equipped with a left invariant pseudo-Riemannian metric $\tilde{g}$ and let $(TG,Π_{TG},\tilde{g}^{c})$ be the Sanchez de Alvarez tangent Poisson-Lie group of $G$ equipped with the left invariant pseudo-Riemannian metric $\tilde{g}^{c}$, complete lift of $\tilde{g}$. In …

Symplectic manifolds which are homogeneous spaces of Poisson-Lie groups are studied in this paper. We show that these spaces are, under certain assumptions, covering spaces of dressing orbits of the Poisson-Lie groups which act on them. The effect of the Poisson induction procedure on such spaces is also examined, thus…

Unified framework for exceptional and generalised geometry, and Poisson-Lie duality.

New approach to T-duality using Courant algebroids.

We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson actions, the double group of a Poisson-Lie group and the reduction of Poisson manifold…

Extends T-duality to more general fibrations, proving isomorphic cohomology and algebroids.

We construct a Poisson isomorphism between the formal Poisson manifolds g^* and G^*, where g is a finite dimensional quasitriangular Lie bialgebra. Here g^* is equipped with its Lie-Poisson (or Kostant-Kirillov-Souriau) structure, and G^* with its Poisson-Lie structure. We also quantize Poisson-Lie dynamical r-matrices…

New spherical T-duality for higher degree forms in fiber bundles.

Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of mot…

We establish a higher generalization of super L-infinity-algebraic T-duality of super WZW-terms for super p-branes. In particular, we demonstrate spherical T-duality of super M5-branes propagating on exceptional-geometric 11d super spacetime.

In this paper, we use reduction by extended actions to give a construction of transitive Courant algebroids from string classes. We prove that T-duality commutes with the reductions and thereby determine global conditions for the existence of T-duals in heterotic string theory. In particular we find that T-duality exch…

New approach simplifies topological T-duality for torus bundles.

Extends T-duality to non-principal torus actions with elliptic tangent bundles.

We give a precise formulation of T-duality for Ramond-Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differential K-theory of certain principal torus bundles. Our result combines topological T-duality with the Buscher rules found in physics.

The notions of \emph{Poisson Lie group} and \emph{Poisson homogeneous space} are extended to the Dirac category. The theorem of Drinfel$'$d (\cite{Drinfeld93}) on the one-to-one correspondence between Poisson homogeneous spaces of a Poisson Lie group and a special class of Lagrangian subalgebras of the Lie bialgebra as…

Defines T-duality and generalised Ricci flow relations using Courant algebroid relations.

Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality trivialises the bulk-boundary correspondence in 2 dimensions. In this paper, we partially generalise these results to higher dimensions and briefly discuss the 4D quantum Hall effect.

Spherical T-duality for iterated sphere bundles

The paper defines projective structures for Lie bialgebras and Poisson-Lie groups.

We study generalized almost contact structures on odd-dimensional manifolds. We introduce a notion of integrability and show that the class of these structures is closed under symmetries of the Courant-Dorfman bracket, including T-duality. We define a notion of geometric type for generalized almost contact structures, …

It is known that the topological T-duality exchanges $H$ and $F$-fluxes. In this paper, we reformulate the topological T-duality as an exchange of two Lie algebroids in the generalized tangent bundle. Then, we apply the same formulation to the Poisson-generalized geometry, which is introduced in arXiv:1408.2649 to defi…

We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically distinct torus bundles, and prescribes a method for transporting geometrical structu…

Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that…

Study spherical T-duality and Massey products in iterated sphere bundles.

We introduce spherical T-duality, which relates pairs of the form $(P,H)$ consisting of a principal $SU(2)$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$. Intuitively spherical T-duality exchanges $H$ with the second Chern class $c_2(P)$. Unless $dim(M)\leq 4$, not all pairs admit spherical T-duals and the spheric…

We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group $G$ on a Poisson manifold $M$, we find an explicit description of the lifted hamiltonian act…

Invariant $r^\sharp$ predicts H-flux behavior under T-duality.

A Poisson-Lie group acting by the coadjoint action on the dual of its Lie algebra induces on it a non-trivial class of quadratic Poisson structures extending the linear Poisson bracket on the coadjoint orbits.

Paper establishes loop space T-duality formulae and refines earlier work.

Theory of T-duality for transitive Courant algebroids developed.