Related papers: Plane-parallel waves as Jacobi-Lie models
We observe that the replacement of the Riemann curvature with the generalized Riemann curvature into the corrections to the type II supergravity at order $\alpha'^3$ which are in terms of the contractions of four Riemann curvatures $R^4$,…
We introduce a new class of two dimensional gravity models using ideas motivated by the Teleparallel Equivalent of General Relativity. This leads to a rather natural formulation of a theory that has close links with Jackiw-Teitelboim…
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their…
Lie algebras of dimension $n$ are defined by their structure constants , which can be seen as sets of $N = n^2 (n -- 1)/2$ scalars (if we take into account the skew-symmetry condition) to which the Jacobi identity imposes certain quadratic…
General Relativity reduced to two dimensions possesses a large group of symmetries that exchange classical solutions. The associated Lie algebra is known to contain the affine Kac-Moody algebra $A_1^{(1)}$ and half of a real Witt algebra.…
The purpose of the present thesis is to give a self-contained review of the solvable Lie algebra approach to supergravity problems related with S, T and U dualities. After recalling the general features of dualities in both Superstring…
A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving…
We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves…
Spectral flow in two-dimensional field theories is known to correspond to geometrical twisting between two circles in the gravity dual. We generalize this operation to the geometries which have SO(k+1) x SO(k+1) isometries with k>1 and…
The most general parallelizable pp-wave backgrounds which are non-dilatonic solutions in the NS-NS sector of type IIA and IIB string theories are considered. We demonstrate that parallelizable pp-wave backgrounds are necessarily homogeneous…
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally…
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that…
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…
The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory, whose mathematical structure can be…
Extreme 4-dimensional dilaton black holes embedded into 10-dimensional geometry are shown to be dual to the gravitational waves in string theory. The corresponding gravitational waves are the generalization of pp-fronted waves, called…
We study the noncommutative superspace of arbitrary dimensions in a systematic way. Superfield theories on a noncommutative superspace can be formulated in two folds, through the star product formalism and in terms of the supermatrices. We…
Poisson-Lie T-plurality constructs a chain of supergravity solutions from a Poisson-Lie symmetric solution. We study the Poisson-Lie T-plurality for supergravity solutions with $H$-flux, which are not Poisson-Lie symmetric but admit…
We introduce the concept of duality between quantum field theories in the Batalin-Vilkovisky formalism, which is interpreted either as a BV morphism, the result of dual BV pushforwards or a combination of both. When a BV morphism affects…
We examine the known Riemann curvature corrections to the supergravity action at order $\alpha'^3$ under the T-duality transformations. Using the compatibility of the action with the linear T-duality and with the S-matrix calculations as…
We introduce a new 2-parameter family of sigma models exhibiting Poisson-Lie T-duality on a quasitriangular Poisson-Lie group $G$. The models contain previously known models as well as a new 1-parameter line of models having the novel…