Search

In this paper we will consider noncommutativity that arises from bosonic T‐dualization of type II superstring in presence of Ramond‐Ramond (RR) field, which linearly depends on the bosonic coordinates xμ$x^\mu$. The derivative of the RR field Cμαβ$C^{\alpha \beta }_\mu$ is infinitesimal. We will employ generalized Buscher procedure that can be applied to cases that have coordinate dependent background fields. Bosonic part of newly obtained T‐dual theory is non‐local. It is defined in non‐geometric space spanned by Lagrange multipliers yμ$y_\mu$. We will apply generalized Buscher procedure once more on T‐dual theory and prove that original theory can be salvaged. Finally, we will use T‐dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T‐dual theory and nonassociativity relation. Noncommutativity parameter depends on the supercoordinates xμ$x^\mu$, θα$\theta ^\alpha$ and θ¯α$\bar{\theta }^\alpha$, while nonassociativity parameter is a constant tensor containing infinitesimal Cμαβ$C^{\alpha \beta }_\mu$. Here noncommutativity will be considered that arises from bosonic T‐dualization of type II superstring in presence of Ramond‐Ramond (RR) field, which linearly depends on the bosonic coordinates xμ. The derivative of the RR field Cμαβ is infinitesimal. A generalized Buscher procedure will be employed that can be applied to cases that have coordinate dependent background fields. Bosonic part of newly obtained T‐dual theory is non‐local. It is defined in non‐geometric space spanned by Lagrange multipliers yμ. The authors will apply generalized Buscher procedure once more on T‐dual theory and prove that original theory can be salvaged. Finally, they will use T‐dual transformation laws along with Poisson brackets of original theory to derive Poisson bracket structure of T‐dual theory and nonassociativity relation. Noncommutativity parameter depends on the supercoordinates xμ, θα, while nonassociativity parameter is a constant tensor containing infinitesimal Cμαβ. [ABSTRACT FROM AUTHOR]

We consider the symmetries of a closed bosonic string, starting with the general coordinate transformations. Their generator takes vector components ξμ as its parameter and its Poisson bracket algebra gives rise to the Lie bracket of its parameters. We are going to extend this generator in order for it to be invariant upon self T-duality, i.e. T-duality realized in the same phase space. The new generator is a function of a 2D double symmetry parameter Λ, that is a direct sum of vector components ξμ, and 1-form components λμ. The Poisson bracket algebra of a new generator produces the Courant bracket in a same way that the algebra of the general coordinate transformations produces Lie bracket. In that sense, the Courant bracket is T-dual invariant extension of the Lie bracket. When the Kalb-Ramond field is introduced to the model, the generator governing both general coordinate and local gauge symmetries is constructed. It is no longer self T-dual and its algebra gives rise to the B-twisted Courant bracket, while in its self T-dual description, the relevant bracket becomes the θ-twisted Courant bracket. Next, we consider the T-duality and the symmetry parameters that depend on both the initial coordinates xμ and T-dual coordinates yμ. The generator of these transformations is defined as an inner product in a double space and its algebra gives rise to the C-bracket. [ABSTRACT FROM AUTHOR]

Bosonic string moving in coordinate dependent background fields is considered. We calculate the generalized currents Poisson bracket algebra and find that it gives rise to the Courant bracket, twisted by a 2-form 2 B μ ν . Furthermore, we consider the T-dual generalized currents and obtain their Poisson bracket algebra. It gives rise to the Roytenberg bracket, equivalent to the Courant bracket twisted by a bi-vector Π μ ν , in case of Π μ ν = 2 ⋆ B μ ν = κ θ μ ν . We conclude that the twisted Courant and Roytenberg brackets are T-dual, when the quantities used for their deformations are mutually T-dual. [ABSTRACT FROM AUTHOR]

The role of double space is essential in the new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of the open string is missing in such an approach because until now there has been no appropriate formulation of open string T-duality. In the previous paper (Sazdović, From geometry to non-geometry via T-duality, arXiv:1606.01938, 2017), we showed how to introduce vector gauge fields AaN and AiD at the end-points of an open string in order to enable open string invariance under local gauge transformations of the Kalb–Ramond field and its T-dual “restricted general coordinate transformations”. We demonstrated that gauge fields AaN and AiD are T-dual to each other. In the present article we prove that all above results can be interpreted as coordinate permutations in double space. [ABSTRACT FROM AUTHOR]

We consider the closed string moving in a weakly curved background and its totally T-dualized background. Using T-duality transformation laws, we find the structure of the Poisson brackets in the T-dual space corresponding to the fundamental Poisson brackets in the original theory. From this structure we see that the commutative original theory is equivalent to the non-commutative T-dual theory, whose Poisson brackets are proportional to the background fluxes times winding and momentum numbers. The non-commutative theory of the present article is more nongeometrical than T-folds and in the case of three space-time dimensions corresponds to the nongeometric space-time with $$R$$ -flux. [ABSTRACT FROM AUTHOR]

We investigate the open string propagation in a weakly curved background with the Kalb-Ramond field containing an infinitesimal part, linear in the coordinate. Solving the Neumann boundary conditions, we find the expression for the space-time coordinates in terms of the effective ones. So, the initial theory reduces to the effective one. This effective theory is defined on the non-geometric doubled space $(q^{\mu},\tilde{q}_{\mu})$, where q is the effective coordinate and $\tilde{q}_{\mu}$ is its T-dual. The effective metric depends on the coordinate q and there exists a non-trivial effective Kalb-Ramond field which depends on the T-dual coordinate $\tilde{q}_{\mu}$. The fact that $\tilde{q}_{\mu}$ is Ω-odd leads to the nonvanishing effective Kalb-Ramond field. [ABSTRACT FROM AUTHOR]

In the present article, we derive the space-time action of the bosonic string in terms of geometrical quantities. First, we study the space-time geometry felt by a probe bosonic string moving in antisymmetric and dilaton background fields. We show that the presence of the antisymmetric field leads to space-time torsion, and the presence of the dilaton field leads to space-time non-metricity. Using these results we obtain the integration measure for space-time with stringy non-metricity, requiring its preservation under parallel transport. We derive the Lagrangian depending on stringy curvature, torsion and non-metricity. [ABSTRACT FROM AUTHOR]

It is well known that the space-time coordinates $x^\mu$ and the corresponding D p-brane world-volume become non-commutative when the ends of the open string are attached to a D p-brane with the Neveu-Schwarz background field $B_{\mu \nu}$ . In this paper, we extend these considerations by including an additional dilaton field $\Phi$ , linear in $x^\mu$ . In that case, the conformal part of the world-sheet metric becomes a new non-commutative variable, while the coordinate in the direction orthogonal to the hyper plane $\Phi = {\mathrm {const}}$ becomes commutative. [ABSTRACT FROM AUTHOR]

We investigate classical dynamics of the bosonic string in the background metric, antisymmetric and dilaton fields. We use canonical methods to find Hamiltonian in terms of energy–momentum tensor components. The later are secondary constraints of the theory. Due to the presence of the dilaton field the Virasoro generators have nonlinear realization. We find that, in the curve space–time, opposite chirality currents do not commute. As a consequence of the two-dimensional general covariance, the energy–momentum tensor components satisfy two Virasoro algebras, even in the curve space–time. We emphasize that background antisymmetric and dilaton fields are the origin of space–time torsion and space–time nonmetricity, respectively. [ABSTRACT FROM AUTHOR]

Using the canonical method developed for anomalous theories, we present the independent rederivation of the quantum relationship between the massive Thirring and the sine-Gordon models. The same method offers the possibility to obtain the Mandelstam soliton operators as a solution of the Poisson brackets "equation" for the fermionic fields. We checked the anticommutation and basic Poisson brackets relations for these composite operators. The transition from the Flamiltonian to the corresponding Lagrangian variables produces the known Mandelstam's result. [ABSTRACT FROM AUTHOR]

Using canonical method the Liouville theory has been obtained as a gravitational Wess-Zumino action of the Polyakov string. From this approach it is clear that the form of the Liouville action is the consequence of the bosonic representation of the Virasoro algebra, and that the coefficient in front of the action is proportional to the central charge and measures the quantum braking of the classical symmetry. [ABSTRACT FROM AUTHOR]

A generalized BRST formalism is developed and used to study the quantization of the Siegel superparticle. The method provides an off-shell nilpotent BRST symmetry of the gauge-fixed, quantum action. The construction relies on the structure of the classical gauge algebra, and is realized by introducing a set of auxiliary, nonphysical variables. The elimination of these variables reduces the theory to the Batalin-Vilkovisky form. [ABSTRACT FROM AUTHOR]

In this article we present bosonic T-dualization in double space of the type II superstring theory in the pure spinor formulation. We use the action with constant background fields obtained from the general case under some physically and mathematically justified assumptions. Unlike Nikolić and Sazdović (EPJ C 77:197, 2017), where we used the first-order theory, in this article fermionic momenta are integrated out. Full T-dualization in double space is represented as a permutation of the initial x μ and T-dual coordinates y μ . Requiring that a T-dual transformation law of the T-dual double coordinate ⋆ Z M = (y μ , x μ) to be of the same form as for initial one Z M = (x μ , y μ) , we obtain the form of the T-dual background fields in terms of the initial ones. The advantage of using the action with integrated fermionic momenta is that it gives all T-dual background fields in terms of the initial ones. In the case of the first-order theory Nikolić and Sazdović (2017) a T-dual R-R field strength was obtained out of the double space formalism under additional assumptions. [ABSTRACT FROM AUTHOR]

In this article we consider simultaneous T-dualization of the type II superstring action in a pure spinor formulation. Simultaneous T-dualization means that we make T-dualization at the same time along some subset of initial coordinates denoted by xa. The only imposed assumption stems from the applicability of the Buscher T-dualization procedure—background fields do not depend on the dualized directions xa. In this way we obtain the full form of the T-dual background fields and T-dual transformation laws. Because the two chiral sectors transform differently, there are two sets of vielbeins and gamma matrices connected by a local Lorentz transformation. Its spinorial representation is the same as in the constant background case. We also found the full expression for the T-dual dilaton field. [ABSTRACT FROM AUTHOR]