T-duality diagram for a weakly curved background

Davidović, Ljubica; Nikolić, B.; Sazdović, B.

doi:10.1140/epjc/s10052-015-3808-8

Cited by 13 publications

(13 citation statements)

References 30 publications

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“…In this subsection we will finalize the process of T‐dualization dualizing along remaining z direction. For this purpose we will use generalized T‐dualization procedure . The result is a theory which is not well defined even locally and is known in literature as theory with R ‐flux.…”

Section: T‐dualization Of the Bosonic Closed String Actionmentioning

confidence: 99%

“…But, except this standard Buscher procedure, there is a generalized Buscher procedure dealing with background fields depending on all coordinates. The generalized procedure was applied to the case of bosonic string moving in the weakly curved background and in the case where metric is quadratic in coordinates and Kalb‐Ramond field is linear function of coordinates . The generalized procedure enables us to make T‐dualization in mentioned cases along arbitrary subset of coordinates.…”

Section: Introductionmentioning

confidence: 99%

“…This is a consequence of the imposed trivial winding conditions. Having in mind the generalized T‐duality procedure, T‐dualization along z coordinate produces R flux nonlocal theory because it depends on the variable

Δ V

which is defined as line integral. Calculating Poisson brackets of the T‐dual coordinates we obtain two nonzero Poisson brackets and show that there is a correlation between non‐locality and closed string noncommutativity.…”

Section: Introductionmentioning

confidence: 99%

“…Nonassociativity parameter, R flux, is proportional to the field strength H . Using generalized T‐duality we obtain the concrete form of nonassociativity from string dynamics. Similar as noncommutativity, discovery of nonassociativity pushes the scientists to explore the effects of nonassociativity in the field of renormalisability of ϕ 4 theory as well as formulation of nonassociative gravity…”

Section: Introductionmentioning

confidence: 99%

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Noncommutativity and Nonassociativity of Closed Bosonic String on T‐dual Toroidal Backgrounds

Nikolić

Obrić

2018

Fortschritte der Physik

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In this article we consider closed bosonic string in the presence of constant metric and Kalb‐Ramond field with one non‐zero component, Bxy=Hz, where field strength H is infinitesimal. Using Buscher T‐duality procedure we dualize along x and y directions and using generalized T‐duality procedure along z direction imposing trivial winding conditions. After first two T‐dualizations we obtain Q flux theory which is just locally well defined, while after all three T‐dualizations we obtain nonlocal R flux theory. Origin of non‐locality is variable ΔV defined as line integral, which appears as an argument of the background fields. Rewriting T‐dual transformation laws in the canonical form and using standard Poisson algebra, we obtained that Q flux theory is commutative one and the R flux theory is noncommutative and nonassociative one. Consequently, there is a correlation between non‐locality and closed string noncommutativity and nonassociativity.

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Section: T‐dualization Of the Bosonic Closed String Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Δ V

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Noncommutativity and Nonassociativity of Closed Bosonic String on T‐dual Toroidal Backgrounds

Nikolić

Obrić

2018

Fortschritte der Physik

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“…The same relation, however, does not hold in more complicated backgrounds, when T-duality is performed along the nonisometry directions or in backgrounds without the global shift symmetry. These backgrounds were discussed in [17][18][19] where the generalized T-dualization procedure, applicable along an arbitrary spacetime direction was presented and elaborated.…”

Section: T-duality Of the Closed String Symmetry Generatorsmentioning

confidence: 99%

The T-dual symmetries of a bosonic string

Davidović

Sazdović

2018

Eur. Phys. J. C

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We investigate whether the symmetry transformations of a bosonic string are connected by T-duality. We start with a standard closed string theory. We continue with a modified open string theory, modified to preserve the symmetry transformations possessed by the closed string theory. Because the string theory is conformally invariant worldsheet field theory, in order to find the transformations which preserve the physics, one has to demand the isomorphism between the conformal field theories corresponding to the initial and the transformed field configurations. We find the symmetry transformations corresponding to the similarity transformation of the energy-momentum tensor, and find that their generators are T-dual. Particularly, we find that the general coordinate and local gauge transformations are T-dual, so we conclude that T-duality in addition to the well-known exchanges, transforms symmetries of the initial and its T-dual theory into each other.

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Noncommutativity and Nonassociativity of Type II Superstring with Coordinate Dependent RR Field

Nikolić

Obrić

Sazdović

2022

Fortschritte der Physik

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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 trueθ¯α$\bar{\theta }^\alpha$, while nonassociativity parameter is a constant tensor containing infinitesimal Cμαβ$C^{\alpha \beta }_\mu$.

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T-duality diagram for a weakly curved background

Cited by 13 publications

References 30 publications

Noncommutativity and Nonassociativity of Closed Bosonic String on T‐dual Toroidal Backgrounds

Noncommutativity and Nonassociativity of Closed Bosonic String on T‐dual Toroidal Backgrounds

The T-dual symmetries of a bosonic string

Noncommutativity and Nonassociativity of Type II Superstring with Coordinate Dependent RR Field

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