(Non-)commutative closed string on T-dual toroidal backgrounds

Andriot, David; Larfors, Magdalena; Lüst, Dieter; Patalong, Peter

doi:10.1007/jhep06(2013)021

Cited by 81 publications

(182 citation statements)

References 76 publications

Supporting

Mentioning

172

Contrasting

Order By: Relevance

“…M 3 also appeared as part of the internal manifold in the first example of axion monodromy inflation mechanism [36] (see [37,38] on the ten-dimensional completion of this cosmological model). A partial quantisation of closed strings on M 3 appeared in [39]. Since twisted tori are used as internal manifolds, it is important for string phenomenology to determine the corresponding low-energy effective theory in four dimensions.…”

Section: Jhep06(2016)169mentioning

confidence: 99%

Towards Kaluza-Klein Dark Matter on nilmanifolds

Andriot

Cacciapaglia

Deandrea

et al. 2016

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We present a first study of the field spectrum on a class of negatively-curved compact spaces: nilmanifolds or twisted tori. This is a case where analytical results can be obtained, allowing to check numerical methods. We focus on the Kaluza-Klein expansion of a scalar field. The results are then applied to a toy model where a natural Dark Matter candidate arises as a stable massive state of the bulk scalar.

show abstract

Section: Jhep06(2016)169mentioning

confidence: 99%

Towards Kaluza-Klein Dark Matter on nilmanifolds

Andriot

Cacciapaglia

Deandrea

et al. 2016

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…As the relations (2.4) describe a Heisenberg Lie algebra, the resulting quantum geometry is still associative. The same closed string noncommutativity relations were obtained by a linearized conformal field theory analysis in [48,14,20,5]. To linear order in the H-flux one can neglect the curvature backreaction of the geometry and still work on flat target space.…”

Section: Pos(icmp 2013)007mentioning

confidence: 64%

“…For example, both 2-cyclicity and 3-cyclicity hold, i.e., 5) showing that physical closed string states do not see noncommutativity or nonassociativity of the non-geometric flux background. In particular, when restricted to functions on configuration space M, the 3-product (4.3) reproduces the triproduct of [14] which was conjectured to reproduce offshell correlation functions of closed string tachyon vertex operators in R-space in a linearized conformal field theory analysis.…”

Section: Pos(icmp 2013)007mentioning

confidence: 99%

Nonassociative geometry and twist deformations in non-geometric string theory

Mylonas¹,

Schupp²,

Szabo

2014

Proceedings of Third International Satellite Conference on Mathematical Methods in Physics — PoS(ICMP 2013)

View full text Add to dashboard Cite

We describe nonassociative deformations of geometry probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of open membranes whose boundaries propagate in the phase space of the target space compactification, equiped with a twisted Poisson structure. The effective membrane target space is determined by the standard Courant algebroid over the target space twisted by an abelian gerbe in momentum space. Quantization of the membrane sigma-model leads to a proper quantization of the non-geometric background, which we relate to Kontsevich's formalism of global deformation quantization that constructs a noncommutative nonassociative star product on phase space. We construct Seiberg-Witten type maps between associative and nonassociative backgrounds, and show how they may realise a nonassociative deformation of gravity. We also explain how this approach is related to the quantization of certain Lie 2-algebras canonically associated to the twisted Courant algebroid, and cochain twist quantization using suitable quasi-Hopf algebras of symmetries in the phase space description of R-space which constructs a Drinfel'd twist with non-trivial 3-cocycle. We illustrate and apply our formalism to present a consistent phase space formulation of nonassociative quantum mechanics.

show abstract

“…In the cases we examined we found a mixing of the original coordinates and the would-be dual coordinates, which is indicative of doubled formulations, such as the doubled sigma models considered by Hull [32] or the ones recently studied in [33]. Last but not least, it would be very interesting to apply this formalism in the case of the triple T-dual of a torus with H flux, or equivalently to the T-dual of the Q flux background where no isometry is available (recent attempts to understand this problem include [34][35][36]), and even more so in cases of true string backgrounds. We will report on these and other issues in future publications.…”

Section: Jhep01(2016)154mentioning

confidence: 99%

T-duality without isometry via extended gauge symmetries of 2D sigma models

Chatzistavrakidis

Deser

Jonke

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail the possibility to perform T-duality along non-isometric directions. In particular, based on a recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge invariance for an extended set of gauge transformations imposes weaker constraints than in the standard case, notably the corresponding vector fields are not Killing. This formulation enables us to follow a procedure analogous to the derivation of the Buscher rules and obtain two dual models, by integrating out once the Lagrange multipliers and once the gauge fields. We show that this construction indeed works in non-trivial cases by examining an explicit class of examples based on step 2 nilmanifolds.

show abstract

(Non-)commutative closed string on T-dual toroidal backgrounds

Cited by 81 publications

References 76 publications

Towards Kaluza-Klein Dark Matter on nilmanifolds

Towards Kaluza-Klein Dark Matter on nilmanifolds

Nonassociative geometry and twist deformations in non-geometric string theory

T-duality without isometry via extended gauge symmetries of 2D sigma models

Contact Info

Product

Resources

About