T-Duality and Doubling of the Isotropic Rigid Rotator

Self Cite

We introduce a two-dimensional sigma model associated with a Jacobi manifold. The model is a generalisation of a Poisson sigma model providing a topological open string theory. In the Hamiltonian approach first class constraints are derived, which generate gauge invariance of the model under diffeomorphisms. The reduced phase space is finite-dimensional. By introducing a metric tensor on the target, a non-topological sigma model is obtained, yielding a Polyakov action with metric and B-field, whose target space is a Jacobi manifold.

Section: Jhep03(2021)110mentioning

confidence: 61%

Jacobi sigma models

Bascone

Pezzella

Vitale

2021

Self Cite

“…The notion of Poisson-Lie symmetry can also be formulated in the Hamiltonian formalism [73,75,[87][88][89]. We may state the following JHEP09(2020)060…”

Section: Jhep09(2020)060mentioning

confidence: 99%

“…In this paper we will follow an approach already proven to be successful for the Principal Chiral Model (PCM) [73], where Poisson-Lie symmetries of the PCM with target space the manifold of SU (2) are investigated. The guiding idea is already present in ref.s [74][75][76] where the simplest example of dynamics on a Lie group, the three-dimensional Isotropic Rigid Rotator, was considered as a one-dimensional sigma model having R as source space and SU (2) as target space. It is interesting to note that already in such a simple case, many aspects of Poisson-Lie T-duality can be exploited, and especially some relations with Doubled Geometry, although the model is too simple to exhibit manifest invariance.…”

Section: Introductionmentioning

confidence: 99%

Poisson-Lie T-duality of WZW model via current algebra deformation

Bascone¹,

Pezzella²,

Vitale³

2020

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Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of SU(2) as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $$ \mathfrak{su}(2)\left(\mathrm{\mathbb{R}}\right)\overset{\cdot }{\oplus}\mathfrak{a} $$ su 2 ℝ ⊕ ⋅ a , to the fully semisimple Kac-Moody algebra $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{C}}\right)\left(\mathrm{\mathbb{R}}\right) $$ sl 2 ℂ ℝ . A two-parameter family of models with SL(2, ℂ) as target phase space is obtained so that Poisson-Lie T-duality is realised as an O(3, 3) rotation in the phase space. The dual family shares the same phase space but its configuration space is SB(2, ℂ), the Poisson-Lie dual of the group SU(2). A parent action with doubled degrees of freedom on SL(2, ℂ) is defined, together with its Hamiltonian description.

“…Using this gauged one-form, we can define a gauge invariant and (arguably) physically meaningful proper length in doubled spacetime as a path integral over the gauge connection [76], recover the doubled (and gauged) string action by Hull [29] [31], and extend to Green-Schwarz superstring [34], U-duality covariant exceptional string actions [35,36] as well as point-like particle actions [33,[37][38][39] (see (2.12) later).…”

Section: Coordinate Gauge Symmetrymentioning

confidence: 99%

“…The section condition has been argued to imply that the doubled coordinates are actually gauged: a gauge orbit or an equivalence class in the doubled coordinate space corresponds to a single physical point [28]. This idea of 'coordinate gauge symmetry' is naturally realized in sigma models where the doubled target spacetime coordinates are dynamical fields and thus can be genuinely gauged [29][30][31][32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

A note on Faddeev-Popov action for doubled-yet-gauged particle and graded Poisson geometry

Basile

Joung

Park

2020

The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev-Popov ghosts matches with the graded Poisson geometry that has been recently used to describe the symmetries of Double Field Theory. Besides, by requiring target spacetime diffeomorphisms at the quantum level, we derive quantum corrections to the classical action involving dilaton, which are analogous to the Fradkin-Tseytlin term on string worldsheet. arXiv:1910.13120v1 [hep-th] 29 Oct 2019 to DFT. Section 2 contains our main results which split into three parts. Firstly, we introduce a constant projector into a section, and using this we reformulate the section condition as well as the coordinate gauge symmetry. Secondly, we consider the BRST formulation of the doubled-yet-gauged particle action [33], and point out its connection to the graded Poisson geometry [62,63]. Thirdly, by requiring target space-