T-dualities and Doubled Geometry of the Principal Chiral Model

Marotta, Vincenzo; Pezzella, Franco; Vitale, Patrizia

doi:10.1007/jhep11(2019)060

Cited by 13 publications

(36 citation statements)

References 120 publications

(124 reference statements)

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“…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%

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

Basile

Joung

Park

2020

J. High Energ. Phys.

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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-

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Section: Coordinate Gauge Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Basile

Joung

Park

2020

J. High Energ. Phys.

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“…Recent developments, some of which are reported on here at this workshop, have related these Poisson-Lie models to the target space DFT defined on the group manifold D [132,133,134] and also [135,136], elucidated the Courant algebroids that underlie them [137,138,139], and developed the worldsheet doubled formalism [140,141,142].…”

Section: A Target Space Perspectivementioning

confidence: 99%

An Introduction to Generalised Dualities and their Applications to Holography and Integrability

Thompson¹

2019

Proceedings of Corfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2018)

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These pedagogical lectures given at the Corfu Summer Institute 2018 review two generalised notions of T-duality, non-Abelian T-duality and Poisson-Lie duality, and their applications. We explain how each of these has seen recent application in the context of holography. Non-Abelian T-duality has been used to construct new holographic dual geometries. Poisson-Lie duality has been used to construct new integrable string sigma-models including the η-and λ -deformations of the AdS 5 × S 5 superstring thought to encode quantum group deformations of holography. We also comment on the doubled worldsheet description that makes such dualities manifest. duality serves to interchange a conservation law, that associated to the U(1) global symmetry of the compact boson θ of radius R, with the Bianchi identity for the dual bosonθ :( 1.3) Just as with bosonisation the connection between the two variables involves derivatives, i.e. the map between variables is a non-local one. Also akin to the Abelian bosonisation, the dual theory can be established through an analogous path integral manipulation 1 known as the Buscher procedure [22,23]. Given the close analogy between T-duality and Abelian bosonisation one might wonder if there is a T-duality equivalent to non-Abelian bosonisation. More specifically, in string theory we are immediately prompted to ask if there is an extension of T-duality to the case of a non-Abelian set of isometries, or even if there are still more exotic notions of T-duality? A secondary question is then, if such dualities exist, what are they useful for? The remainder of these lectures seek to outline some answers to these two questions.Our journey will involve exploring a hierarchy of possible dualities in the following string theory scenarios:

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“…This has its geometric counterpart in Generalized and Double Geometry (see e.g. [26,27] and [28]- [32]). Moreover, the doubling of configuration space has also been related to Drinfel'd doubles in the context of Lie groups dynamics [33]- [37] with interesting implications for the mathematical and physical interpretation of the auxiliary variables.…”

Section: Introductionmentioning

confidence: 97%

Lagrangian formulation for electric charge in a magnetic monopole distribution

Marmo¹,

Scardapane²,

Stern

et al. 2019

Phys. Rev. D

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We give a Lagrangian description of an electric charge in a field sourced by a continuous magnetic monopole distribution. The description is made possible thanks to a doubling of the configuration space. The Legendre transform of the nonrelativistic Lagrangian agrees with the Hamiltonian description given recently by Kupriyanov and Szabo [1]. The covariant relativistic version of the Lagrangian is shown to introduce a new gauge symmetry, in addition to standard reparametrizations. The generalization of the system to open strings coupled to a magnetic monopole distribution is also given, as well as the generalization to particles in a non-Abelian gauge field which does not satisfy Bianchi identities in some region of the space-time. *

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T-dualities and Doubled Geometry of the Principal Chiral Model

Cited by 13 publications

References 120 publications

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

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

An Introduction to Generalised Dualities and their Applications to Holography and Integrability

Lagrangian formulation for electric charge in a magnetic monopole distribution

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