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Journal of High Energy Physics

, 2019:60 | Cite as

T-dualities and Doubled Geometry of the Principal Chiral Model

  • Vincenzo E. Marotta
  • Franco PezzellaEmail author
  • Patrizia Vitale
Open Access
Regular Article - Theoretical Physics
  • 11 Downloads

Abstract

The Principal Chiral Model (PCM) defined on the group manifold of SU(2) is here investigated with the aim of getting a further deepening of its relation with Generalized Geometry and Doubled Geometry. A one-parameter family of equivalent Hamiltonian descriptions is analysed, and cast into the form of Born geometries. Then O(3, 3) duality transformations of the target phase space are performed and we show that the resulting dual models are defined on the group SB(2, ℂ) which is the Poisson-Lie dual of SU(2) in the Iwasawa decomposition of the Drinfel’d double SL(2, ℂ). A parent action with doubled degrees of freedom and configuration space SL(2, ℂ) is then defined that reduces to either one of the dually related models, once suitable constraints are implemented.

Keywords

Sigma Models Differential and Algebraic Geometry String Duality 

Notes

Open Access

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Authors and Affiliations

  1. 1.Department of MathematicsHeriot-Watt UniversityEdinburghU.K.
  2. 2.INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6NapoliItaly
  3. 3.Dipartimento di Fisica “E. Pancini”Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6NapoliItaly

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