Principal Chiral Model without and with WZ term: Symmetries and Poisson-Lie T-Duality

Bascone, Francesco; Pezzella, Franco

doi:10.48550/arxiv.2005.02069

Cited by 5 publications

(5 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is interesting to note the form of the background metric h in (6.13). This metric has been already obtained in the context of Poisson-Lie duality of SU (2) sigma models [32,[34][35][36][37][38] as a non-degenerate metric for the group manifold of SB(2, C), the Borel subgroup of SL(2, C) of upper triangular matrices with complex elements with real diagonal and unit determinant. The latter plays the role of the Poisson-Lie dual of SU (2) in the Manin triple decomposition of the group SL(2, C).…”

Section: Dynamical Model On Su (2)mentioning

confidence: 88%

Topological and dynamical aspects of Jacobi sigma models

Bascone,

Pezzella,

Vitale

2021

Preprint

Self Cite

View full text Add to dashboard Cite

The geometrical properties of sigma models with target space a Jacobi manifold will be here investigated. In their basic formulation, these are topological field theories -recently introduced by the authors -which share and generalise relevant features of Poisson sigma models, such as gauge invariance under diffeomorphisms and finite dimension of the reduced phase space. Analogously to Poisson sigma models a generalisation is possible, which is fully dynamical and yields a Polyakov string action with target space a Jacobi manifold. After reviewing the main novelties and peculiarities of these models, we further analyse the target phase space and in particular the dimension of the latter, which results to be finite, as well as the integration of the auxiliary fields for contact and locally conformal symplectic manifolds, resulting in a Polyakov string action with background metric and B-field related to the defining structures of the Jacobi manifolds. .

show abstract

Section: Dynamical Model On Su (2)mentioning

confidence: 88%

Topological and dynamical aspects of Jacobi sigma models

Bascone,

Pezzella,

Vitale

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this work we analyse the integrability of a parametric family of Poisson-Lie dual models which was introduced in [12] by means of current algebra deformation techniques [13][14][15][16]. The resulting current algebra is a two-parameter deformation of the original algebra of the model, the semi-direct sum (su(2) ⊕R 3 )(R), into a fully non-Abelian algebra, following the procedure adopted by Rajeev and collaborators in [17][18][19].…”

Section: Jhep01(2023)127mentioning

confidence: 99%

On the classical integrability of Poisson-Lie T-dual WZW models

Bascone

Pezzella

Vitale

2023

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Geometric framework: The two-dimensional SU(2) principal chiral model [54][55][56] (also referred to as SU(2) ⊗ SU(2)-invariant or O(4) non-linear sigma model) is a non-linear sigma model on the source space (ℝ 2 , 𝜂) (i.e. two-dimensional Minkowski space-time endowed with the metric tensor 𝜂 ≡ diag (+1, −1)) and with the target space G = SU(2), i.e.…”

Section: Reminder: Two-dimensional Su(2) Principal Chiral Modelmentioning

confidence: 99%

Improvement of a Conserved Current Density Versus Adding a Total Derivative to a Lagrangian Density

Gieres

2022

Fortschritte der Physik

View full text Add to dashboard Cite

For classical relativistic field theory in Minkowski space‐time, the addition of a superpotential term to a conserved current density is trivial in the sense that it does not modify the local conservation law nor change the conserved charge, though it may allow us to obtain a current density with some improved properties. The addition of a total derivative term to a Lagrangian density is also trivial in the sense that it does not modify the equations of motion of the theory. These facts suggest that both operations are related and possibly equivalent to each other for any global symmetry of an action functional. We address this question following the study of two quite different (and well known) instances: the Callan‐Coleman‐Jackiw improvement of the canonical energy‐momentum tensor for scalar and vector fields (providing an on‐shell traceless energy‐momentum tensor) and the construction of a current density satisfying a zero curvature condition for two‐dimensional sigma models on deformed spaces (notably the squashed three‐sphere and warped AdS spaces). These instances correspond to fairly different implementations of the general results. An appendix addresses the precise relationship between the approaches to local conservation laws based on active and passive symmetry transformations, respectively.

show abstract

Principal Chiral Model without and with WZ term: Symmetries and Poisson-Lie T-Duality

Cited by 5 publications

References 42 publications

Topological and dynamical aspects of Jacobi sigma models

Topological and dynamical aspects of Jacobi sigma models

On the classical integrability of Poisson-Lie T-dual WZW models

Improvement of a Conserved Current Density Versus Adding a Total Derivative to a Lagrangian Density

Contact Info

Product

Resources

About