scholarly journals Topological and Dynamical Aspects of Jacobi Sigma Models

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1205
Author(s):  
Francesco Bascone ◽  
Franco Pezzella ◽  
Patrizia Vitale
Keyword(s):  
Sigma Models ◽  
Finite Dimension ◽  
Symplectic Manifolds ◽  
Target Space ◽  
Contact Manifolds ◽  
Gauge Symmetries ◽  
Jacobi Manifolds ◽  
Topological Field ◽  
Jacobi Manifold ◽  
Locally Conformal

The geometric properties of sigma models with target space a Jacobi manifold are 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. After reviewing the main novelties and peculiarities of these models, we perform a detailed analysis of constraints and ensuing gauge symmetries in the Hamiltonian approach. Contact manifolds as well as locally conformal symplectic manifolds are discussed, as main instances of Jacobi manifolds.

scholarly journals Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Grgur Šimunić
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Target Space ◽  
Two Dimensional ◽  
Courant Algebroids ◽  
Dirac Structures ◽  
Courant Algebroid ◽  
Abelian Case ◽  
Jacobi Manifolds ◽  
Jacobi Structure

Abstract We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we investigate the conditions for consistent gauging of sigma models in the presence of a nonclosed 3-form. In the Abelian case, we find that the target of the gauged theory has the structure of a contact Courant algebroid, twisted by a 3-form and two 2-forms. Gauge invariance constrains the theory to (small) Dirac structures of the contact Courant algebroid. In the non-Abelian case, we draw a similar parallel between the gauged sigma model and certain transitive Courant algebroids and their corresponding Dirac structures. In the second part of the paper, we study two-dimensional sigma models related to Jacobi structures. The latter generalise Poisson and contact geometry in the presence of an additional vector field. We demonstrate that one can construct a sigma model whose gauge symmetry is controlled by a Jacobi structure, and moreover we twist the model by a 3-form. This construction is then the analogue of WZW-Poisson structures for Jacobi manifolds.

scholarly journals GENERALIZED MATHAI-QUILLEN TOPOLOGICAL SIGMA MODELS

1996 ◽  
Vol 11 (32n33) ◽  
pp. 2585-2600
Author(s):  
PABLO M. LLATAS
Keyword(s):  
Quantum Mechanics ◽  
Sigma Models ◽  
Topological Field Theories ◽  
Theoretical Approach ◽  
Sigma Model ◽  
Target Space ◽  
Field Theories ◽  
Internal Space ◽  
Topological Quantum ◽  
Topological Field

A simple field theoretical approach to Mathai-Quillen topological field theories of maps X : MI→MT from an internal space to a target space is presented. As an example of applications of our formalism we compute by applying our formulas the action and Q-variations of the fields of two well-known topological systems: topological quantum mechanics and type-A topological sigma model.

ON LIE–RINEHART–JACOBI ALGEBRAS

2008 ◽  
Vol 07 (06) ◽  
pp. 749-772 ◽  
Author(s):  
EUGÈNE OKASSA
Keyword(s):  
Symplectic Manifolds ◽  
Lie Algebroids ◽  
Contact Manifolds ◽  
Poisson Algebras ◽  
Locally Conformal

We show that Jacobi algebras (Poisson algebras respectively) can be defined only as Lie–Rinehart–Jacobi algebras (as Lie–Rinehart–Poisson algebras respectively). Also we show that contact manifolds, locally conformal symplectic manifolds (symplectic manifolds respectively) can be defined only as symplectic Lie–Rinehart–Jacobi algebras (only as symplectic Lie–Rinehart–Poisson algebras respectively). We define symplectic Lie algebroids.

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

scholarly journals Affine varieties, singularities and the growth rate of wrapped Floer cohomology

2018 ◽  
Vol 10 (03) ◽  
pp. 493-530
Author(s):  
Mark McLean
Keyword(s):  
Growth Rate ◽  
Cotangent Bundle ◽  
Betti Numbers ◽  
Symplectic Manifolds ◽  
Isolated Singularity ◽  
Contact Manifolds ◽  
Floer Cohomology ◽  
Complex Singularities ◽  
Smooth Affine ◽  
Simply Connected

In this paper, we give partial answers to the following questions: Which contact manifolds are contactomorphic to links of isolated complex singularities? Which symplectic manifolds are symplectomorphic to smooth affine varieties? The invariant that we will use to distinguish such manifolds is called the growth rate of wrapped Floer cohomology. Using this invariant we show that if [Formula: see text] is a simply connected manifold whose unit cotangent bundle is contactomorphic to the link of an isolated singularity or whose cotangent bundle is symplectomorphic to a smooth affine variety then M must be rationally elliptic and so it must have certain bounds on its Betti numbers.

scholarly journals Deformed $$\sigma $$-models, Ricci flow and Toda field theories

2021 ◽  
Vol 111 (6) ◽  
Author(s):  
Dmitri Bykov ◽  
Dieter Lüst
Keyword(s):  
Sigma Models ◽  
Ricci Flow ◽  
Flag Manifold ◽  
Flow Equation ◽  
Target Space ◽  
Field Theories ◽  
Two Dimensional

AbstractIt is shown that the Pohlmeyer map of a $$\sigma $$ σ -model with a toric two-dimensional target space naturally leads to the ‘sausage’ metric. We then elaborate the trigonometric deformation of the $$\mathbb {CP}^{n-1}$$ CP n - 1 -model, proving that its T-dual metric is Kähler and solves the Ricci flow equation. Finally, we discuss a relation between flag manifold $$\sigma $$ σ -models and Toda field theories.

scholarly journals Beyond the standard gauging: gauge symmetries of Dirac sigma models

2016 ◽  
Vol 2016 (8) ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Andreas Deser ◽  
Larisa Jonke ◽  
Thomas Strobl
Keyword(s):  
Sigma Models ◽  
Gauge Symmetries

scholarly journals First-order supersymmetric sigma models and target space geometry

2006 ◽  
Vol 2006 (01) ◽  
pp. 144-144 ◽  
Author(s):  
Andreas Bredthauer ◽  
Ulf Lindström ◽  
Jonas Persson
Keyword(s):  
Sigma Models ◽  
Target Space ◽  
First Order ◽  
Space Geometry

scholarly journals Classical boundary field theory of Jacobi sigma models by Poissonization

2021 ◽  
Author(s):  
Ion Vancea
Keyword(s):  
Field Theory ◽  
Phase Space ◽  
Sigma Models ◽  
Sigma Model ◽  
Classical Field Theory ◽  
Classical Field ◽  
Second Order ◽  
Contact Manifolds ◽  
Boundary Field ◽  
Classical Boundary

In this paper, we are going to construct the classical field theory on the boundary of the embedding of \mathbb{R} \times S^{1}ℝ×S1 into the manifold MM by the Jacobi sigma model. By applying the poissonization procedure and by generalizing the known method for Poisson sigma models, we express the fields of the model as perturbative expansions in terms of the reduced phase space of the boundary. We calculate these fields up to the second order and illustrate the procedure for contact manifolds.

Sign in / Sign up

Export Citation Format

Share Document