scholarly journals PSEUDODUALITY AND COMPLEX GEOMETRY IN SIGMA MODELS

2013 ◽  
Vol 10 (07) ◽  
pp. 1350034
Author(s):  
MUSTAFA SARISAMAN
Keyword(s):  
Sigma Models ◽  
Complex Geometry ◽  
Kähler Manifolds ◽  
Target Space ◽  
Kahler Manifolds ◽  
Two Dimensional ◽  
Additional Constraints

We study the pseudoduality transformations in two-dimensional N = (2, 2) sigma models on Kähler manifolds. We show that structures on the target space can be transformed into the pseudodual manifolds by means of (anti)holomorphic preserving mapping. This map requires that torsions related to individual spaces and riemann connection on pseudodual manifold must vanish. We also consider holomorphic isometries which puts additional constraints on the pseudoduality.

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 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 On isometry anomalies in minimal 𝒩 = (0,1) and 𝒩 = (0,2) sigma models

2016 ◽  
Vol 31 (27) ◽  
pp. 1650147 ◽  
Author(s):  
Jin Chen ◽  
Xiaoyi Cui ◽  
Mikhail Shifman ◽  
Arkady Vainshtein
Keyword(s):  
Sigma Models ◽  
Local Level ◽  
Exceptional Case ◽  
Target Space ◽  
Two Dimensional ◽  
Fermion Loop ◽  
Pontryagin Class ◽  
Text Model ◽  
Anomaly Analysis ◽  
Minimal Formula

The two-dimensional minimal supersymmetric sigma models with homogeneous target spaces [Formula: see text] and chiral fermions of the same chirality are revisited. In particular, we look into the isometry anomalies in [Formula: see text] and [Formula: see text] models. These anomalies are generated by fermion loop diagrams which we explicitly calculate. In the case of [Formula: see text] sigma models the first Pontryagin class vanishes, so there is no global obstruction for the minimal [Formula: see text] supersymmetrization of these models. We show that at the local level isometries in these models can be made anomaly free by specifying the counterterms explicitly. Thus, there are no obstructions to quantizing the minimal [Formula: see text] models with the [Formula: see text] target space while preserving the isometries. This also includes [Formula: see text] (equivalent to [Formula: see text]) which is an exceptional case from the [Formula: see text] series. For other [Formula: see text] models, the isometry anomalies cannot be rescued even locally, this leads us to a discussion on the relation between the geometric and gauged formulations of the [Formula: see text] models to compare the original of different anomalies. A dual formalism of [Formula: see text] model is also given, in order to show the consistency of our isometry anomaly analysis in different formalisms. The concrete counterterms to be added, however, will be formalism dependent.

scholarly journals BIHARMONIC LAGRANGIAN SUBMANIFOLDS IN KÄHLER MANIFOLDS

2013 ◽  
Vol 55 (2) ◽  
pp. 465-480 ◽  
Author(s):  
SHUN MAETA ◽  
HAJIME URAKAWA
Keyword(s):  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Sufficient Conditions ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Two Dimensional ◽  
Space Forms ◽  
Lagrangian Surfaces ◽  
Necessary And Sufficient ◽  
Complex Space Forms

AbstractWe give the necessary and sufficient conditions for Lagrangian submanifolds in Kähler manifolds to be biharmonic. We classify biharmonic PNMC Lagrangian H-umbilical submanifolds in the complex space forms. Furthermore, we classify biharmonic PNMC Lagrangian surfaces in the two-dimensional complex space forms.

scholarly journals New extended superconformal sigma models and quaternion Kähler manifolds

2009 ◽  
Vol 2009 (09) ◽  
pp. 119-119 ◽  
Author(s):  
Sergei M Kuzenko ◽  
Ulf Lindström ◽  
Rikard von Unge
Keyword(s):  
Sigma Models ◽  
Kähler Manifolds ◽  
Kahler Manifolds

scholarly journals THE RADIAL PART OF THE ZERO-MODE HAMILTONIAN FOR SIGMA MODELS WITH GROUP TARGET SPACE

2004 ◽  
Vol 16 (05) ◽  
pp. 603-628 ◽  
Author(s):  
DOUG PICKRELL
Keyword(s):  
Sigma Models ◽  
Lie Group ◽  
Sigma Model ◽  
Zero Mode ◽  
Target Space ◽  
Two Dimensional ◽  
Radial Part ◽  
Group Target ◽  
Simply Connected ◽  
Connected Lie Group

In this note, we use geometric arguments to derive a possible form for the radial part of the "zero-mode Hamiltonian" for the two-dimensional sigma model with target space S3, or more generally a compact simply connected Lie group.

scholarly journals Supersymmetric nonlinear sigma models on Ricci-flat Kähler manifolds with O(N) symmetry

2001 ◽  
Vol 515 (3-4) ◽  
pp. 421-425 ◽  
Author(s):  
Kiyoshi Higashijima ◽  
Tetsuji Kimura ◽  
Muneto Nitta
Keyword(s):  
Sigma Models ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Ricci Flat ◽  
Nonlinear Sigma Models
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