FLAT CURRENTS OF A GREEN–SCHWARZ SIGMA MODEL ON SUPERCOSET TARGETS WITH ℤ4m GRADING

2008 ◽  
Vol 23 (25) ◽  
pp. 4219-4243 ◽  
Author(s):  
SAN-MIN KE ◽  
KANG-JIE SHI ◽  
CHUN WANG
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Parameter Family ◽  
Target Space ◽  
Suitable Choice ◽  
Kinetic Term ◽  
Classical Solutions ◽  
Virasoro Constraint ◽  
The One

We construct actions of Green–Schwarz sigma models on supercoset targets with ℤ4m grading whose kinetic terms only contain the target-space bosons. We consider a simple case of such kinetic term and show that there exist a one-parameter family of flat currents of the model by requiring a suitable choice of the Wess–Zumino term. Such flat currents naturally lead to a hierarchy of classical conserved nonlocal charges. We also find that the one-parameter flat currents of the model satisfy equations of motion and the Virasoro constraint. This implies that one can generate a series of classical solutions from an existing one. When m = 1, our model coincides with the well-known model given by Metsaev and Tseytlin on a supercoset PSU (2, 2|4)/[ SO (4, 1) × SO (5)] and similar models.

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 A non-relativistic limit of NS-NS gravity

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
E. A. Bergshoeff ◽  
J. Lahnsteiner ◽  
L. Romano ◽  
J. Rosseel ◽  
C. Şimşek
Keyword(s):  
Scale Invariance ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Geometric Constraints ◽  
Target Space ◽  
Kinetic Term ◽  
Scale Invariant ◽  
Relativistic Limit ◽  
Cartan Geometry ◽  
Form Field

Abstract We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.

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 Extended sigma-model in nontrivially deformed field–antifield formalism

2015 ◽  
Vol 30 (29) ◽  
pp. 1550141 ◽  
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov
Keyword(s):  
Sigma Models ◽  
Canonical Form ◽  
Sigma Model ◽  
General Setting ◽  
Kinetic Term ◽  
Classical Motion ◽  
Motion Equations

We propose an action for the extended sigma-models in the most general setting of the kinetic term allowed in the nontrivially deformed field–antifield formalism. We show that the classical motion equations do naturally take their desired canonical form.

scholarly journals ON THE RELATIONSHIP BETWEEN SIGMA MODELS AND SPIN CHAINS

2005 ◽  
Vol 19 (30) ◽  
pp. 4449-4465 ◽  
Author(s):  
D. CONTROZZI ◽  
E. HAWKINS
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Linear Sigma Model ◽  
Nucl Phys ◽  
Strong Coupling Regime ◽  
Lattice Regularization ◽  
Energy Behaviour ◽  
The One ◽  
The Relationship ◽  
Topological Term

We consider the two-dimensional O (3) non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl. Phys. B336, 457 (1990)], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient θ of the topological term is quantized as θ=2πs, with s integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-s Heisenberg model. We generalize the analysis to sigma models with other symmetries.

scholarly journals Integrable deformed T1,1 sigma models from 4D Chern-Simons theory

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Osamu Fukushima ◽  
Jun-ichi Sakamoto ◽  
Kentaroh Yoshida
Keyword(s):  
Boundary Conditions ◽  
Sigma Models ◽  
Sigma Model ◽  
Target Space ◽  
Simons Theory ◽  
Non Linear ◽  
Linear Sigma Models ◽  
Chern Simons ◽  
Parameter Deformation ◽  
Chern Simons Theory

Abstract Recently, a variety of deformed T1,1 manifolds, with which 2D non-linear sigma models (NLSMs) are classically integrable, have been presented by Arutyunov, Bassi and Lacroix (ABL) [46]. We refer to the NLSMs with the integrable deformed T1,1 as the ABL model for brevity. Motivated by this progress, we consider deriving the ABL model from a 4D Chern-Simons (CS) theory with a meromorphic one-form with four double poles and six simple zeros. We specify boundary conditions in the CS theory that give rise to the ABL model and derive the sigma-model background with target-space metric and anti-symmetric two-form. Finally, we present two simple examples 1) an anisotropic T1,1 model and 2) a G/H λ-model. The latter one can be seen as a one-parameter deformation of the Guadagnini-Martellini-Mintchev model.

scholarly journals NNLO classical solution for Lipatov’s effective action for reggeized gluons

2019 ◽  
Vol 34 (20) ◽  
pp. 1950111
Author(s):  
S. Bondarenko ◽  
S. Pozdnyakov
Keyword(s):  
Effective Action ◽  
Equations Of Motion ◽  
The Self ◽  
Classical Solutions ◽  
Transversality Conditions ◽  
Loop Contribution ◽  
Recursive Scheme ◽  
Fermion Loop ◽  
The One ◽  
Self Consistency

We consider the formalism of small-[Formula: see text] effective action for reggeized gluons[Formula: see text] and, following the approach developed in Refs. 11–17, calculate the classical gluon field to NNLO precision with fermion loops included. It is demonstrated that for each perturbative order, the self-consistency of the equations of motion is equivalent to the transversality conditions applied to the solution of the equations, these conditions allow to construct the general recursive scheme for the solution’s calculation. The one fermion loop contribution to the classical solutions and application of the obtained results are also discussed.

scholarly journals New integrable coset sigma models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Gleb Arutyunov ◽  
Cristian Bassi ◽  
Sylvain Lacroix
Keyword(s):  
Sigma Models ◽  
General Framework ◽  
Sigma Model ◽  
Hamiltonian Formulation ◽  
Integrable Model ◽  
Target Space ◽  
New Class ◽  
Free Parameters ◽  
Gaudin Models ◽  
Diagonal Subgroup

Abstract By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of N copies of a Lie group over some diagonal subgroup and they depend on 3N − 2 free parameters. For N = 1 the corresponding model coincides with the well-known symmetric space sigma model. Starting from the Hamiltonian formulation, we derive the Lagrangian for the N = 2 case and show that it admits a remarkably simple form in terms of the classical ℛ-matrix underlying the integrability of these models. We conjecture that a similar form of the Lagrangian holds for arbitrary N. Specifying our general construction to the case of SU(2) and N = 2, and eliminating one of the parameters, we find a new three-parametric integrable model with the manifold T1,1 as its target space. We further comment on the connection of our results with those existing in the literature.

scholarly journals CLASSICAL SOLUTIONS OF SIGMA MODELS IN CURVED BACKGROUNDS BY THE POISSON–LIE T-PLURALITY

2007 ◽  
Vol 22 (05) ◽  
pp. 1039-1052 ◽  
Author(s):  
LADISLAV HLAVATÝ ◽  
JAN HÝBL ◽  
MIROSLAV TUREK
Keyword(s):  
Sigma Models ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Classical Solutions ◽  
Auxiliary Functions ◽  
Drinfel’D Double ◽  
Flat Background ◽  
Model Solutions ◽  
Lie Transformation ◽  
Lie Transformations

Classical equations of motion for three-dimensional σ-models in curved background are solved by a transformation that follows from the Poisson–Lie T-plurality and transform them into the equations in the flat background. Transformations of coordinates that make the metric constant are found and used for solving the flat model. The Poisson–Lie transformation is explicitly performed by solving the PDE's for auxiliary functions and finding the relevant transformation of coordinates in the Drinfel'd double. String conditions for the solutions are preserved by the Poisson–Lie transformations. Therefore we are able to specify the type of σ-model solutions that solve also equations of motion of three-dimensional relativistic strings in the curved backgrounds. Some simple examples are given.

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.

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