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 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 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 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 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 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.

SIGMA MODELS WITH (2, 2) WORLD SHEET SUPERSYMMETRY

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3725-3739 ◽  
Author(s):  
F. DELDUC ◽  
E. SOKATCHEV
Keyword(s):  
Sigma Models ◽  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Sigma Model ◽  
Space Dimension ◽  
Target Space ◽  
World Sheet ◽  
Chiral Superfields

We propose a new mechanism for constructing (2, 2) superspace actions for WZWN sigma models. We use the already known semi-chiral superfields, but we choose the Lagrangian in a special way, so that it has a gauge invariance capable of eliminating half of the initially propagating degrees of freedom. Thus we avoid the doubling of the target space dimension. The nonlinear differential conditions on the Lagrangian are derived and it is shown that this type of action corresponds to the general (2, 2) sigma model.

scholarly journals Born sigma-models for para-Hermitian manifolds and generalized T-duality

2021 ◽  
pp. 2150031
Author(s):  
Vincenzo Emilio Marotta ◽  
Richard J. Szabo
Keyword(s):  
Sigma Models ◽  
Degrees Of Freedom ◽  
Sigma Model ◽  
Hermitian Manifold ◽  
Geometric Interpretation ◽  
Closed String ◽  
Target Space ◽  
Model Description ◽  
Hermitian Geometry ◽  
Leaf Space

We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely defines a worldsheet sigma-model with a para-Hermitian target space, and we describe its Lie algebroid gauging as a means of recovering the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold. Applying the Kotov–Strobl gauging leads to a generalized notion of T-duality when combined with transformations that act on Born geometries. We obtain a geometric interpretation of the self-duality constraint that halves the degrees of freedom in doubled sigma-models, and we give geometric characterizations of non-geometric string backgrounds in this setting. We illustrate our formalism with detailed worldsheet descriptions of closed string phase spaces, of doubled groups where our notion of generalized T-duality includes non-abelian T-duality, and of doubled nilmanifolds.

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 Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

scholarly journals GAUSS DECOMPOSITION, WAKIMOTO REALIZATION AND GAUGED WZNW MODELS

1994 ◽  
Vol 09 (11) ◽  
pp. 1009-1023
Author(s):  
H. ARFAEI ◽  
N. MOHAMMEDI
Keyword(s):  
Field Strength ◽  
Sigma Model ◽  
Target Space ◽  
Gauge Fields ◽  
Nonlinear Sigma Model ◽  
Model Interpretation ◽  
Gauss Decomposition ◽  
Wznw Model ◽  
Wakimoto Realization

The implications of gauging the Wess-Zumino-Novikov-Witten (WZNW) model using the Gauss decomposition of the group elements are explored. We show that, contrary to the standard gauging of WZNW models, this gauging is carried out by minimally coupling the gauge fields. We find that this gauging, in the case of gauging and Abelian vector subgroup, differs from the standard one by terms proportional to the field strength of the gauge fields. We prove that gauging an Abelian vector subgroup does not have a nonlinear sigma model interpretation. This is because the target-space metric resulting from the integration over the gauge fields is degenerate. We demonstrate, however, that this kind of gauging has a natural interpretation in terms of Wakimoto variables.

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