scholarly journals Dual description of η-deformed OSP sigma models

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mikhail Alfimov ◽  
Boris Feigin ◽  
Ben Hoare ◽  
Alexey Litvinov
Keyword(s):  
Sigma Models ◽  
Lie Groups ◽  
Sigma Model ◽  
Scattering Matrix ◽  
Tree Level ◽  
Particle Scattering ◽  
Continuous Parameter ◽  
Perturbative Regime ◽  
Gaussian Theory

Abstract We study the dual description of the η-deformed OSP(N|2m) sigma model in the asymptotically free regime (N > 2m + 2). Compared to the case of classical Lie groups, for supergroups there are inequivalent η-deformations corresponding to different choices of simple roots. For a class of such deformations we propose the system of screening charges depending on a continuous parameter b, which defines the η-deformed OSP(N|2m) sigma model in the limit b → ∞ and a certain Toda QFT as b → 0. In the sigma model regime we show that the leading UV asymptotic of the η-deformed model coincides with a perturbed Gaussian theory. In the perturbative regime b → 0 we show that the tree-level two-particle scattering matrix matches the expansion of the trigonometric OSP(N|2m) S-matrix.

scholarly journals NON-CANONICAL PERTURBATION THEORY OF NONLINEAR SIGMA MODELS

2011 ◽  
Vol 26 (02) ◽  
pp. 127-138 ◽  
Author(s):  
V. ALDAYA ◽  
M. CALIXTO ◽  
F. F. LÓPEZ-RUIZ
Keyword(s):  
Perturbation Theory ◽  
Sigma Models ◽  
Sigma Model ◽  
Free Field ◽  
Linear Sigma Model ◽  
Commutation Relations ◽  
And Topology ◽  
Canonical Perturbation ◽  
Target Manifold ◽  
Perturbative Regime

We explore the O(N)-invariant Non-Linear Sigma Model (NLSM) in a different perturbative regime from the usual relativistic-free-field one, by using non-canonical basic commutation relations adapted to the underlying O(N) symmetry of the system, which also account for the nontrivial (nonflat) geometry and topology of the target manifold.

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 On differential operators and unifying relations for 1-loop Feynman integrands

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Kang Zhou
Keyword(s):  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Maxwell Theory ◽  
Scalar Theory ◽  
Yang Mills ◽  
Loop Level ◽  
Wide Range ◽  
Non Linear

Abstract We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

scholarly journals Algebra of Nonlocal Charges in Supersymmetric Nonlinear Sigma Models

1997 ◽  
Vol 12 (02) ◽  
pp. 419-436 ◽  
Author(s):  
L. E. Saltini ◽  
A. Zadra
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Graphic Method ◽  
Two Dimensional ◽  
Conserved Charges ◽  
Classical Algebra ◽  
Dirac Brackets ◽  
Yangian Algebra ◽  
Graphic Methods ◽  
Nonlinear Sigma Models

We propose a graphic method to derive the classical algebra (Dirac brackets) of nonlocal conserved charges in the two-dimensional supersymmetric nonlinear O(N) sigma model. As in the purely bosonic theory we find a cubic Yangian algebra. We also consider the extension of graphic methods to other integrable theories.

scholarly journals PSEUDODUALITY IN SUPERSYMMETRIC SIGMA MODELS

2010 ◽  
Vol 25 (15) ◽  
pp. 2997-3023 ◽  
Author(s):  
MUSTAFA SARISAMAN
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Expansion Method ◽  
Normal Coordinates ◽  
Classical Construction

We study the pseudoduality transformation in supersymmetric sigma models. We generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold [Formula: see text] and by orthonormal coframe method on manifold [Formula: see text]. The component expansion method yields the result that pseudoduality tranformation is not invertible at all points and occurs from all points on one manifold to only one point where Riemann normal coordinates are valid on the second manifold. Torsion of the sigma model on [Formula: see text] must vanish while it is nonvanishing on [Formula: see text], and curvatures of the manifolds must be constant and the same. In the case of super-WZW sigma models, pseudoduality equations result in three different pseudoduality conditions; identity, chiral and antichiral pseudoduality.

KÄHLER SIGMA MODELS FROM SUPERSYMMETRIC GAUGE THEORIES

1989 ◽  
Vol 04 (17) ◽  
pp. 4391-4436 ◽  
Author(s):  
A. C. W. KOTCHEFF ◽  
G. M. SHORE
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Gauge Theories ◽  
Chiral Symmetry Breaking ◽  
Supersymmetric Gauge Theories ◽  
Target Manifold ◽  
Alignment Problem ◽  
Kähler Potential ◽  
Supersymmetric Gauge

The geometrical structure of the noncompact, nonhomogeneous Kähler sigma models arising from supersymmetric gauge theories is described. Topics discussed include the choice of target manifold for the sigma model, the supersymmetric vacuum alignment problem and the nature of chiral symmetry breaking, the role of isometry anomalies, the construction of the Kähler potential and metric, and the embedding of the conventional compact coset space sigma model in the supersymmetric Kähler model.

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.

CHIRAL SYMMETRY RESTORATION IN THE LINEAR SIGMA MODEL

1992 ◽  
Vol 03 (05) ◽  
pp. 993-1009 ◽  
Author(s):  
H. MEYER-ORTMANNS ◽  
H.-J. PIRNER ◽  
A. PATKÓS
Keyword(s):  
Chiral Symmetry ◽  
Sigma Model ◽  
Chiral Limit ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Gradual Change ◽  
Chiral Symmetry Restoration ◽  
Meson Octet ◽  
First Order Transition ◽  
Experimental Values

We report on results about the mass sensitivity of chiral symmetry restoration in the linear sigma model. For masses of the pseudoscalar meson octet which are close to the experimental values, we observed only a gradual change in the order parameters, when the temperature was changed. To estimate the size of the first order transition region around the chiral limit, we have varied the mass input for the tree level parametrization in several ways. The point with realistic meson masses turned out to lie well inside the crossover region.

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