scholarly journals Sigma models on flags

2019 ◽  
Vol 6 (2) ◽  
Author(s):  
Kantaro Ohmori ◽  
Nathan Seiberg ◽  
Shu-Heng Shao
Keyword(s):  
Sigma Models ◽  
Flag Manifold ◽  
Target Space ◽  
Global Symmetry ◽  
Specific Focus ◽  
Non Linear ◽  
Linear Sigma Models ◽  
Special Case

We study (1+1)-dimensional non-linear sigma models whose target space is the flag manifold U(N)\over U(N_1)\times U(N_2)\cdots U(N_m), with a specific focus on the special case U(N)/U(1)^{N}U(N)/U(1)N. These generalize the well-known \mathbb{CP}^{N-1}ℂℙN−1 model. The general flag model exhibits several new elements that are not present in the special case of the \mathbb{CP}^{N-1}ℂℙN−1 model. It depends on more parameters, its global symmetry can be larger, and its ’t Hooft anomalies can be more subtle. Our discussion based on symmetry and anomaly suggests that for certain choices of the integers N_INI and for specific values of the parameters the model is gapless in the IR and is described by an SU(N)_1SU(N)1 WZW model. Some of the techniques we present can also be applied to other cases.

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 Supersymmetric black rings and non-linear sigma models

2010 ◽  
Vol 829 (1-2) ◽  
pp. 161-175 ◽  
Author(s):  
Yi-Xin Chen ◽  
Yong-Qiang Wang
Keyword(s):  
Sigma Models ◽  
Black Rings ◽  
Non Linear ◽  
Linear Sigma Models

scholarly journals Quantum corrections to generic branes: DBI, NLSM, and more

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Garrett Goon ◽  
Scott Melville ◽  
Johannes Noller
Keyword(s):  
Sigma Models ◽  
Quantum Corrections ◽  
Higher Dimensional ◽  
Symmetry Properties ◽  
Non Linear ◽  
Quantum Action ◽  
Manifest Covariance ◽  
Linear Sigma Models ◽  
Scalar Sector ◽  
Explicit Comparison

Abstract We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

scholarly journals Loop calculations in quantum-mechanical non-linear sigma models

1995 ◽  
Vol 446 (1-2) ◽  
pp. 211-222 ◽  
Author(s):  
Jan de Boer ◽  
Bas Peeters ◽  
Kostas Skenderis ◽  
Peter van Nieuwenhuizen
Keyword(s):  
Sigma Models ◽  
Quantum Mechanical ◽  
Non Linear ◽  
Linear Sigma Models

SUPERSYMMETRIC TENSOR GAUGE THEORIES

1989 ◽  
Vol 04 (14) ◽  
pp. 1343-1353 ◽  
Author(s):  
T.E. CLARK ◽  
C.-H. LEE ◽  
S.T. LOVE
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
Sigma Models ◽  
Gauge Field ◽  
Gauge Theories ◽  
Symmetric Tensor ◽  
Global Symmetry ◽  
Invariant Action ◽  
Symmetry Transformations ◽  
Linear Sigma Models

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

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.

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