EFFECTIVE ACTION OF SIGMA MODEL ANOMALIES WITH EXTERNAL GAUGE FIELDS

1986 ◽  
Vol 01 (01) ◽  
pp. 23-27 ◽  
Author(s):  
YIE-LIANG WU ◽  
YAN-BO XIE ◽  
GUANG-ZHAO ZHOU
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Effective Action ◽  
Sigma Model ◽  
Original Model ◽  
Gauge Fields ◽  
Nonlinear Sigma Model ◽  
Consistency Conditions ◽  
Goldstone Bosons ◽  
External Gauge

The nonlinear sigma model describes Goldstone bosons originating from spontaneous symmetry breaking. A set of local counterterms is found to shift the anomaly of the nonlinear sigma model to that of the original model with fermions interacting with external gauge fields. The ‘t Hooft consistency conditions are matched automatically.

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.

scholarly journals Gauge theory approach to branes and spontaneous symmetry breaking

2017 ◽  
Vol 29 (03) ◽  
pp. 1750009 ◽  
Author(s):  
A. A. Zheltukhin
Keyword(s):  
Gauge Theory ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Vector Fields ◽  
Theory Approach ◽  
Tensor Fields ◽  
Broken Symmetries ◽  
Goldstone Bosons ◽  
Dimensional Minkowski Space ◽  
Poincaré Symmetry

We discuss the gauge theory approach to consideration of the Nambu–Goldstone bosons as gauge and vector fields represented by the Cartan forms of spontaneously broken symmetries. The approach is generalized to describe the fundamental branes in terms of [Formula: see text]-dimensional worldvolume gauge and massless tensor fields consisting of the Nambu–Goldstone bosons associated with the spontaneously broken Poincaré symmetry of the [Formula: see text]-dimensional Minkowski space.

EFFECTIVE ACTION AND ADIABATIC EXPANSIONS FOR THE 1-D AND 2-D HUBBARD MODELS AT HALF-FILLING

1994 ◽  
Vol 08 (10) ◽  
pp. 1391-1416 ◽  
Author(s):  
M. DI STASIO ◽  
E. ERCOLESSI ◽  
G. MORANDI ◽  
R. RIGHI ◽  
A. TAGLIACOZZO ◽  
...  
Keyword(s):  
Effective Action ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Adiabatic Expansion ◽  
Hubbard Models ◽  
Half Filling ◽  
Fermionic Representation ◽  
Two Space Dimensions ◽  
The Continuum ◽  
Expansion Scheme

We analyze here the occurrence of antiferromagnetic (AFM) correlations in the half-filled Hubbard model in one and two space dimensions using a natural fermionic representation of the model and a newly proposed way of implementing the half-filling constraint. We find that our way of implementing the constraint is capable of enforcing it exactly already at the lowest levels of approximation. We discuss how to develop a systematic adiabatic expansion for the model and how Berry’s phase contributions arise quite naturally from the adiabatic expansion. At low temperatures and in the continuum limit the model gets mapped onto an O(3) nonlinear sigma model (NLσ). A topological, Wess-Zumino term is present in the effective action of the 1D NLσ as expected, while no topological terms are present in 2D. Some specific difficulties that arise in connection with the implementation of an adiabatic expansion scheme within a thermodynamic context are also discussed, and we hint at possible solutions.

scholarly journals An introduction to spontaneous symmetry breaking

2019 ◽  
Author(s):  
Aron Beekman ◽  
Louk Rademaker ◽  
Jasper van Wezel
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Condensed Matter ◽  
Topological Defects ◽  
High Energy ◽  
Quantum Corrections ◽  
Gauge Fields ◽  
Singular Limits ◽  
Definition Of ◽  
Goldstone Modes

Perhaps the most important aspect of symmetry in physics is the idea that a state does not need to have the same symmetries as the theory that describes it. This phenomenon is known as spontaneous symmetry breaking. In these lecture notes, starting from a careful definition of symmetry in physics, we introduce symmetry breaking and its consequences. Emphasis is placed on the physics of singular limits, showing the reality of symmetry breaking even in small-sized systems. Topics covered include Nambu-Goldstone modes, quantum corrections, phase transitions, topological defects and gauge fields. We provide many examples from both high energy and condensed matter physics. These notes are suitable for graduate students.

scholarly journals Corrections to Wigner–Eckart Relations by Spontaneous Symmetry Breaking

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1120
Author(s):  
Carlo Heissenberg ◽  
Franco Strocchi
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Irreducible Representations ◽  
Matrix Elements ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Goldstone Bosons ◽  
The Matrix ◽  
Symmetry Breaking Term ◽  
Breaking Term

The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group G are governed by the well-known Wigner–Eckart relations. In the case of infinite-dimensional systems, with G spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases.

scholarly journals The Quantum Yang-Baxter Conditions: The Fundamental Relations behind the Nambu-Goldstone Theorem

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 803 ◽  
Author(s):  
Ivan Arraut
Keyword(s):  
Dispersion Relation ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Goldstone Theorem ◽  
Goldstone Bosons

We demonstrate that when there is spontaneous symmetry breaking in any system, relativistic or non-relativistic, the dynamic of the Nambu-Goldstone bosons is governed by the Quantum Yang-Baxter equations. These equations describe the triangular dynamical relations between pairs of Nambu-Goldstone bosons and the degenerate vacuum. We then formulate a theorem and a corollary showing that these relations guarantee the appropriate dispersion relation and the appropriate counting for the Nambu-Goldstone bosons.

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