scholarly journals Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds

2018 ◽  
Vol 30 (05) ◽  
pp. 1850012 ◽  
Author(s):  
C. I. Lazaroiu ◽  
C. S. Shahbazi
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Mathematical Formulation ◽  
Global Solutions ◽  
Mathematical Object ◽  
Mathematical Structure ◽  
Quantization Condition ◽  
Local Analysis ◽  
Abelian Gauge ◽  
Abelian Gauge Theory

We give the global mathematical formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields on a Lorentzian four-manifold, for the generalized situation when the duality structure of the Abelian gauge theory is described by a flat symplectic vector bundle [Formula: see text] defined over the scalar manifold [Formula: see text]. The construction uses a taming of [Formula: see text], which we find to be the correct mathematical object globally encoding the inverse gauge couplings and theta angles of the “twisted” Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of [Formula: see text] to the bundle [Formula: see text] and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over [Formula: see text] and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows, in particular, that a generalization of part of the mathematical structure familiar from [Formula: see text] supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.

scholarly journals TOPOLOGICAL FEATURES IN NON-ABELIAN GAUGE THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 1937-1949 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Decomposition Theorem ◽  
Laplacian Operator ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Topological Features ◽  
Brst Cohomology ◽  
Topological Field

We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two-dimensional free non-Abelian gauge theory (having no interaction with matter fields). The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants with respect to BRST and co-BRST charges on the two-dimensional compact manifold and show that the Lagrangian density of the theory can be expressed as the sum of terms that are BRST and co-BRST invariants. Thus, this theory captures together some of the salient features of both Witten and Schwarz type of topological field theories.

scholarly journals ONE-FORM ABELIAN GAUGE THEORY AS THE HODGE THEORY

2007 ◽  
Vol 22 (21) ◽  
pp. 3521-3562 ◽  
Author(s):  
R. P. MALIK
Keyword(s):  
Gauge Theory ◽  
Theoretical Model ◽  
Equations Of Motion ◽  
Hodge Theory ◽  
Laplacian Operator ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
De Rham ◽  
Symmetry Transformations ◽  
Field Theoretical Model

We demonstrate that the two (1+1)-dimensional (2D) free 1-form Abelian gauge theory provides an interesting field theoretical model for the Hodge theory. The physical symmetries of the theory correspond to all the basic mathematical ingredients that are required in the definition of the de Rham cohomological operators of differential geometry. The conserved charges, corresponding to the above continuous symmetry transformations, constitute an algebra that is reminiscent of the algebra obeyed by the de Rham cohomological operators. The topological features of the above theory are discussed in terms of the BRST and co-BRST operators. The super-de Rham cohomological operators are exploited in the derivation of the nilpotent (anti-)BRST, (anti-)co-BRST symmetry transformations and the equations of motion for all the fields of the theory, within the framework of the superfield formulation. The derivation of the equations of motion, by exploiting the super-Laplacian operator, is a completely new result in the framework of the superfield approach to BRST formalism. In an Appendix, the interacting 2D Abelian gauge theory (where there is a coupling between the U(1) gauge field and the Dirac fields) is also shown to provide a tractable field theoretical model for the Hodge theory.

Regge behavior of spontaneously broken non-Abelian gauge theory

1978 ◽  
Vol 17 (2) ◽  
pp. 585-597 ◽  
Author(s):  
J. B. Bronzan ◽  
R. L. Sugar
Keyword(s):  
Gauge Theory ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Regge Behavior

scholarly journals Static force potential of a non-Abelian gauge theory in a finite box in Coulomb gauge

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Tomohiro Furukawa ◽  
Keiichi Ishibashi ◽  
H. Itoyama ◽  
Satoshi Kambayashi
Keyword(s):  
Gauge Theory ◽  
Coulomb Gauge ◽  
Static Force ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Force Potential

Non-Abelian gauge theory from the Poisson bracket

2018 ◽  
Vol 33 (30) ◽  
pp. 1850182
Author(s):  
Mu Yi Chen ◽  
Su-Long Nyeo
Keyword(s):  
Gauge Theory ◽  
Poisson Bracket ◽  
Commutation Relation ◽  
Maxwell Equations ◽  
Dynamical Variable ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Generalized Poisson ◽  
Lie Algebraic Structure

The Hamiltonian of a nonrelativistic particle coupled to non-Abelian gauge fields is defined to construct a non-Abelian gauge theory. The Hamiltonian which includes isospin as a dynamical variable dictates the dynamics of the particle and isospin according to the Poisson bracket that incorporates the Lie algebraic structure of isospin. The generalized Poisson bracket allows us to derive Wong’s equations, which describe the dynamics of isospin, and the homogeneous (sourceless) equations for non-Abelian gauge fields by following Feynman’s proof of the homogeneous Maxwell equations.It is shown that the derivation of the homogeneous equations for non-Abelian gauge fields using the generalized Poisson bracket does not require that Wong’s equations be defined in the time-axial gauge, which was used with the commutation relation. The homogeneous equations derived by using the commutation relation are not Galilean and Lorentz invariant. However, by using the generalized Poisson bracket, it can be shown that the homogeneous equations are not only Galilean and Lorentz invariant but also gauge independent. In addition, the quantum ordering ambiguity that arises from using the commutation relation can be avoided when using the Poisson bracket.From the homogeneous equations, which define the “electric field” and “magnetic field” in terms of non-Abelian gauge fields, we construct the gauge and Lorentz invariant Lagrangian density and derive the inhomogeneous equations that describe the interaction of non-Abelian gauge fields with a particle.

scholarly journals Nilpotent symmetries and Curci–Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

2017 ◽  
Vol 32 (33) ◽  
pp. 1750193 ◽  
Author(s):  
N. Srinivas ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
The Self ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Abelian Theory ◽  
Matter Fields

We derive the off-shell nilpotent symmetries of the two [Formula: see text]-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi–Rouet–Stora–Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci–Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen [Formula: see text]-dimensional supermanifold. The latter is parametrized by the superspace coordinates [Formula: see text] where [Formula: see text] (with [Formula: see text]) are the bosonic coordinates and a pair of Grassmannian variables [Formula: see text] obey the relationships: [Formula: see text], [Formula: see text]. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

scholarly journals Review of strongly-coupled composite dark matter models and lattice simulations

2016 ◽  
Vol 31 (22) ◽  
pp. 1643004 ◽  
Author(s):  
Graham D. Kribs ◽  
Ethan T. Neil
Keyword(s):  
Dark Matter ◽  
Gauge Theory ◽  
Direct Detection ◽  
Bound State ◽  
New Physics ◽  
Abelian Gauge ◽  
Strongly Coupled ◽  
Abelian Gauge Theory ◽  
Lattice Calculations ◽  
Composite Description

We review models of new physics in which dark matter arises as a composite bound state from a confining strongly-coupled non-Abelian gauge theory. We discuss several qualitatively distinct classes of composite candidates, including dark mesons, dark baryons, and dark glueballs. We highlight some of the promising strategies for direct detection, especially through dark moments, using the symmetries and properties of the composite description to identify the operators that dominate the interactions of dark matter with matter, as well as dark matter self-interactions. We briefly discuss the implications of these theories at colliders, especially the (potentially novel) phenomenology of dark mesons in various regimes of the models. Throughout the review, we highlight the use of lattice calculations in the study of these strongly-coupled theories, to obtain precise quantitative predictions and new insights into the dynamics.

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