scholarly journals Antisymmetric tensor gauge fields on S4

2004 ◽  
Vol 82 (7) ◽  
pp. 541-548
Author(s):  
D.G.C. McKeon
Keyword(s):  
Field Model ◽  
Free Field ◽  
Flat Space ◽  
Antisymmetric Tensor ◽  
Gauge Fields ◽  
Scalar Model ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Higher Dimensional

Antisymmetric tensor gauge fields ϕab(η) are formulated on the surface of a sphere S4(η2 = a2) embedded in five dimensions. Such compact manifolds occur in the dimensional reduction of higher dimensional spaces that naturally occur in string theories. The free field model is equivalent to a scalar model on this sphere. Interactions with gauge fields are discussed. It is feasable to formulate models for interactions with U(1) gauge fields Aa(η) that are akin to those of Freedman and Townsend in flat space. In addition, it proves possible to have a novel interaction of ϕab with Aa and a spinor field Ψ(η) on S4 with both Abelian and non-Abelian gauge invariance. In these models, Aa plays the role of a Stueckelberg field.PACS No.: 11.30.Ly

scholarly journals PARTICLE SPECTRUM OF NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (14) ◽  
pp. 1137-1161 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Field ◽  
Free Field ◽  
Gauge Fields ◽  
Particle Spectrum ◽  
Field Equations ◽  
Abelian Gauge ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
Extended Field ◽  
Rank 2

We review the non-Abelian tensor gauge field theory and analyze its free field equations for lower rank gauge fields when the interaction coupling constant tends to zero. The free field equations are written in terms of the first-order derivatives of extended field strength tensors similar to the electrodynamics and non-Abelian gauge theories. We determine the particle content of the free field equations and count the propagating modes which they describe. In four-dimensional spacetime the rank-2 gauge field describes propagating modes of helicity two and zero. We show that the rank-3 gauge field describes propagating modes of helicity-three and a doublet of helicity-one gauge bosons. Only four-dimensional spacetime is physically acceptable, because in five- and higher-dimensional spacetime the equation has solutions with negative norm states. We discuss the structure of the particle spectrum for higher rank gauge fields.

scholarly journals Analytical holographic superconductors in AdSN-Lifshitz topological black holes

2015 ◽  
Vol 12 (02) ◽  
pp. 1550015 ◽  
Author(s):  
D. Momeni ◽  
R. Myrzakulov ◽  
L. Sebastiani ◽  
M. R. Setare
Keyword(s):  
Critical Temperature ◽  
Gauge Field ◽  
Field Model ◽  
Abelian Gauge ◽  
Ginzburg Landau ◽  
Holographic Superconductors ◽  
Energy Issue ◽  
Breaking Parameter ◽  
Second Order Phase Transition

We present the analytic Lifshitz solutions for a scalar field model minimally coupled with the abelian gauge field in N-dimensions. We also consider the presence of cosmological constant Λ. The Lifshitz parameter z appearing in the solution plays the role of the Lorentz breaking parameter of the model. We investigate the thermodynamical properties of the solutions and discuss the energy issue. Furthermore, we study the hairy black hole solutions in which the abelian gauge field breaks the symmetry near to the horizon. In the holographic picture, it is equivalent to a second-order phase transition. Explicitly we show that there exists a critical temperature which is a function of the Lifshitz parameter z. The system below the critical temperature becomes superconductor, but the critical exponent of the model remains the same of the usual holographic superconductors without the higher-order gravitational corrections, in agreement with Ginzburg–Landau theories.

scholarly journals Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Daniele Dorigoni ◽  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Modular Forms ◽  
Free Field ◽  
Perturbation Expansion ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Infinite Sums

Abstract The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/$$ {g}_{YM}^2 $$ g YM 2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ($$ {g}_{YM}^2 $$ g YM 2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O($$ {g}_{YM}^{-2w} $$ g YM − 2 w ) when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ q ¯ k f ̂ g YM , where $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ f ̂ g YM = O g YM 2 w when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.

A COVARIANT GENERALIZATION OF BERRY’S PHASE

1989 ◽  
Vol 04 (12) ◽  
pp. 1143-1149 ◽  
Author(s):  
Y.Q. CAI ◽  
G. PAPINI
Keyword(s):  
Proper Time ◽  
Rest Mass ◽  
Gauge Fields ◽  
Isotopic Spin ◽  
Spin Space ◽  
Abelian Gauge ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Degenerate Eigenvalues

A covariant generalization of Berry’s phase is obtained from the proper time Schrödinger equation in which the role of Hamiltonian is played by the rest mass square operator. When this has degenerate eigenvalues, non-Abelian gauge fields arise in the manner shown by Wilczek and Zee for non-relativistic systems. The manifold of degenerate states corresponds to isotopic spin space.

scholarly journals The Bargmann-Wigner equations in spherical space

2006 ◽  
Vol 84 (1) ◽  
pp. 37-52
Author(s):  
D.G.C. McKeon ◽  
T N Sherry
Keyword(s):  
Gauge Invariance ◽  
Wave Equations ◽  
Antisymmetric Tensor ◽  
Spherical Space ◽  
Point Function ◽  
Tensor Fields ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Spherical Surfaces ◽  
The One

The Bargmann–Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.PACS No.: 11.30–j

scholarly journals NAKED SINGULARITIES IN HIGHER DIMENSIONAL GRAVITATIONAL COLLAPSE

2003 ◽  
Vol 12 (07) ◽  
pp. 1255-1263 ◽  
Author(s):  
ASIT BANERJEE ◽  
UJJAL DEBNATH ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Dimensional Space ◽  
Naked Singularity ◽  
Space Time ◽  
Naked Singularities ◽  
Five Dimensions ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Five Dimension

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space–time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space–time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space–time is discussed in details. The five-dimensional space–time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.

FUNCTIONAL AND SEMANTIC CHARACTERS OF AN ADDRESS IN UKRAINIAN AND FRENCH

2019 ◽  
Vol 18 (28) ◽  
pp. 129-138 ◽  
Author(s):  
Tetiana Korolova ◽  
Nadiia Demianova
Keyword(s):  
Field Model ◽  
Semantic Field ◽  
The Status ◽  
Semantically Heterogeneous

The vocative function of an address being the basic one is supplemented and modified by a number of other functions actualized in communication, i.e. the phatic one (establishing and developing the contact with the addressee), the status one (reflecting the status responsibility of the communicants), the emotional and attitudinal one (characterizing the addressee and the attitude of the speaker towards the uttered information). Such modification explains the polyfunctional character of the address in communication. All units of address, just like the components of the addressing functional field, are polysemantic and polysemy comprises every type of an address. According to the communicative tasks the following functions can be stated within the vocative one: nominative (naming the addressee), deixis (identifying the addressee), vocative proper (attracting the addressee’s attention). The field model of addresses’ semantic structures allows to research standard and nonstandard vocatives. The standard addresses form the nucleus of the semantic field under research and characterize stability of their application in one of the above-mentioned functions. Nonstandard vocative lexemes (1 % of the total amount of the experimental material) can play the role of an address under certain circumstances. They form semantically heterogeneous (conditioned by a situation) group, located in the periphery area of the semantic field of addresses. The addresses that include anthroponyms form the most widely used group (64,5 % in Ukrainian and 68,1 % in French), the second place belongs to the addresses with appellatives (34,6 % and 29,9 %, correspondingly). As to the composition of appellatives in the status and role addresses they comprise 36,4 % in Ukrainian and 34,9 % in French. Attitudinal addresses reach 63 % and 65,1 %, correspondingly.

scholarly journals Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Yi Yang ◽  
Bo Zhen ◽  
John D. Joannopoulos ◽  
Marin Soljačić
Keyword(s):  
Quantum Hall ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Spin Orbit ◽  
Abelian Gauge ◽  
Experimental Realization ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

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