Compact gauge group representations without triangular anomalies

1984 ◽  
Vol 25 (3) ◽  
pp. 673-677
Author(s):  
L. Saliu ◽  
L. Tătaru
Keyword(s):  
Gauge Group ◽  
Group Representations ◽  
Compact Gauge Group

Self-duality in four-dimensional Riemannian geometry

1978 ◽  
Vol 362 (1711) ◽  
pp. 425-461 ◽  
Keyword(s):  
Gauge Group ◽  
Riemannian Geometry ◽  
Complex Analysis ◽  
Three Dimensional ◽  
The Self ◽  
Full Detail ◽  
Yang Mills ◽  
Self Duality ◽  
Compact Gauge Group

We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group. Results previously announced are treated with full detail and extended in a number of directions.

On the gauge orbit types for theories with classical compact gauge group

2010 ◽  
Vol 66 (3) ◽  
pp. 331-353 ◽  
Author(s):  
A. Hertsch ◽  
G. Rudolph ◽  
M. Schmidt
Keyword(s):  
Gauge Group ◽  
Orbit Types ◽  
Compact Gauge Group

YANG-MILLS FIELD QUANTIZATION WITH NON-COMPACT GAUGE GROUP

1992 ◽  
Vol 07 (29) ◽  
pp. 2747-2752 ◽  
Author(s):  
A. E. MARGOLIN ◽  
V. I. STRAZHEV
Keyword(s):  
State Space ◽  
Gauge Group ◽  
Physical State ◽  
Indefinite Metric ◽  
Yang Mills ◽  
S Matrix ◽  
Field Quantization ◽  
Compact Gauge Group ◽  
Mills Field

Yang-Mills field quantization in BRST-formalism with non-compact semi-simple gauge group is performed. The S-matrix unitarity in the physical state space, having indefinite metric is determined.

scholarly journals EXACT SOLUTION OF THE SCHWINGER MODEL WITH COMPACT U(1)

2001 ◽  
Vol 16 (03) ◽  
pp. 121-133
Author(s):  
ROMÁN LINARES ◽  
LUIS F. URRUTIA ◽  
J. DAVID VERGARA
Keyword(s):  
Exact Solution ◽  
Harmonic Oscillator ◽  
Gauge Group ◽  
Electric Charge ◽  
Axial Current ◽  
Gauge Invariant ◽  
Schwinger Model ◽  
Zero Modes ◽  
Compact Gauge Group ◽  
Θ Vacuum

The exact solution of the Schwinger model with compact gauge group U(1) is presented. The compactification is imposed by demanding that the only surviving true electromagnetic degree of freedom c has angular character. Not surprisingly, this topological condition defines a version of the Schwinger model which is different from the standard one, where c takes values on the line. The main consequences are: The spectra of the zero modes is not degenerated and does not correspond to the equally spaced harmonic oscillator, both the electric charge and a modified gauge-invariant chiral charge are conserved (nevertheless, the axial-current anomaly is still present) and, finally, there is no need to introduce a θ-vacuum. A comparison with the results of the standard Schwinger model is pointed out along the text.

scholarly journals Conformal blocks from celestial gluon amplitudes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Wei Fan ◽  
Angelos Fotopoulos ◽  
Stephan Stieberger ◽  
Tomasz R. Taylor ◽  
Bin Zhu
Keyword(s):  
Gauge Group ◽  
Correlation Functions ◽  
Delta Function ◽  
Adjoint Representation ◽  
Conformal Block ◽  
Group Representations ◽  
Conformal Blocks ◽  
Four Dimensions ◽  
Point Correlation ◽  
Complex Spin

Abstract In celestial conformal field theory, gluons are represented by primary fields with dimensions ∆ = 1 + iλ, λ ∈ ℝ and spin J = ±1, in the adjoint representation of the gauge group. All two- and three-point correlation functions of these fields are zero as a consequence of four-dimensional kinematic constraints. Four-point correlation functions contain delta-function singularities enforcing planarity of four-particle scattering events. We relax these constraints by taking a shadow transform of one field and perform conformal block decomposition of the corresponding correlators. We compute the conformal block coefficients. When decomposed in channels that are “compatible” in two and four dimensions, such four-point correlators contain conformal blocks of primary fields with dimensions ∆ = 2 + M + iλ, where M ≥ 0 is an integer, with integer spin J = −M, −M + 2, …, M − 2, M. They appear in all gauge group representations obtained from a tensor product of two adjoint representations. When decomposed in incompatible channels, they also contain primary fields with continuous complex spin, but with positive integer dimensions.

Sign in / Sign up

Export Citation Format

Share Document