scholarly journals Analysis of an SU(8) model with a spin-1 2 field directly coupled to a gauged Rarita–Schwinger spin-3 2 field

2019 ◽  
Vol 34 (33) ◽  
pp. 1950230
Author(s):  
Stephen L. Adler
Keyword(s):  
Representation Formula ◽  
Root Lattice ◽  
Anomaly Cancellation ◽  
Text Field ◽  
Text Model ◽  
Gauge Anomaly ◽  
Chiral Representation

In earlier work we analyzed an abelianized model in which a gauged Rarita–Schwinger spin-[Formula: see text] field is directly coupled to a spin-[Formula: see text] field. Here, we extend this analysis to the gauged [Formula: see text] model for which the abelianized model was a simplified substitute. We calculate the gauge anomaly, show that anomaly cancellation requires adding an additional left chiral representation [Formula: see text] spin-[Formula: see text] fermion to the original fermion complement of the [Formula: see text] model, and give options for restoring boson–fermion balance. We conclude with a summary of attractive features of the reformulated [Formula: see text] model, including a possible connection to the [Formula: see text] root lattice.

scholarly journals A note on gauge anomaly cancellation in effective field theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ferruccio Feruglio
Keyword(s):  
Effective Field Theories ◽  
Effective Field ◽  
Field Theories ◽  
Anomaly Cancellation ◽  
Charge Assignment ◽  
The Standard Model ◽  
Renormalizable Theory ◽  
Complete Set ◽  
Gauge Anomalies ◽  
Gauge Anomaly

Abstract The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

scholarly journals On Gauge Invariance of the Bosonic Measure in Chiral Gauge Theories

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 283
Author(s):  
Gabriel de Lima e Silva ◽  
Thalis José Girardi ◽  
Sebastião Alves Dias
Keyword(s):  
Hilbert Space ◽  
Gauge Theory ◽  
Path Integral ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Direct Calculation ◽  
Identity Operator ◽  
Anomaly Cancellation ◽  
Gauge Anomaly ◽  
General Gauge

Gauge invariance of the measure associated with the gauge field is usually taken for granted, in a general gauge theory. We furnish a proof of this invariance, within Fujikawa’s approach. To stress the importance of this fact, we briefly review gauge anomaly cancellation as a consequence of gauge invariance of the bosonic measure and compare this cancellation to usual results from algebraic renormalization, showing that there are no potential inconsistencies. Then, using a path integral argument, we show that a possible Jacobian for the gauge transformation has to be the identity operator, in the physical Hilbert space. We extend the argument to the complete Hilbert space by a direct calculation.

scholarly journals Gauge anomaly cancellation in chiral gauge theories

2012 ◽  
Vol 327 (6) ◽  
pp. 1435-1449 ◽  
Author(s):  
Gabriel Di Lemos Santiago Lima ◽  
Rafael Chaves ◽  
Sebastião Alves Dias
Keyword(s):  
Gauge Theories ◽  
Anomaly Cancellation ◽  
Gauge Anomaly

scholarly journals Ambitwistor strings in six and five dimensions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Yvonne Geyer ◽  
Lionel Mason ◽  
David Skinner
Keyword(s):  
Conformal Group ◽  
Anomaly Cancellation ◽  
Null Geodesics ◽  
Five Dimensions ◽  
Yang Mills ◽  
Conformally Invariant ◽  
Gravity Theories ◽  
Supersymmetric Gauge ◽  
Invariant Gauge ◽  
Gauge Anomaly

Abstract Ambitwistor strings are chiral (holomorphic) strings whose target is the space of complex null geodesics, ambitwistor space. We introduce twistor representations of ambitwistor space in 6 and 5 dimensions. In 6d the twistor representation is naturally conformally invariant. Anomaly cancellation leads to models that describe biadjoint scalar amplitudes and certain conformally invariant gauge and gravity theories, respectively of 4th and 6th order. There are three such models, reflecting triality for the conformal group SO(8) associated to these 6d models. On reduction to five dimensions, gauge anomaly cancellation requires supersymmetry and the resulting models describe maximally supersymmetric Yang-Mills and gravity. The twistor representation of these ambitwistor strings lead to formulæ for maximally supersymmetric gauge and gravity amplitudes based on the polarized scattering equations in 5d, found earlier by the first two authors.

COMMENTS ON ORIENTIFOLD OF BRANE TILINGS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2299-2306
Author(s):  
YOSUKE IMAMURA ◽  
KEISUKE KIMURA ◽  
MASAHITO YAMAZAKI
Keyword(s):  
Conservation Law ◽  
Gauge Theories ◽  
Anomaly Cancellation ◽  
Charge Conservation ◽  
Gauge Anomaly

The relation between brane charge conservation law in fivebrane system described by orientifolded brane tilings and the gauge anomaly cancellation in the corresponding gauge theories is summarized.

scholarly journals Supersymmetric gauge anomaly with general homotopic paths

2001 ◽  
Vol 596 (1-2) ◽  
pp. 315-347 ◽  
Author(s):  
S.James Gates ◽  
Marcus T. Grisaru ◽  
Marcia E. Knutt ◽  
Silvia Penati ◽  
Hiroshi Suzuki
Keyword(s):  
Supersymmetric Gauge ◽  
Gauge Anomaly

scholarly journals Connected perimeter of planar sets

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
François Dayrens ◽  
Simon Masnou ◽  
Matteo Novaga ◽  
Marco Pozzetta
Keyword(s):  
Minimization Problem ◽  
Existence Of Solutions ◽  
Lower Semicontinuous ◽  
Representation Formula ◽  
Steiner Trees ◽  
Lower Semicontinuous Envelope ◽  
Simply Connected

AbstractWe introduce a notion of connected perimeter for planar sets defined as the lower semicontinuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is also studied. We prove a representation formula which links the connected perimeter, the classical perimeter, and the length of suitable Steiner trees. We also discuss the application of this notion to the existence of solutions to a nonlocal minimization problem with connectedness constraint.

The Text-model: a Key to Heidegger's Thought?

1980 ◽  
Vol 47 (4) ◽  
pp. 286-295
Author(s):  
Thomas J. Wilson
Keyword(s):  
Text Model

scholarly journals Composition Identities of Chebyshev Polynomials, via 2 × 2 Matrix Powers

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 746
Author(s):  
Primo Brandi ◽  
Paolo Emilio Ricci
Keyword(s):  
Chebyshev Polynomials ◽  
Representation Formula ◽  
Complex Matrices ◽  
Lucas Polynomials ◽  
Standard Composition

Starting from a representation formula for 2 × 2 non-singular complex matrices in terms of 2nd kind Chebyshev polynomials, a link is observed between the 1st kind Chebyshev polinomials and traces of matrix powers. Then, the standard composition of matrix powers is used in order to derive composition identities of 2nd and 1st kind Chebyshev polynomials. Before concluding the paper, the possibility to extend this procedure to the multivariate Chebyshev and Lucas polynomials is touched on.

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