scholarly journals Hermitian(ϵ,δ)-Freudenthal-Kantor Triple Systems and Certain Applications of*-Generalized Jordan Triple Systems to Field Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple System ◽  
Structure Theorem ◽  
Higgs Mechanism ◽  
The Novel ◽  
Yang Mills ◽  
Triple Systems ◽  
Jordan Triple Systems ◽  
Chern Simons

We define Hermitian(ϵ,δ)-Freudenthal-Kantor triple systems and prove a structure theorem. We also give some examples of triple systems that are generalizations of theu(N)⊕u(M)andsp(2N)⊕u(1)Hermitian 3-algebras. We apply a*-generalized Jordan triple system to a field theory and obtain a Chern-Simons gauge theory. We find that the novel Higgs mechanism works, where the Chern-Simons gauge theory reduces to a Yang-Mills theory in a certain limit.

Hermitian generalized Jordan triple systems and certain applications to field theory

2014 ◽  
Vol 29 (13) ◽  
pp. 1450071 ◽  
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple System ◽  
Structure Theorem ◽  
Triple Systems ◽  
Jordan Triple System ◽  
Mathematical Properties ◽  
Jordan Triple Systems ◽  
Chern Simons

We define Hermitian generalized Jordan triple systems and prove a structure theorem. We also give some examples of the systems and study mathematical properties. We apply a Hermitian generalized Jordan triple system to a field theory and obtain a Chern–Simons gauge theory.

scholarly journals A class of Hermitian generalized Jordan triple systems and Chern–Simons gauge theory

2014 ◽  
Vol 29 (29) ◽  
pp. 1450156
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple Systems ◽  
Fundamental Matter ◽  
Jordan Triple Systems ◽  
Chern Simons

We find a class of Hermitian generalized Jordan triple systems (HGJTSs) and Hermitian (ϵ, δ)-Freudenthal–Kantor triple systems (HFKTSs). We apply one of the most simple HGJTSs which we find to a field theory and obtain a typical u(N) Chern–Simons gauge theory with a fundamental matter.

scholarly journals BATALIN–VILKOVISKY YANG–MILLS THEORY AS A HOMOTOPY CHERN–SIMONS THEORY VIA STRING FIELD THEORY

2009 ◽  
Vol 24 (07) ◽  
pp. 1309-1331 ◽  
Author(s):  
ANTON M. ZEITLIN
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Simons Theory ◽  
Yang Mills ◽  
Algebraic Constructions ◽  
Chern Simons ◽  
Chern Simons Theory

We show explicitly how Batalin–Vilkovisky Yang–Mills action emerges as a homotopy generalization of Chern–Simons theory from the algebraic constructions arising from string field theory.

scholarly journals A CHERN–SIMONS E8 GAUGE THEORY OF GRAVITY IN D = 15, GRAND UNIFICATION AND GENERALIZED GRAVITY IN CLIFFORD SPACES

2007 ◽  
Vol 04 (08) ◽  
pp. 1239-1257 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Gauge Theory ◽  
Grand Unification ◽  
De Sitter ◽  
Sitter Group ◽  
Yang Mills ◽  
Theory Of Gravity ◽  
M Theory ◽  
Chern Simons ◽  
Topological Part ◽  
Gauge Theory Of Gravity

A novel Chern–Simons E8 gauge theory of gravity in D = 15 based on an octicE8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern–Simons E8 gauge theory. We review the construction showing why the ordinary 11D Chern–Simons gravity theory (based on the Anti de Sitter group) can be embedded into a Clifford-algebra valued gauge theory and that an E8 Yang–Mills field theory is a small sector of a Clifford (16) algebra gauge theory. An E8 gauge bundle formulation was instrumental in understanding the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E8 gauge theory remains unknown. We hope that the Chern–Simons E8 gauge theory of gravity in D = 15 advanced in this work may shed some light into solving this problem after a dimensional reduction.

scholarly journals A Yang–Mills Theory in Loop Space and Chapline–Manton Coupling

1997 ◽  
Vol 12 (02) ◽  
pp. 111-119 ◽  
Author(s):  
Shinichi Deguchi ◽  
Tadahito Nakajima
Keyword(s):  
Field Theory ◽  
Local Field ◽  
Loop Space ◽  
Tensor Field ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Yang Mills ◽  
Local Field Theory ◽  
Antisymmetric Tensor Field ◽  
Chern Simons

We consider a Yang–Mills theory in loop space with the affine gauge group. From this theory, we derive a local field theory with Yang–Mills fields and Abelian antisymmetric and symmetric tensor fields of the second rank. The Chapline–Manton coupling, i.e. coupling of Yang–Mills fields and a second-rank antisymmetric tensor field via the Chern–Simons three-form is obtained systematically.

scholarly journals PLANAR HOMOLOGICAL MIRROR SYMMETRY

2007 ◽  
Vol 22 (29) ◽  
pp. 5351-5368 ◽  
Author(s):  
EIJI KONISHI
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Associative Algebra ◽  
String Field Theory ◽  
Mirror Symmetry ◽  
Open String ◽  
Homological Mirror Symmetry ◽  
Chern Simons

In this paper, we formulate a planar limited version of the B-side in homological mirror symmetry that formularizes Chern–Simons-type topological open string field theory using homotopy associative algebra (A∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We show that our formularization includes gravity/gauge theory correspondence which originates in the AdS/CFT duality of Dijkgraaf–Vafa theory.

AN EXCEPTIONAL E8 GAUGE THEORY OF GRAVITY IN D = 8, CLIFFORD SPACES AND GRAND UNIFICATION

2009 ◽  
Vol 06 (06) ◽  
pp. 911-930 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Gauge Theory ◽  
Gravitational Theory ◽  
Grand Unification ◽  
Quantum Level ◽  
Yang Mills ◽  
Group Invariant ◽  
Gravitational Model ◽  
Theory Of Gravity ◽  
Chern Simons ◽  
Gauge Theory Of Gravity

A candidate action for an Exceptional E8 gauge theory of gravity in 8D is constructed. It is obtained by recasting the E8 group as the semi-direct product of GL(8,R) with a deformed Weyl–Heisenberg group associated with canonical-conjugate pairs of vectorial and antisymmetric tensorial generators of rank two and three. Other actions are proposed, like the quarticE8 group-invariant action in 8D associated with the Chern–Simons E8 gauge theory defined on the 7-dim boundary of a 8D bulk. To finalize, it is shown how the E8 gauge theory of gravity can be embedded into a more general extended gravitational theory in Clifford spaces associated with the Cl(16) algebra and providing a solid geometrical program of a grand unification of gravity with Yang–Mills theories. The key question remains if this novel gravitational model based on gauging the E8 group may still be renormalizable without spoiling unitarity at the quantum level.

scholarly journals S-duality wall of SQCD from Toda braiding

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
B. Le Floch
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Domain Wall ◽  
Gauge Group ◽  
Domain Walls ◽  
Three Dimensional ◽  
Vertex Operators ◽  
Dual Operator ◽  
Yang Mills ◽  
Agt Correspondence

Abstract Exact field theory dualities can be implemented by duality domain walls such that passing any operator through the interface maps it to the dual operator. This paper describes the S-duality wall of four-dimensional $$ \mathcal{N} $$ N = 2 SU(N) SQCD with 2N hypermultiplets in terms of fields on the defect, namely three-dimensional $$ \mathcal{N} $$ N = 2 SQCD with gauge group U(N − 1) and 2N flavours, with a monopole superpotential. The theory is self-dual under a duality found by Benini, Benvenuti and Pasquetti, in the same way that T[SU(N)] (the S-duality wall of $$ \mathcal{N} $$ N = 4 super Yang-Mills) is self-mirror. The domain-wall theory can also be realized as a limit of a USp(2N − 2) gauge theory; it reduces to known results for N = 2. The theory is found through the AGT correspondence by determining the braiding kernel of two semi-degenerate vertex operators in Toda CFT.

scholarly journals Quadratic Jordan Triple Systems

2019 ◽  
Vol 11 (2) ◽  
pp. 68
Author(s):  
Amir Baklouti
Keyword(s):  
Triple System ◽  
Triple Systems ◽  
Jordan Triple System ◽  
Jordan Triple Systems ◽  
Dimension One

In this work, We show that every Jordan triple system can be viewed as a T∗extension of another one or an ideal of co-dimension one of a Jordan triple system whose represent the T∗extension of another Jordan triple system. Moreover, several result involving the structure of quadratic Jordan triple systems are given.

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