scholarly journals GRADED GEOMETRIC STRUCTURES UNDERLYING F-THEORY RELATED DEFECT THEORIES

2013 ◽  
Vol 28 (21) ◽  
pp. 1350106
Author(s):  
V. K. OIKONOMOU
Keyword(s):  
Vector Space ◽  
Dimensional Space ◽  
Composite Fiber ◽  
Fiber Bundles ◽  
Canonical Bundle ◽  
Geometric Structures ◽  
Yang Mills ◽  
Zero Modes ◽  
Fermionic Fields ◽  
Related Defect

In the context of F-theory, we study the related eight-dimensional super-Yang–Mills theory and reveal the underlying supersymmetric quantum mechanics algebra that the fermionic fields localized on the corresponding defect theory are related to. Particularly, the localized fermionic fields constitute a graded vector space, and in turn this graded space enriches the geometric structures that can be built on the initial eight-dimensional space. We construct the implied composite fiber bundles, which include the graded affine vector space and demonstrate that the composite sections of this fiber bundle are in one-to-one correspondence to the sections of the square root of the canonical bundle corresponding to the submanifold on which the zero modes are localized.

GEOMETRIC STRUCTURE OF THE HILBERT–YANG–MILLS FUNCTIONAL

2008 ◽  
Vol 05 (03) ◽  
pp. 387-405 ◽  
Author(s):  
A. PATÁK ◽  
D. KRUPKA
Keyword(s):  
Einstein Equations ◽  
Fiber Bundles ◽  
Variational Theory ◽  
Geometric Structures ◽  
Variation Formula ◽  
Yang Mills ◽  
Variational Functional ◽  
Fibered Manifolds ◽  
Prolongation Theory ◽  
Principal Fiber Bundles

The global variational functional, defined by the Hilbert–Yang–Mills Lagrangian over a smooth manifold, is investigated within the framework of prolongation theory of principal fiber bundles, and global variational theory on fibered manifolds. The principal Lepage equivalent of this Lagrangian is constructed, and the corresponding infinitesimal first variation formula is obtained. It is shown, in particular, that the Noether currents, associated with isomorphisms of the underlying geometric structures, split naturally into several terms, one of which is the exterior derivative of the Komar–Yang–Mills superpotential. Consequences of invariance of the Hilbert–Yang–Mills Lagrangian under isomorphisms of underlying geometric structures such as Noether's conservation laws for global currents are then established. As an example, a general formula for the Komar–Yang–Mills superpotential of the Reissner–Nordström solution of the Einstein equations is found.

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

scholarly journals About renormalized effective action for the Yang-Mills theory in four-dimensional space-time

2018 ◽  
Vol 191 ◽  
pp. 06001
Author(s):  
A.V. Ivanov
Keyword(s):  
Infinite Series ◽  
Effective Action ◽  
Dimensional Space ◽  
Space Time ◽  
Coupling Constant ◽  
Asymptotic Approach ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Bare Coupling Constant ◽  
Renormalization Theory

This work is related to the asymptotic approach in the renormalization theory and its problems. As the main example, the Yang-Mills theory in four-dimensional space-time is considered. It has been shown earlier [16] that using the asymptotic of the bare coupling constant one can find an expression for the renormalized effective action, however, this formula has problems (divergence ln " and infinite series). This work shows the relation of these values and provides an answer for the renormalized effective action.

scholarly journals SPIN GAUGE THEORY OF GRAVITY IN CLIFFORD SPACE: A REALIZATION OF KALUZA–KLEIN THEORY IN FOUR-DIMENSIONAL SPACE–TIME

2006 ◽  
Vol 21 (28n29) ◽  
pp. 5905-5956 ◽  
Author(s):  
MATEJ PAVŠIČ
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Dirac Field ◽  
Spin Connection ◽  
Yang Mills ◽  
Object A ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
The Right ◽  
Kaluza Klein

A theory in which four-dimensional space–time is generalized to a larger space, namely a 16-dimensional Clifford space (C-space) is investigated. Curved Clifford space can provide a realization of Kaluza–Klein. A covariant Dirac equation in curved C-space is explored. The generalized Dirac field is assumed to be a polyvector-valued object (a Clifford number) which can be written as a superposition of four independent spinors, each spanning a different left ideal of Clifford algebra. The general transformations of a polyvector can act from the left and/or from the right, and form a large gauge group which may contain the group U (1) × SU (2) × SU (3) of the standard model. The generalized spin connection in C-space has the properties of Yang–Mills gauge fields. It contains the ordinary spin connection related to gravity (with torsion), and extra parts describing additional interactions, including those described by the antisymmetric Kalb–Ramond fields.

scholarly journals ON UNITARITY OF A LINEARIZED YANG–MILLS FORMULATION FOR MASSLESS AND MASSIVE GRAVITY WITH PROPAGATING TORSION

2010 ◽  
Vol 25 (26) ◽  
pp. 4911-4932
Author(s):  
ROLANDO GAITAN DEVERAS
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Massive Gravity ◽  
Dynamical Variable ◽  
General Covariance ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Perturbative Regime ◽  
Massive Theory ◽  
Extended Theories

A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang–Mills formulation for gravity in a (2+1)-dimensional space–time. In the massless case, we show that the theory contains three degrees of freedom and only one is a nonunitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert–Einstein–Fierz–Pauli unitary massive theory plus three massless modes, two of them represents nonunitary ones. Finally, we confirm the existence of a family of unitary Yang–Mills-extended theories which are classically consistent with Einstein's solutions coming from nonmassive and topologically massive gravity. The unitarity of these Yang–Mills-extended theories is shown in a perturbative regime. A possible way to perform a nonperturbative study is remarked.

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