Searcharxiv⌕ Search

arXiv subjects

Hironobu Kihara

Publications and source records attributed to Hironobu Kihara.

16 recordsLinked to original sources
arXiv2014

Absence of Non-Trivial Supersymmetries and Grassmann Numbers in Physical State Spaces

This paper reviews the well-known fact that nilpotent Hermitian operators on physical state spaces are zero, thereby indicating that the supersymmetries and "Grassmann numbers" are also zero on these spaces. Next, a positive definite inner product of a Grassmann algebra is demonstrated, constructed using a Hodge dual operator which is similar to that of differential forms. From this example, it is shown that the Hermitian conjugates of the basis do not anticommute with the basis and, therefore, the property that "Grassmann numbers" commute with "bosonic quantities" and anticommute with "fermionic quantities", must be revised. Hence, the fundamental principles of supersymmetry must be called into question.

physics.gen-ph↗
arXiv2012

Equations of Motion Solved by the Cremmer-Scherk Configuration on Even-Dimensional Spheres

Equations of motion of low-energy effective theories of quantum electrodynamics include infinitely many interaction terms, which make them difficult to solve. The self-duality property has facilitated research on the solutions to these equations. In this paper, equations of motion of systems of non-Abelian gauge fields on even-dimensional spheres are considered. It is demonstrated that the Cremmer-Scherk configuration, which satisfies certain generalized self-duality equations, becomes the classical solution for the class of systems that are given by arbitrary functions of class C^1 of 2m+1 quantities. For instance, Lagrangians consisting of multi-trace terms are included in this class. This result is likely to generate several new and interesting directions of research, including the classification of actions with respect to the stability condition against the Cremmer-Scherk configuration.

hep-th↗
arXiv2011

Generalized Self-Duality Equations of Polynomial Type in Yang-Mills Theories

The purpose of this paper is to generalize the self-duality equation by Tchrakian and Corrigan et. al.. Novel generalized self-duality equations on higher-dimensional spaces are discussed. This class of equations includes the usual self-duality equation for four-dimensional spaces. Some of the generalized self-duality equations over-determine configurations and the existence of solutions is not trivial. Several examples of solutions of the equations are demonstrated. %Application of these solutions in various models is attractive as shown in the case of instanton. As an application of the equations, it is proved that some of those solutions solve the equations of motion derived from rotationally-invariant actions, which consist of single-trace terms and are second-order in the time derivative.

hep-th↗
arXiv2011

Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.

hep-th↗
arXiv2011

A Classical Solution in Six-dimensional Gauge Theory with Higher Derivative Coupling

We show that the spin connection of the standard metric on a six-dimensional sphere gives an exact solution to the generalized self-dual equations suggested by Tchrakian some years ago. We work on an SO(6) gauge theory with a higher-derivative coupling term. The model consists of vector fields only. The pseudo-energy is bound from below by a topological charge which is proportional to the winding number of spatial S^5 around the internal space SO(6). The fifth homotopy group of SO(6) is, indeed, Z. The coupling constant of higher derivative term is quadratic in the radius of the underlying space S^6.

hep-th↗
arXiv2011

Generalized Monopoles in Six-dimensional Non-Abelian Gauge Theory

A spherically symmetric monopole solution is found in SO(5) gauge theory with Higgs scalar fields in the vector representation in six-dimensional Minkowski spacetime. The action of the Yang-Mills fields is quartic in field strengths. The solution saturates the Bogomolny bound and is stable.

hep-th↗
arXiv2011

Grand Partition Functions of Little Matrix Models with ABCD

Itoyama-Tokura type USp matrix model is discussed. Non-Abelian Berry's phases in a T-dualized model of IT model were reconsidered. These phases describe the higher dimensional monopoles; Yang monopole and nine-dimensional monopole. They are described by the connections of the BPST instanton on S^4 and the Tchrakian-GKS instanton on S^8, respectively. As a preparation to understand their effect in original zero-dimensional model, we consider partition function of simplified matrix models. We compute partition functions of SU, SO and USp reduced matrix models. Groups SO and USp appear in low energy effective theories of string against orientifold background. In this evaluation we chose different poles from that of Moore-Nekrasov-Shatashvili and our previous result. The position of poles explain branes' and the orientifold's configurations. There is a brane which is sitting on the orientifold in the SO(2N) model, while in USp(2N) and SO(2N+1) model there are no branes on the orientifold. The grand partition functions of these models are considered. They follow to linear second order ordinary differential equations and their singularities are q=0,\infty. Their solutions can be analytically continued to whole q plane. We show the expectation values of the number N of A and C cases as examples. There is an ambiguity coming from the problem on sign. Grand partition functions with minus sign give effective actions which have cusp singularities.

hep-th↗
arXiv2009

Gauge symmetry breaking in ten-dimensional Yang-Mills theory dynamically compactified on S^6

We study fluctuation modes in ten-dimensional Yang-Mills theory with a higher derivative term for the gauge field. We consider the ten-dimensional space-time to be a product of a four-dimensional space-time and six-dimensional sphere which exhibits dynamical compactification. Because of the isometry on S^6, there are flat directions corresponding to the Nambu-Goldstone zero modes in the effective theory on the solution. The zero modes are absorbed into gauge fields and form massive vector fields as a consequence of the Higgs-Kibble mechanism. The mass of the vector fields is proportional to the inverse of the radius of the sphere and larger than the mass scale set by the radius because of the higher derivative term.

hep-th↗
arXiv2009

Dynamical Compactification and Inflation in Einstein-Yang-Mills Theory with Higher Derivative Coupling

We study cosmology of the Einstein-Yang-Mills theory in ten dimensions with a quartic term in the Yang-Mills field strength. We obtain analytically a class of cosmological solutions in which the extra dimensions are static and the scale factor of the four-dimensional Friedmann-Lemaitre-Robertson-Walker metric is an exponential function of time. This means that the model can explain inflation. Then we look for solutions that describe dynamical compactification of the extra dimensions. The effective cosmological constant $λ_1$ in the four-dimensional universe is determined from the gravitational coupling, ten-dimensional cosmological constant, gauge coupling and higher derivative coupling. By numerical integration, the solution with $λ_1=0$ is found to behave as a matter-dominated universe which asymptotically approaches flat space-time, while the solution with a non-vanishing $λ_1$ approaches de Sitter space-time in the asymptotic future.

hep-th↗
arXiv2009

Self-Duality Equations on S^6 from R^7 monopole

In this note we identify a correspondence between a seven-dimensional monopole configuration of the Yang-Mills-Higgs system and the generalized self-dual configuration of the Yang-Mills system on a six-dimensional sphere. In particular, the topological charge of the self-duality configurations belongs to the sixth homotopy group of the coset G/H associated with the symmetry breaking G -> H induced by a non-trivial Higgs configuration in seven-dimensions.

hep-th↗
arXiv2008

Finite Energy Monopoles in Non-Abelian Gauge Theories on Odd-dimensional Spaces

In higher dimensional gauge theory, we need energies with higher power terms of field strength in order to realize point-wise monopoles. We consider new models with higher power terms of field strength and extraordinary kinetic term of scalar field. Monopole charges are computed as integrals over spheres and they are related to mapping class degree. Hedge-Hog solutions are investigated in these models. Every differential equation for these solutions is Abel's differential equation. A condition for existence of finite energy solution is shown. Spaces of 1-jets of these equations are defined as sets of zeros of polynomials. Those spaces can be interpreted as singular quartic surfaces in three-dimensional complex projective space.

hep-th↗
arXiv2008

Generalized Instantons on Complex Projective Spaces

We study a class of generalized self-duality relations in gauge theories on the complex projective space with the Fubini-Study metric. Our theories consist of only gauge fields with gauge group U(n). The pseudo-energies which we consider contain higher orders of field strength and are labeled by an integer p smaller than or equal to [n/2]. For making the Bogomol'nyi completion we need non-single trace terms in the pseudo-energies, unlike the models defined on spheres, which were studied previously. We construct an explicit solution of codimension 2n to generalized self-duality equations as Bogomol'nyi equations, by using a part of the spin connection.

hep-th↗
arXiv2007

Exact Solutions of Einstein-Yang-Mills Theory with Higher-Derivative Coupling

We construct a classical solution of an Einstein-Yang-Mills system with a fourth order term with respect to the field strength of the Yang-Mills field. The solution provides a spontaneous compactification proposed by Cremmer and Scherk; ten-dimensional space-time with a cosmological constant is compactified to the four-dimensional Minkowski space with a six-dimensional sphere S^6 on which an instanton solution exists. The radius of the sphere is not a modulus but is determined by the gauge coupling and the four-derivative coupling constants and the Newton's constant. We also construct a solution of ten-dimensional theory without a cosmological constant compactified to AdS_4 x S^6.

hep-th↗
arXiv2005

Scalar Laplacian on Sasaki-Einstein Manifolds Y^{p,q}

We study the spectrum of the scalar Laplacian on the five-dimensional toric Sasaki-Einstein manifolds Y^{p,q}. The eigenvalue equation reduces to Heun's equation, which is a Fuchsian equation with four regular singularities. We show that the ground states, which are given by constant solutions of Heun's equation, are identified with BPS states corresponding to the chiral primary operators in the dual quiver gauge theories. The excited states correspond to non-trivial solutions of Heun's equation. It is shown that these reduce to polynomial solutions in the near BPS limit.

hep-th↗