Tomoaki Nagasawa

Supersymmetry in quantum mechanics with point interactions

We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N=2 supersymmetric models on a circle with two point interactions as well as a superpotential. A hidden su(2) structure inherent in the system plays a crucial role to construct the N=2 supercharges. Spontaneous supersymmetry breaking due to point interactions and an extension to higher N-extended supersymmetry are also discussed.

Quark mass hierarchy and mixing via geometry of extra dimension with point interactions

We propose a new model which can simultaneously and naturally explain the origins of fermion generation, quark mass hierarchy, and the Cabibbo–Kobayashi–Maskawa matrix from the geometry of an extra dimension. We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermions at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fermion flavor mixing but the form of the nondiagonal elements of fermion mass matrices is found to be severely restricted due to the geometry of the extra dimension. The Robin boundary condition for a scalar leads to an extra coordinate-dependent vacuum expectation value, which can naturally explain the fermion mass hierarchy.

Supersymmetry in gauge theories with extra dimensions

We show that a quantum-mechanical N=2 supersymmetry is hidden in 4d mass spectrum of any gauge invariant theories with extra dimensions. The N=2 supercharges are explicitly constructed in terms of differential forms. The analysis can be extended to extra dimensions with boundaries, and for a single extra dimension we clarify a possible set of boundary conditions consistent with 5d gauge invariance, although some of the boundary conditions break 4d gauge symmetries.

Supersymmetry in 5D gravity

We study a 5d gravity theory with a warped metric and show that two N=2 supersymmetric quantum-mechanical systems are hidden in the 4d spectrum. The supersymmetry can be regarded as a remnant of higher-dimensional general coordinate invariance and turns out to become a powerful tool to determine the physical 4d spectrum and the allowed boundary conditions. Possible extensions of the N=2 supersymmetry are briefly discussed.

Gauge fixing and residual symmetries in gauge/gravity theories with extra dimensions

We study compactified pure gauge/gravitational theories with gauge-fixing terms and show that these theories possess quantum mechanical supersymmetriclike symmetries between unphysical degrees of freedom. These residual symmetries are global symmetries and generated by quantum mechanical N=2 supercharges. Also, we establish a new one-parameter family of gauge choices for higher-dimensional gravity and calculate as a check of its validity one graviton exchange amplitude in the lowest tree-level approximation. We confirm that the result is indeed {xi} independent and the cancellation of the {xi} dependence is ensured by the residual symmetries. We also give a simple interpretation of the van Dam-Veltman-Zakharov discontinuity, which arises in the lowest tree-level approximation, from the supersymmetric point of view.

Phase Structure of Gauge Theories on an Interval

We discuss gauge symmetry breaking in a general framework of gauge theories on an interval. We first derive a possible set of boundary conditions for a scalar field, which are compatible with several consistency requirements. It is shown that with these boundary conditions the scalar field can acquire a nontrivial vacuum expectation value even if the scalar mass square is positive. Any nonvanishing vacuum expectation value cannot be a constant but, in general, depends on the extra dimensional coordinate of the interval. The phase diagram of broken/unbroken gauge symmetry possesses a rich structure in the parameter space of the length of the interval, the scalar mass and the boundary conditions. We also discuss 4d chiral fermions and fermion mass hierarchies in our gauge symmetry breaking scenario.

Higgsless Gauge Symmetry Breaking with a Large Mass Hierarchy

We propose a higher dimensional scenario to solve the gauge hierarchy problem. In our formulation, a crucial observation is that a supersymmetric structure is hidden in the 4d spectrum of any gauge invariant theories with compact extra dimensions and that the gauge symmetry breaking is directly related to the supersymmetry breaking.We propose a mechanism of Higgsless gauge symmetry breaking with a large mass hierarchy. We consider a 5D gauge theory on the orbifold S 1 /Z 2 . The gauge symmetry is broken by orbifolding and also nontrivial boundary conditions at fixed points. All 4D modes that survive at low energies are found to be localized around fixed points. Supersymmetry plays an important role in this mechanism. The tree-level unitarity in our model is briefly discussed.

Supersymmetry and discrete transformations on S1 with point singularities

Abstract We investigate N -extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer n , N =2 n supercharges are explicitly constructed and a class of point singularities compatible with supersymmetry is clarified. Key ingredients in our construction are n sets of discrete transformations, each of which forms an su (2) algebra of spin 1/2. The degeneracy of the spectrum and spontaneous supersymmetry breaking are briefly discussed.

Hierarchy of QM SUSYs on a Bounded Domain

We systematically formulate a hierarchy of isospectral Hamiltonians in one-dimensional supersymmetric quantum mechanics on an interval and on a circle, in which two successive Hamiltonians form supersymmetry. We find that boundary conditions compatible with supersymmetry are severely restricted. In the case of an interval, a hierarchy of, at most, three isospectral Hamiltonians is possible with unique boundary conditions, while in the case of a circle an infinite tower of isospectral Hamiltonians can be constructed with a two-parameter family of boundary conditions.

Extended supersymmetry and its reduction on a circle with point singularities

We investigate N-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer n, N = 2n + 1 supercharges are explicitly constructed in terms of discrete transformations, and a class of singularities compatible with supersymmetry is clarified. In our formulation, the supersymmetry can be reduced to M-extended supersymmetry for any integer M < N. The degeneracy of the spectrum and spontaneous supersymmetry breaking are also studied.