arXiv subjects

Norisuke Sakai

Publications and source records attributed to Norisuke Sakai.

At least 127 records · Page 7Linked to original sources

arXiv2001

SUSY Breaking by Stable non-BPS Walls

A new simple mechanism for SUSY breaking is proposed due to the coexistence of BPS domain walls. It is assumed that our world is on a BPS domain wall and that the other BPS wall breaks the SUSY preserved by our wall. This mechanism requires no messenger fields nor complicated SUSY breaking sector on any of the walls. We obtain an ${\cal N}=1$ model in four dimensions which has an exact solution of a stable non-BPS configuration of two walls. We propose that the overlap of the wave functions of the N-G fermion and those of physical fields provides a practical method to evaluate SUSY breaking mass splitting on our wall thanks to a low-energy theorem. This is based on our recent works hep-th/0009023 and hep-th/0107204.

hep-th↗

arXiv2001

Our World as an Intersection of Walls and a String

A solution of Einstein equations is obtained for our four-dimensional world as an intersection of a wall and a string-like defect in seven-dimensional spacetime with a negative cosmological constant. A matter energy-momentum tensor localized on the wall and on the string is needed. A single massless graviton is found and is localized around the intersection. The leading correction to the gravitational Newton potential from massive spin 2 graviton is found to be almost identical to that of a wall in five dimensions, contrary to the case of a string in six dimensions. The generalization to the intersection of a string and $n$ orthogonally intersecting walls is also obtained and a similar result is found for the gravitational potential.

hep-th↗

arXiv2000

An Exact Solution of BPS Junctions and Its Properties

We have obtained an exact solution for the BPS domain wall junction for a N=1 supersymmetric theory in four dimensions and studied its properties. The model is a simplified version of the N=2 SU(2) gauge theory with N_f=1 broken to N=1 by the mass of the adjoint chiral superfield. We define mode equations and demonstrate explicitly that fermion and boson with the same mass have to come in pairs except massless modes. We work out explicitly massless Nambu-Goldstone (NG) modes on the BPS domain wall junction. We find that their wave functions extend along the wall to infinity (not localized) and are not normalizable. It is argued that this feature is a generic phenomenon of NG modes on domain wall junctions in the bulk flat space in any dimensions. NG fermions exhibit a chiral structure in accordance with unitary representations of (1, 0) supersymmetry algebra where fermion and boson with the same mass come in pairs except massless modes which can appear singly.

hep-th↗

arXiv2000

SUSY Breaking by Overlap of Wave Functions in Coexisting Walls

SUSY breaking without messenger fields is proposed. We assume that our world is on a wall and SUSY is broken only by the coexistence of another wall with some distance from our wall. The Nambu-Goldstone fermion is localized on the distant wall. Its overlap with the wave functions of physical fields on our wall gives the mass splitting of physical fields on our wall thanks to a low-energy theorem. We propose that this overlap provides a practical method to evaluate mass splitting in models with SUSY breaking due to the coexisting walls.

hep-th↗

arXiv2000

D0 and D1 Brane With $κ_-$ and $κ_+$ Extended Symmetry

D0 brane (D-particle) and D1 brane actions possess first and second class constraints that result in local $κ$ symmetry. The $κ$ symmetry of the D-particle and the D1 brane is extended here into a larger symmetry ($κ_-$ and $κ_+$) in a larger phase space by turning second class constraints into first class. Different gauge fixings of these symmetries result in different presentations of these systems while a "unitary" gauge fixing of the new $ κ_+$ symmetry retrieves the original action with $κ_- = κ$ symmetry. For D1 brane our extended phase space makes all constraints into first class in the case of vanishing world sheet electric field (namely $(0, 1)$ string).

hep-th↗

arXiv2000

Nonnormalizable Zero Modes on BPS Junctions

Using an exact solution as a concrete example, Nambu-Goldstone modes on the BPS domain wall junction are worked out for N=1 supersymmetric theories in four dimensions. Their wave functions extend along the wall to infinity (not localized) and are not normalizable. It is argued that this feature is a generic phenomenon of Nambu-Goldstone modes on domain wall junctions in the bulk flat space in any dimensions. We formulate mode equations and show that fermion and boson with the same mass come in pairs except massless modes which can appear singly, in accordance with unitary representations of (1, 0) supersymmetry.

hep-th↗

arXiv1999

An Exact Solution of BPS Domain Wall Junction

An exact solution of domain wall junction is obtained in a four-dimensional N=1 supersymmetric U(1) X U(1)' gauge theory with three pairs of chiral superfields which is motivated by the N=2 SU(2) gauge theory with one flavor perturbed by an adjoint scalar mass. The solution allows us to evaluate various quantities including a new central charge Y_k associated with the junction besides Z_k which appears already in domain walls. We find that the new central charge Y_k gives a negative contribution to the mass of the domain wall junction whereas the central charge Z_k gives a dominant positive contribution. One has to be cautious to identify the central charge Y_k alone as the mass of the junction.

hep-th↗

arXiv1998

M theory and the ``integrating in'' method with an antisymmetric tensor

Recently, a non-hyperelliptic curve describing the Coulomb branch of N=2 SUSY $SU(N_c)$ Yang-Mills theory with an antisymmetric tensor matter was proposed using a configuration of a single M theory five-brane. We study the singular surface in the moduli space of the curve to compare it with results from the ``integrating in'' method in field theory. In order to achieve the consistency, we find it necessary to take account of an additional superpotential $W_Δ$ which has been neglected so far. The explicit form of $W_Δ$ is worked out.

hep-th↗

arXiv1996

Gauge Symmetry Breaking through Soft Masses in Supersymmetric Gauge Theories

Effects of soft breaking in N=1 supersymmetric gauge theories are studied. For N_f < N_c, we include the dynamics of the non-perturbative superpotential and use the original (s)quark and gauge fields. For N_f > N_c +1, we formulate the dynamics in terms of dual (s)quarks and a dual gauge group SU(N_f-N_c). The mass squared of the squarks can be negative triggering spontaneous breakdown of flavor and color symmetry. The general condition for stability of the vacuum is derived. We determine the breaking pattern, determine the spectrum and argue that the masses vary smoothly as one crosses from the Higgs phase into the confining phase, thus exhibiting complementarity.

hep-ph↗

arXiv1996

Vacuum Structures of Supersymmetric Yang-Mills Theories in $1+1$ Dimensions

Vacuum structures of supersymmetric (SUSY) Yang-Mills theories in $1+1$ dimensions are studied with the spatial direction compactified. SUSY allows only periodic boundary conditions for both fermions and bosons. By using the Born-Oppenheimer approximation for the weak coupling limit, we find that the vacuum energy vanishes, and hence the SUSY is unbroken. Other boundary conditions are also studied, especially the antiperiodic boundary condition for fermions which is related to the system in finite temperatures. In that case we find for gaugino bilinears a nonvanishing vacuum condensation which indicates instanton contributions.

hep-th↗

arXiv1996

Gauge Symmetry Breaking through Soft Masses in Supersymmetric Gauge Theories

We analyze the effects of soft supersymmetry breaking terms on N=1 supersymmetric QCD with $N_f$ flavors and color gauge group $SU(N_c)$. The mass squared of some squarks may be negative, as long as vacuum stability is ensured by a simple mass inequality. For $N_f N_c+1$, we formulate the dynamics in terms of dual (s)quarks and a dual gauge group $SU(N_f-N_c)$. The presence of negative squark mass squared terms leads to spontaneous breakdown of flavor and color symmetry. We determine this breaking pattern, derive the spectrum, and argue that the masses vary smoothly as one crosses from the Higgs phase into the confining phase.

hep-th↗

arXiv1996

String scattering off the (2+1)-dimensional rotationg black hole

The $SL(2, R)/Z$ WZW orbifold describes the (2+1)-dimensional black hole which approaches anti-de~Sitter space asymptotically. We study the $1 \rightarrow 1$ tachyon scattering off the rotating black hole background and calculate the Hawking temperature using the Bogoliubov transformation.

hep-th↗

arXiv1995

Mass Spectra of Supersymmetric Yang-Mills Theories in 1+1 Dimensions

Physical mass spectra of supersymmetric Yang-Mills theories in 1+1 dimensions are evaluated in the light-cone gauge with a compact spatial dimension. The supercharges are constructed and the infrared regularization is unambiguously prescribed for supercharges, instead of the light-cone Hamiltonian. This provides a manifestly supersymmetric infrared regularization for the discretized light-cone approach. By an exact diagonalization of the supercharge matrix between up to several hundred color singlet bound states, we find a rapidly increasing density of states as mass increases.

hep-th↗

arXiv1995

Vacuum Energies and Effective Potential in Light-Cone Field Theories

Vacuum energies are computed in light-cone field theories to obtain effective potentials which determine vacuum condensate. Quantization surfaces interpolating between the light-like surface and the usual spatial one are useful to define the vacuum energies unambiguously. The Gross-Neveu, SU(N) Thirring, and O(N) vector models are worked out in the large $N$ limit. The vacuum energies are found to be independent of the interpolating angle to define the quantization surface. Renormalization of effective potential is explicitly performed. As an example of the case with nonconstant order parameter, two-dimensional QCD is also studied. Vacuum energies are explicitly obtained in the large $N$ limit which give the gap equation as the stationary point.

hep-th↗

arXiv1995

Renormalization group flow in one- and two-matrix models

Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling constants by taking account of reparametrization identities. Despite the nonlinearity of the equation, the location of fixed points and the scaling exponents can be extracted from the equation. They agree with the spectrum of relevant operators in the exact solution. A linearized $β$-function approximates well the global phase structure which includes several nontrivial fixed points. The global renormalization group flow suggests a kind of $c$-theorem in two-dimensional quantum gravity.

hep-th↗

arXiv1993

Nonlinear Renormalization Group Equation for Matrix Models

An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to linear for vector models. An algorithm for determining the critical coupling constant and the critical exponent is obtained. As concrete examples, one-matrix models with one and two coupling constants are analyzed and the exact values of the critical coupling constant and the associated critical exponent are found.

hep-th↗

arXiv1993

Renormalization Group Approach to Matrix Models and Vector Models

The renormalization group approach is studied for large $N$ models. The approach of Brézin and Zinn-Justin is explained and examined for matrix models. The validity of the approach is clarified by using the vector model as a similar and simpler example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space provides infinitely many identities which reduce the infinite dimensional coupling constant space to that of finite dimensions. The effective beta functions give exact values for the fixed points and the susceptibility exponents. A detailed study of the effective renormalization group flow is presented for cases with up to two coupling constants. We draw the two-dimensional flow diagram.

hep-th↗

arXiv1993

Exact Beta Functions in the Vector Model and Renormalization Group Approach

The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization freedom in field space provides infinitely many identities which reduce the infinite dimensional coupling constant space to that of finite dimensions. The effective beta functions give exact values for the fixed points and the susceptibility exponents.

hep-th↗