We argue that the tensionless branes found recently on non-BPS D-branes using non-commutative field theory are in fact gauge equivalent to the vacuum under a discrete gauge symmetry. We also give a simple construction of the D(2p)-branes in IIA theory starting from a single non-BPS D9-brane. It has been shown recently that D-branes can be constructed as exact solitons in open string field theor...

In the study of nonlinear systems, completely integrable systems play special roles. They are not independent at all, but are strongly correlated with each other owing to the large symmetries shared among themselves. We like to know how far we can extend such systems without loosing integrability. The question could be answered if we know how much we can deform the symmetries characterizing the...

In this paper, we consider a three-dimensional discrete neural network model with delay. The characteristic equation of the linearized system at the zero solution is a polynomial equation involving very high order terms. We derive some sufficient and necessary conditions on the asymptotic stability and multiple bifurcations of the zero solution. We give computer simulations to support the theor...

The generalized symmetry method is applied to a class of completely discrete equations including the Adler-Bobenko-Suris list. Assuming the existence of a generalized symmetry, we derive a few integrability conditions suitable for testing and classifying equations of this class. Those conditions are used at the end to test for integrability discretizations of some well-known hyperbolic equations.

A discrete symmetry of the string field tachyon condensate noted by Hata and Shinohara is identified as a discrete subgroup of an SU(1,1) symmetry acting on the ghost coordinates. This symmetry, known from early studies of free gauge invariant string field actions, extends to off-shell interactions only for very restricted kinds of string vertices, among them the associative vertex of cubic str...

We study classes of models which are based on some discrete family symmetry which is completely broken such that the observed neutrino flavour symmetry emerges indirectly as an accidental symmetry. For such “indirect” models we discuss the D-term flavon vacuum alignments which are required for such an accidental flavour symmetry consistent with tri-bimaximal lepton mixing to emerge. We identify...

With the ansatz that there exist local or global discrete symmetries in the special branes’ neighborhoods, we can construct the extra dimension models with only zero modes, or the models which have large extra dimensions and arbitrarily heavy KK modes because there is no simple relation between the mass scales of extra dimensions and the masses of KK states. In addition, the bulk gauge symmetry...

Based on a new approach to quark and lepton masses, where the mass spectra originate in vacuum expectation values of O(3)-flavor 1+5 (gauge singlet) scalars, a neutrino mass matrix of a new type is speculated. The mass matrix is described in terms of the up-quark and charged lepton masses, and it can lead to a nearly tribimaximal mixing without assuming any discrete symmetry. Quark mass relatio...

The spontaneous breaking of an approximate discrete symmetry is considered, with the resulting protodomains of true and false vacuum being separated by domain walls. Given a strong, symmetric Yukawa coupling of the real scalar field to a generic fermion, the domain walls accumulate a gas of fermions, which modify the domain wall dynamics. The splitting of the degeneracy of the ground states res...

In the present tutorial we address a problem with a long history, which remains of great interest to date due to its many important applications: It concerns the existence and stability of periodic and quasiperiodic orbits in N degree of freedom Hamiltonian systems and their connection with discrete symmetries. Of primary importance in our study is what we call nonlinear normal modes (NNMs), i....