Stability of the Rotating Ellipsoidal D0-brane System

In this note we prove the complete stability of the classical fluctuation modes of the rotating ellipsoidal membrane. The analysis is carried out in the full SU(N) setting, with the conclusion that the fluctuation matrix has only positive eigenvalues. This proves that the solution will remain close to the original one for all time, under arbitrary infinitesimal perturbations of the gauge fields.Comment: 10 pages, LaTe

D0-branes with non-zero angular momentum

In my talk I shall consider the mechanism of self-expansion of a system of N D0-branes into high-dimensional non-commutative world-volume investigated by Harmark and Savvidy. Here D2-brane is formed due to the internal angular momentum of D0-brane system. The idea is that attractive force of tension should be cancelled by the centrifugal motion preventing a D-brane system from collapse to a lower-dimensional one. I shall also present a new extended solution where a total of 9 space dimensions is used to embed a D0-brane system. In the last section, by performing linear analysis, the stability of the system is demonstrated.Comment: 10 pages, Latex, aipxfm.sty, fix2col.sty; Based on talk given at 10th Tohwa International Symposium on String Theory, Tohwa Univ., Fukuoka, (Japan), July 3-7, 200

The Spectrum of the Loop Transfer Matrix on Finite Lattice

We consider the model of random surfaces with extrinsic curvature term embedded into 3d Euclidean lattice $Z^3$. On a 3d Euclidean lattice it has equivalent representation in terms of transfer matrix $K(Q_{i},Q_{f})$, which describes the propagation of loops $Q$. We study the spectrum of the transfer matrix $K(Q_{i},Q_{f})$ on finite dimensional lattices. The renormalisation group technique is used to investigate phase structure of the model and its critical behaviour.Comment: 10 pages, 5 figures, Latex, psfi

Dual Statistical Systems and Geometrical String

We analyse statistical system with interface energy proportional to the length of the edges of interface. We have found the dual system high temperature expansion of which equally well generates surfaces with linear amplitude. These dual systems are in the same relation as 3D Ising ferromagnet to the 3D Gauge spin system.Comment: 8 pages, Late

A Lower Estimate for the Modified Steiner Functional

We prove inequality (1) for the modified Steiner functional A(M), which extends the notion of the integral of mean curvature for convex surfaces.We also establish an exression for A(M) in terms of an integral over all hyperplanes intersecting the polyhedralral surface M.Comment: 6 pages, Late

A dual lagrangian for non-Abelian tensor gauge fields

For non-Abelian tensor gauge fields of the lower rank we have found an alternative expression for the field strength tensors, which transform homogeneously with respect to the complementary gauge transformations and allow us to construct the dual Lagrangian.Comment: 13 pages, LaTex fil

Connection between non-Abelian tensor gauge fields and open strings

We compare the structure of the tree level scattering amplitudes in non-Abelian tensor gauge field theory and in open string theory with Chan-Paton charges. We limit ourselves considering only lower rank tensor fields in both theories. We identify the symmetric and antisymmetric components of the second rank tensor gauge field with the string excitations on the third and forth levels. In the process of this identification we have been selecting only those parts of the tree level scattering amplitudes in the open string theory which have dimensionless coupling constants in four dimensions. It seems that this subclass of tree level scattering amplitudes may provide important information about the structure of the open string theory and most probably it is equivalent to the non-Abelian tensor gauge field theory.Comment: 30 pages, 5 figures, published versio

Propagating modes of non-Abelian tensor gauge field of second rank

In the recently proposed extension of the YM theory, non-Abelian tensor gauge field of the second rank is represented by a general tensor whose symmetric part describes the propagation of charged gauge boson of helicity two and its antisymmetric part - the helicity zero charged gauge boson. On the non-interacting level these polarizations are similar to the polarizations of the graviton and of the Abelian antisymmetric B field, but the interaction of these gauge bosons carrying non-commutative internal charges cannot be directly identified with the interaction of gravitons or B field. Our intention here is to illustrate this result from different perspectives which would include Bianchi identity for the corresponding field strength tensor and the analysis of the second-order partial differential equation which describes in this theory the propagation of non-Abelian tensor gauge field of the second rank.Comment: 22 pages, Latex fil