The hamiltonian study of supersymmetric Yang-Mills quantum mechanics

The hamiltonian formulation of Supersymmetric Yang-Mills quantum mechanics (SYMQM) is discussed. We focus on the Fock space formulation of the models since it is convenient for the numerical analysis, however some novel analytical results are also pointed out.Comment: 3 page

String Theory and the Fuzzy Torus

We outline a brief description of non commutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.Comment: Invited review for IJMPA rev1: an imprecision corrected and a reference adde

Supersymmetric Quantum Mechanics for String-Bits

We develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. We focus principally on space dimensions $d=1,2,4,8$, the transverse dimensionalities of superstring in $3,4,6,10$ space-time dimensions. These are the cases for which ``classical'' superstring makes sense, and also the values of $d$ for which Hooke's force law is compatible with the simplest superparticle dynamics. The basic question we address is: When is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. We show that the answer is affirmative for $d=1,2$, negative for $d=8$, and so far inconclusive for $d=4$.Comment: 17 pages, Late

Exact Witten Index in D=2 supersymmetric Yang-Mills quantum mechanics

A new, recursive method of calculating matrix elements of polynomial hamiltonians is proposed. It is particularly suitable for the recent algebraic studies of the supersymmetric Yang-Mills quantum mechanics in any dimensions. For the D=2 system with the SU(2) gauge group, considered here, the technique gives exact, closed expressions for arbitrary matrix elements of the hamiltonian and of the supersymmetric charge, in the occupation number representation. Subsequent numerical diagonalization provides the spectrum and restricted Witten index of the system with very high precision (taking into account up to $10^5$ quanta). Independently, the exact value of the restricted Witten index is derived analytically for the first time.Comment: 13 pages, 1 figur

Proposal of a topological M(atrix) theory

Keeping in mind the several models of M(atrix) theory we attempt to understand the possible structure of the topological M(atrix) theory ``underlying'' these approaches. In particular we are motivated by the issue about the nature of the structure of the vacuum of the topological M(atrix) theory and how this could be related to the vacuum of the electroweak theory. In doing so we are led to a simple topological matrix model. Moreover it is intuitively expected from the current understanding that the noncommutative nature of ``spacetime'' and background independence should lead to a topological Model. The main purpose of this note is to propose a simple topological Matrix Model which bears relation to F and M theories. Suggestions on the origin of the chemical potential term appearing in the matrix models are given.Comment: 14 pages revte

Why Matrix theory works for oddly shaped membranes

We give a simple proof of why there is a Matrix theory approximation for a membrane shaped like an arbitrary Riemann surface. As corollaries, we show that noncompact membranes cannot be approximated by matrices and that the Poisson algebra on any compact phase space is U(infinity). The matrix approximation does not appear to work properly in theories such as IIB string theory or bosonic membrane theory where there is no conserved 3-form charge to which the membranes couple.Comment: 8 pages, 4 figures, revtex; references adde

Deformed Matrix Theories with N=8 and Fivebranes in the PP Wave Background

M(atrix) theory is known to be mass-deformed in the pp-wave background and still retains all 16 dynamical supersymmetries. We consider generalization of such deformations on super Yang-Mills quantum mechanics (SYQM) with less supersymmetry. In particular this includes N=8 U(N) SYQM with a single adjoint and any number of fundamental hypermultiplets, which is a pp-wave deformation of DLCQ matrix theory of fivebranes. With k >= 1 fivebranes, we show that a rich vacuum structure exists, with many continuous family of solutions that preserve all dynamical supersymmetries. The vacuum moduli space contains copies of CP^{k-1} of various sizes.Comment: latex file, 23 pages, no figures, typos corrected, now in JHEP styl

Continuum limit of proton decay matrix elements in quenched lattice QCD

We present a lattice QCD calculation of the parameters \alpha and \beta which are necessary in the theoretical estimation of the proton lifetime in grand unified theories (GUTs) using chiral lagrangian approach. The simulation is carried out using the Wilson quark action at three gauge coupling constants in the quenched approximation. We obtain |\alpha(2GeV)|=0.0091(08)(^{+10}_{-19})GeV^3 and |\beta(2GeV)|=0.0098(08)(^{+10}_{-20})GeV^3 in the continuum limit where the first error is statistical and the second one is due to scale setting.Comment: 3 pages, 2 figures, talk presented at Lattice2003(matrix

On maximally supersymmetric Yang-Mills theories

We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L_{\infty}- and A_{\infty}- algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra Omega of (0, k)-forms on some supermanifold; the Lie algebra is tensor product of Omega and matrix algebra . We construct several other algebras that are quasiisomorphic to Omega and, therefore, also can be used to give BV formulation of 10D SUSY YM theory and its reductions. In particular, Omega is quasiisomorphic to the algebra B constructed by Berkovits. The algebras Omega_0 and B_0 obtained from Omega and B by means of reduction to a point can be used to give a BV-formulation of IKKT model. We introduce associative algebra SYM as algebra where relations are defined as equations of motion of IKKT model and show that Koszul dual to the algebra B_0 is quasiisomorphic to SYM.Comment: 43 pages. Details are added in the construction of trace in section 4. Added references. Formula for vector filed E on p.5,11 correcte

A Model Behind the Standard Model

In spite of its many successes, the Standard Model makes many empirical assumptions in the Higgs and fermion sectors for which a deeper theoretical basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2) \times su(3)$ plus the 3 assumptions: (A) scalar fields as vielbeins in internal symmetry space \cite{framevec}, (B) the ``confinement picture'' of symmetry breaking \cite{tHooft,Banovici}, (C) generations as ``dual'' to colour \cite{genmixdsm}, we are led to a scheme which offers: (I) a geometrical significance to scalar fields, (II) a theoretical criterion on what scalar fields are to be introduced, (III) a partial explanation of why $su(2)$ appears broken while $su(3)$ confines, (IV) baryon-lepton number (B - L) conservation, (V) the standard electroweak structure, (VI) a 3-valued generation index for leptons and quarks, and (VII) a dynamical system with all the essential features of an earlier phenomenological model \cite{genmixdsm} which gave a good description of the known mass and mixing patterns of quarks and leptons including neutrino oscillations. There are other implications the consistency of which with experiment, however, has not yet been systematically explored. A possible outcome is a whole new branch of particle spectroscopy from $su(2)$ confinement, potentially as rich in details as that of hadrons from colour confinement, which will be accessible to experiment at high energy.Comment: 66 pages, added new material on phenomenology, and some new reference