157 research outputs found
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 , the transverse dimensionalities of
superstring in space-time dimensions. These are the cases for which
``classical'' superstring makes sense, and also the values of 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 , negative for
, and so far inconclusive for .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 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 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 appears
broken while 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
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
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