3,099 research outputs found
Solving some gauge systems at infinite N
After summarizing briefly some numerical results for four-dimensional
supersymmetric SU(2) Yang-Mills quantum mechanics, we review a recent study of
systems with an infinite number of colours. We study in detail a particular
supersymmetric matrix model which exhibits a phase transition, strong-weak
duality, and a rich structure of supersymmetric vacua. In the planar and strong
coupling limits, this field theoretical system is equivalent to a
one-dimensional XXZ Heisenberg chain and, at the same time, to a gas of
-bosons. This not only reveals a hidden supersymmetry in these well-studied
models; it also maps the intricate pattern of our supersymmetic vacua into that
of the now-popular ground states of the XXZ chain.Comment: 23 pages, 7 figures; lecture given at the XLVI Cracow School of
Theoretical Physics; some typos and references correcte
Recent progress in supersymmetric Yang-Mills quantum mechanics in various dimensions
We review the last year progress in understanding supersymmetric SU(2)
Yang-Mills quantum mechanics in four and ten space-time dimensions. The four
dimensional system is now well under control and the precise spectrum is
obtained in all channels. In D=10 some new results are also available.Comment: 19 pages, 4 figures, presented at the Workshop on Random Geometry,
Krakow, May 15 - 17, 200
Large N, Supersymmetry ... and QCD
This paper consists of two (still only vaguely) related parts: in the first,
we briefly review work done in the past three years on the ``planar
equivalence" between a class of non-supersymmetric theories (including limiting
cases of QCD) and their corresponding supersymmetric "parents"; in the second,
we present details of a new formulation of planar quantum mechanics and
illustrate its effectiveness in an intriguing supersymmetric example.Comment: A contribution to the A. Di Giacomo Festschrift: Physics and Beauty,
21 pages, 8 figure
Quantum systems in a cut Fock space
Standard quantum mechanics is viewed as a limit of a cut system with
artificially restricted dimension of a Hilbert space. Exact spectrum of cut
momentum and coordinate operators is derived and the limiting transition to the
infinite dimensional Hilbert space is studied in detail. The difference between
systems with discrete and continuous energy spectra is emphasized. In
particular a new scaling law, characteristic for nonlocalized, states is found.
Some applications for supersymmetric quantum mechanics are briefly outlined.Comment: 10 page
Lattice study of the simplified model of M-theory for larger gauge groups
Lattice discretization of the supersymmetric Yang-Mills quantum mechanics is
dis cussed. First results of the quenched Monte Carlo simulations, for D=4 and
with higher g auge groups (3 <= N <= 8), are presented. We confirm an earlier
(N=2) evidence tha t the system reveals different behaviours at low and high
temperatures separated by a narrow transiti on region. These two regimes may
correspond to a black hole and elementary excitations phases conjectured in the
M-theory. Dependence of the "transition temperature" on N is consistent with 't
Hooft scaling and shows a smooth saturation of lattice results towards the
large N limit. Is not yet resolved if the observed change between the two
regimes corresponds to a genuine phase transition or to a gentle crossover . A
new, noncompact formulation of the lattice model is also proposed and its
advantages are briefly discussed.Comment: 10 pages, 2 figures, Invited talk presented at the Sixth Workshop on
Non-Perturbative QCD, American University of Paris, Paris, June, 200
Planar Quantum Mechanics: an Intriguing Supersymmetric Example
After setting up a Hamiltonian formulation of planar (matrix) quantum
mechanics, we illustrate its effectiveness in a non-trivial supersymmetric
example. The numerical and analytical study of two sectors of the model, as a
function of 't Hooft's coupling , reveals both a phase transition at
(disappearence of the mass gap and discontinuous jump in Witten's
index) and a new form of strong-weak duality for .Comment: 14 pages, 3 .eps figures (1 figure, 2 acknowledgements added, typos
corrected
Supersymmetry and Combinatorics
We show how a recently proposed supersymmetric quantum mechanics model leads
to non-trivial results/conjectures on the combinatorics of binary necklaces and
linear-feedback shift-registers. Pauli's exclusion principle plays a crucial
role: by projecting out certain states/necklaces, it allows to represent the
supersymmetry algebra in the resulting subspace. Some of our results can be
rephrased in terms of generalizations of the well-known Witten index.Comment: 14 pages, 3 figures, text expanded, references adde
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