3,178 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
On the SO(9) structure of supersymmetric Yang-Mills quantum mechanics
In ten space-time dimensions the number of Majorana-Weyl fermions is not
conserved, not only during the time evolution, but also by rotations. As a
consequence the empty Fock state is not rotationally symmetric. We construct
explicitly the simplest singlet state which provides the starting point for
building up invariant SO(9) subspaces. The state has non-zero fermion number
and is a complicated combination of the 1360 elementary, gauge invariant,
gluinoless Fock states with twelve fermions. Fermionic structure of higher
irreps of SO(9) is also briefly outlined.Comment: 9 page
High energy nucleus-nucleus collisions
Experimental results on high energy nucleus-nucleus interactions are presented. The data are discussed within the framework of standard super-position models and from the point-of-view of the possible formation of new states of matter in heavy ion collisions
Beyond Complex Langevin Equations: a Progress Report
After a short review of one of proposals to avoid complex stochastic
processes in Complex Langevin studies, the recent progress in the former is
reported. In particular, the new developments allow now to construct positive
and normalizable representations for gaussian quantum mechanical, as well as
field theoretical, path integrals directly in the Minkowski time. A relation to
the idea of thimbles is also discussed.Comment: 7 pages, 2 figures, contribution to the Lattice2018 Symposiu
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
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