130 research outputs found
Exceptional points in quantum and classical dynamics
We notice that, when a quantum system involves exceptional points, i.e. the
special values of parameters where the Hamiltonian loses its self-adjointness
and acquires the Jordan block structure, the corresponding classical system
also exhibits a singular behaviour associated with restructuring of classical
trajectories. The system with the crypto-Hermitian Hamiltonian H = (p^2+z^2)/2
-igz^5 and hyper-ellictic classical dynamics is studied in details. Analogies
with supersymmetric Yang-Mills dynamics are elucidated.Comment: References added. Final version to be published in J. Phys.
Adding a Myers Term to the IIB Matrix Model
We show that Yang-Mills matrix integrals remain convergent when a Myers term
is added, and stay in the same topological class as the original model. It is
possible to add a supersymmetric Myers term and this leaves the partition
function invariant.Comment: 8 pages, v2 2 refs adde
Yang-Mills Integrals
Two results are presented for reduced Yang-Mills integrals with different
symmetry groups and dimensions: the first is a compact integral representation
in terms of the relevant variables of the integral, the second is a method to
analytically evaluate the integrals in cases of low order. This is exhibited by
evaluating a Yang-Mills integral over real symmetric matrices of order 3.Comment: LaTeX, 10 pages, references added and minimal change
Direct instantons, topological charge screening and QCD glueball sum rules
Nonperturbative Wilson coefficients of the operator product expansion (OPE)
for the spin-0 glueball correlators are derived and analyzed. A systematic
treatment of the direct instanton contributions is given, based on realistic
instanton size distributions and renormalization at the operator scale. In the
pseudoscalar channel, topological charge screening is identified as an
additional source of (semi-) hard nonperturbative physics. The screening
contributions are shown to be vital for consistency with the anomalous axial
Ward identity, and previously encountered pathologies (positivity violations
and the disappearance of the 0^{-+} glueball signal) are traced to their
neglect. On the basis of the extended OPE, a comprehensive quantitative
analysis of eight Borel-moment sum rules in both spin-0 glueball channels is
then performed. The nonperturbative OPE coefficients turn out to be
indispensable for consistent sum rules and for their reconciliation with the
underlying low-energy theorems. The topological short-distance physics strongly
affects the sum rule results and reveals a rather diverse pattern of glueball
properties. New predictions for the spin-0 glueball masses and decay constants
and an estimate of the scalar glueball width are given, and several
implications for glueball structure and experimental glueball searches are
discussed.Comment: 49 pages, 8 figure
Higher Derivative Operators from Transmission of Supersymmetry Breaking on S_1/Z_2
We discuss the role that higher derivative operators play in field theory
orbifold compactifications on S_1/Z_2 with local and non-local (Scherk-Schwarz)
breaking of supersymmetry. Integrating out the bulk fields generates
brane-localised higher derivative counterterms to the mass of the brane (or
zero-mode of the bulk) scalar field, identified with the Higgs field in many
realistic models. Both Yukawa and gauge interactions are considered and the
one-loop results found can be used to study the ``running'' of the scalar field
mass with respect to the momentum scale in 5D orbifolds. In particular this
allows the study of the behaviour of the mass under UV scaling of the momentum.
The relation between supersymmetry breaking and the presence of higher
derivative counterterms to the mass of the scalar field is investigated. This
shows that, regardless of the breaking mechanism, (initial) supersymmetry
cannot, in general, prevent the emergence of such operators. Some implications
for phenomenology of the higher derivative operators are also presented.Comment: 29 pages, LaTeX. Added Section 4 ("Phenomenological implications:
living with ghosts?") and Appendix
Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature
We investigate thermodynamic properties of one-dimensional U(N)
supersymmetric gauge theories with 4 and 8 supercharges in the planar large-N
limit by Monte Carlo calculations. Unlike the 16 supercharge case, the
threshold bound state with zero energy is widely believed not to exist in these
models. This led A.V. Smilga to conjecture that the internal energy decreases
exponentially at low temperature instead of decreasing with a power law. In the
16 supercharge case, the latter behavior was predicted from the dual black
0-brane geometry and confirmed recently by Monte Carlo calculations. Our
results for the models with 4 and 8 supercharges indeed support the exponential
behavior, revealing a qualitative difference from the 16 supercharge case.Comment: 16 pages, 7 figures, LaTeX2e, minor corrections in section 3, final
version accepted in JHE
Polyakov Lines in Yang-Mills Matrix Models
We study the Polyakov line in Yang-Mills matrix models, which include the
IKKT model of IIB string theory. For the gauge group SU(2) we give the exact
formulae in the form of integral representations which are convenient for
finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper
bounds which decay as a power law at large momentum p. We argue that these
capture the full asymptotic behaviour. We also indicate how to extend the
results to some correlation functions of Polyakov lines.Comment: 19 pages, v2 typos corrected, v3 ref adde
Quantum tunneling as a classical anomaly
Classical mechanics is a singular theory in that real-energy classical
particles can never enter classically forbidden regions. However, if one
regulates classical mechanics by allowing the energy E of a particle to be
complex, the particle exhibits quantum-like behavior: Complex-energy classical
particles can travel between classically allowed regions separated by potential
barriers. When Im(E) -> 0, the classical tunneling probabilities persist.
Hence, one can interpret quantum tunneling as an anomaly. A numerical
comparison of complex classical tunneling probabilities with quantum tunneling
probabilities leads to the conjecture that as ReE increases, complex classical
tunneling probabilities approach the corresponding quantum probabilities. Thus,
this work attempts to generalize the Bohr correspondence principle from
classically allowed to classically forbidden regions.Comment: 12 pages, 7 figure
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