41,522 research outputs found
Quantum Weighted Model Counting
In Weighted Model Counting (WMC) we assign weights to Boolean literals and we
want to compute the sum of the weights of the models of a Boolean function
where the weight of a model is the product of the weights of its literals. WMC
was shown to be particularly effective for performing inference in graphical
models, with a complexity of where is the number of variables and
is the treewidth. In this paper, we propose a quantum algorithm for
performing WMC, Quantum WMC (QWMC), that modifies the quantum model counting
algorithm to take into account the weights. In turn, the model counting
algorithm uses the algorithms of quantum search, phase estimation and Fourier
transform. In the black box model of computation, where we can only query an
oracle for evaluating the Boolean function given an assignment, QWMC solves the
problem approximately with a complexity of oracle
calls while classically the best complexity is , thus achieving a
quadratic speedup
On Lorentz-Violating Supersymmetric Quantum Field Theories
We study the possibility of constructing Lorentz-violating supersymmetric
quantum field theories under the assumption that these theories have to be
described by lagrangians which are renormalizable by weighted power counting.
Our investigation starts from the observation that at high energies
Lorentz-violation and the usual supersymmetry algebra are algebraically
compatible. Demanding linearity of the supercharges we see that the requirement
of renormalizability drastically restricts the set of possible
Lorentz-violating supersymmetric theories. In particular, in the case of
supersymmetric gauge theories the weighted power counting has to coincide with
the usual one and the only Lorentz-violating operators are introduced by some
weighted constant c that explicitly appears in the supersymmetry algebra. This
parameter does not renormalize and has to be very close to the speed of light
at low energies in order to satisfy the strict experimental bounds on Lorentz
violation. The only possible models with non trivial Lorentz-violating
operators involve neutral chiral superfields and do not have a gauge invariant
extension. We conclude that, under the assumption that high-energy physics can
be described by a renormalizable Lorentz-violating extensions of the Standard
Model, the Lorentz fine tuning problem does not seem solvable by the
requirement of supersymmetry.Comment: 22 pages, 2 figure
Calabi-Yau fourfolds for M- and F-Theory compactifications
We investigate topological properties of Calabi-Yau fourfolds and consider a
wide class of explicit constructions in weighted projective spaces and, more
generally, toric varieties. Divisors which lead to a non-perturbative
superpotential in the effective theory have a very simple description in the
toric construction. Relevant properties of them follow just by counting lattice
points and can be also used to construct examples with negative Euler number.
We study nets of transitions between cases with generically smooth elliptic
fibres and cases with ADE gauge symmetries in the N=1 theory due to
degenerations of the fibre over codimension one loci in the base. Finally we
investigate the quantum cohomology ring of this fourfolds using Frobenius
algebras.Comment: 61 pages harvmac, one figure blow.eps, model 16 in tab 6.1 corrected
and other minor corrections, references adde
Weighted power counting and chiral dimensional regularization
We define a modified dimensional-regularization technique that overcomes
several difficulties of the ordinary technique, and is specially designed to
work efficiently in chiral and parity violating quantum field theories, in
arbitrary dimensions greater than 2. When the dimension of spacetime is
continued to complex values, spinors, vectors and tensors keep the components
they have in the physical dimension, therefore the matrices are the
standard ones. Propagators are regularized with the help of evanescent
higher-derivative kinetic terms, which are of the Majorana type in the case of
chiral fermions. If the new terms are organized in a clever way, weighted power
counting provides an efficient control on the renormalization of the theory,
and allows us to show that the resulting chiral dimensional regularization is
consistent to all orders. The new technique considerably simplifies the proofs
of properties that hold to all orders, and makes them suitable to be
generalized to wider classes of models. Typical examples are the
renormalizability of chiral gauge theories and the Adler-Bardeen theorem. The
difficulty of explicit computations, on the other hand, may increase.Comment: 41 pages; v2: minor changes, PRD versio
Projectable Horava-Lifshitz gravity in a nutshell
Approximately one year ago Horava proposed a power-counting renormalizable
theory of gravity which abandons local Lorentz invariance. The proposal has
been received with growing interest and resulted in various different versions
of Horava-Lifshitz gravity theories, involving a colourful potpourri of new
terminology. In this proceedings contribution we first motivate and briefly
overview the various different approaches, clarifying their differences and
similarities. We then focus on a model referred to as projectable
Horava-Lifshitz gravity and summarize the key results regarding its viability.Comment: 8 pages, no figures, to appear in the proceedings of First
Mediterranean Conference on Classical and Quantum Gravity Conference (MCCQG),
Kolymbari (Crete, Greece), September 14-18, 200
Long-range spin-pairing order and spin defects in quantum spin-1/2 ladders
For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range
spin-pairing order can be identified which enables the separation of the space
spanned by finite-range (covalent) valence-bond configurations into w+1
subspaces. Since every subspace has an equivalent counter subspace connected by
translational symmetry, twofold degeneracy, breaking traslational symmetry is
found except for the subspace where the ground state of w=even belongs to. In
terms of energy ordering, (non)degeneracy and the discontinuities introduced in
the long-range spin-pairing order by topological spin defects, the differences
between even and odd ladders are explained in a general and systematic way.Comment: 16 pages, 7 figures, 2 tables. To be publish in The European Physical
J.
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