2,839 research outputs found
On the entropy bound of three dimensional simplicial gravity
It is proven that the partition function of 3-dimensional simplicial gravity
has an exponential upper bound with the following assumption: any three
dimensional sphere is constructed by repeated identification of
neighboring links and neighboring triangles in the boundary of a simplicial
3-ball. This assumption is weaker than the one proposed by other authors.Comment: 6 pages, two figures (in uudecode compressed tar
Soft Bootstrap and Supersymmetry
The soft bootstrap is an on-shell method to constrain the landscape of
effective field theories (EFTs) of massless particles via the consistency of
the low-energy S-matrix. Given assumptions on the on-shell data (particle
spectra, linear symmetries, and low-energy theorems), the soft bootstrap is an
efficient algorithm for determining the possible consistency of an EFT with
those properties. The implementation of the soft bootstrap uses the recently
discovered method of soft subtracted recursion. We derive a precise criterion
for the validity of these recursion relations and show that they fail exactly
when the assumed symmetries can be trivially realized by independent operators
in the effective action. We use this to show that the possible pure (real and
complex) scalar, fermion, and vector exceptional EFTs are highly constrained.
Next, we prove how the soft behavior of states in a supermultiplet must be
related and illustrate the results in extended supergravity. We demonstrate the
power of the soft bootstrap in two applications. First, for the N= 1 and N=2
CP^1 nonlinear sigma models, we show that on-shell constructibility establishes
the emergence of accidental IR symmetries. This includes a new on-shell
perspective on the interplay between N=2 supersymmetry, low-energy theorems,
and electromagnetic duality. We also show that N=2 supersymmetry requires
3-point interactions with the photon that make the soft behavior of the scalar
O(1) instead of vanishing, despite the underlying symmetric coset. Second, we
study Galileon theories, including aspects of supersymmetrization, the
possibility of a vector-scalar Galileon EFT, and the existence of
higher-derivative corrections preserving the enhanced special Galileon
symmetry. This is addressed by soft bootstrap and by application of
double-copy/KLT relations applied to higher-derivative corrections of chiral
perturbation theory.Comment: 71 pages, no figures. v2: significant new material about the N=2 CP^1
NLSM; typos correcte
Geometric constructibility of cyclic polygons and a limit theorem
We study convex cyclic polygons, that is, inscribed -gons. Starting from
P. Schreiber's idea, published in 1993, we prove that these polygons are not
constructible from their side lengths with straightedge and compass, provided
is at least five. They are non-constructible even in the particular case
where they only have two different integer side lengths, provided that . To achieve this goal, we develop two tools of separate interest. First, we
prove a limit theorem stating that, under reasonable conditions, geometric
constructibility is preserved under taking limits. To do so, we tailor a
particular case of Puiseux's classical theorem on some generalized power
series, called Puiseux series, over algebraically closed fields to an analogous
theorem on these series over real square root closed fields. Second, based on
Hilbert's irreducibility theorem, we give a \emph{rational parameter theorem}
that, under reasonable conditions again, turns a non-constructibility result
with a transcendental parameter into a non-constructibility result with a
rational parameter. For even and at least six, we give an elementary proof
for the non-constructibility of the cyclic -gon from its side lengths and,
also, from the \emph{distances} of its sides from the center of the
circumscribed circle. The fact that the cyclic -gon is constructible from
these distances for but non-constructible for exemplifies that some
conditions of the limit theorem cannot be omitted.Comment: 9 pages, 1 figur
The absolute order on the symmetric group, constructible partially ordered sets and Cohen-Macaulay complexes
The absolute order is a natural partial order on a Coxeter group W. It can be
viewed as an analogue of the weak order on W in which the role of the
generating set of simple reflections in W is played by the set of all
reflections in W. By use of a notion of constructibility for partially ordered
sets, it is proved that the absolute order on the symmetric group is homotopy
Cohen-Macaulay. This answers in part a question raised by V. Reiner and the
first author. The Euler characteristic of the order complex of the proper part
of the absolute order on the symmetric group is also computed.Comment: Final version (only minor changes), 10 pages, one figur
A Joint Criterion for Reachability and Observability of Nonuniformly Sampled Discrete Systems
A joint characterization of reachability (controllability) and observability
(constructibility) for linear SISO nonuniformly sampled discrete systems is
presented. The work generalizes to the nonuniform sampling the criterion known
for the uniform sampling. Emphasis is on the nonuniform sampling sequence,
which is believed to be an additional element for analysis and handling of
discrete systems.Comment: 8 pages, 1 figur
Approximation Complexity of Complex-Weighted Degree-Two Counting Constraint Satisfaction Problems
Constraint satisfaction problems have been studied in numerous fields with
practical and theoretical interests. In recent years, major breakthroughs have
been made in a study of counting constraint satisfaction problems (or #CSPs).
In particular, a computational complexity classification of bounded-degree
#CSPs has been discovered for all degrees except for two, where the "degree" of
an input instance is the maximal number of times that each input variable
appears in a given set of constraints. Despite the efforts of recent studies,
however, a complexity classification of degree-2 #CSPs has eluded from our
understandings. This paper challenges this open problem and gives its partial
solution by applying two novel proof techniques--T_{2}-constructibility and
parametrized symmetrization--which are specifically designed to handle
"arbitrary" constraints under randomized approximation-preserving reductions.
We partition entire constraints into four sets and we classify the
approximation complexity of all degree-2 #CSPs whose constraints are drawn from
two of the four sets into two categories: problems computable in
polynomial-time or problems that are at least as hard as #SAT. Our proof
exploits a close relationship between complex-weighted degree-2 #CSPs and
Holant problems, which are a natural generalization of complex-weighted #CSPs.Comment: A4, 10pt, 23 pages. This is a complete version of the paper that
appeared in the Proceedings of the 17th Annual International Computing and
Combinatorics Conference (COCOON 2011), Lecture Notes in Computer Science,
vol.6842, pp.122-133, Dallas, Texas, USA, August 14-16, 201
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