4,269 research outputs found
Finding Disjoint Paths on Edge-Colored Graphs: More Tractability Results
The problem of finding the maximum number of vertex-disjoint uni-color paths
in an edge-colored graph (called MaxCDP) has been recently introduced in
literature, motivated by applications in social network analysis. In this paper
we investigate how the complexity of the problem depends on graph parameters
(namely the number of vertices to remove to make the graph a collection of
disjoint paths and the size of the vertex cover of the graph), which makes
sense since graphs in social networks are not random and have structure. The
problem was known to be hard to approximate in polynomial time and not
fixed-parameter tractable (FPT) for the natural parameter. Here, we show that
it is still hard to approximate, even in FPT-time. Finally, we introduce a new
variant of the problem, called MaxCDDP, whose goal is to find the maximum
number of vertex-disjoint and color-disjoint uni-color paths. We extend some of
the results of MaxCDP to this new variant, and we prove that unlike MaxCDP,
MaxCDDP is already hard on graphs at distance two from disjoint paths.Comment: Journal version in JOC
Bubble-resummation and critical-point methods for -functions at large
We investigate the connection between the bubble-resummation and
critical-point methods for computing the -functions in the limit of
large number of flavours, , and show that these can provide complementary
information. While the methods are equivalent for single-coupling theories, for
multi-coupling case the standard critical exponents are only sensitive to a
combination of the independent pieces entering the -functions, so that
additional input or direct computation are needed to decipher this missing
information. In particular, we evaluate the -function for the quartic
coupling in the Gross-Neveu-Yukawa model, thereby completing the full system at
. The corresponding critical exponents would imply a
shrinking radius of convergence when terms are included,
but our present result shows that the new singularity is actually present
already at , when the full system of -functions is
known.Comment: 11 pages, 7 figures; v2: references added, matches the published
versio
Safe SUSY
We investigate the short distance fate of distinct classes of not
asymptotically free supersymmetric gauge theories. Examples include super QCD
with two adjoint fields and generalised superpotentials, gauge theories without
superpotentials and with two types of matter representation and semi-simple
gauge theories such as quivers. We show that for the aforementioned theories
asymptotic safety is nonperturbatively compatible with all known constraints.Comment: LaTeX 14 pages, several figures, added another exampl
Exact lattice Ward-Takahashi identity for the N=1 Wess-Zumino model
We consider a lattice formulation of the four dimensional N=1 Wess-Zumino
model that uses the Ginsparg-Wilson relation. This formulation has an exact
supersymmetry on the lattice. We show that the corresponding Ward-Takahashi
identity is satisfied, both at fixed lattice spacing and in the continuum
limit. The calculation is performed in lattice perturbation theory up to order
in the coupling constant. We also show that this Ward-Takahashi identity
determines the finite part of the scalar and fermion renormalization wave
functions which automatically leads to restoration of supersymmetry in the
continuum limit. In particular, these wave functions coincide in this limit.Comment: 19 pages, 6 figure
Conditions for the existence of stable strange quark matter
We discuss the possible existence of absolutely stable strange quark matter
within three different types of chiral models. We will show that confinement
plays a crucial role in determining the conditions for the Bodmer-Witten
hypothesis to hold true. We discuss also which are the phenomenological
signatures, related to measurements of masses and radii of compact stars, which
would prove the existence of strange quark stars.Comment: 8 pages, 5 figures, Contribution to the proceedings of XIIth Quark
Confinement and the Hadron Spectrum, 29 August 2016 - 3 September 2016,
Thessaloniki, Greec
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