373 research outputs found
On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
As a step toward uncovering the relation between the weak and the strong
coupling regimes of the super Yang-Mills theory beyond the
specral level, we have developed in a previous paper [arXiv:1410.8533] a novel
group theoretic interpretation of the Wick contraction of the fields, which
allowed us to compute a much more general class of three-point functions in the
SU(2) sector, as in the case of strong coupling [arXiv:1312.3727], directly in
terms of the determinant representation of the partial domain wall partition
funciton. Furthermore, we derived a non-trivial identity for the three point
functions with monodromy operators inserted, being the discrete counterpart of
the global monodromy condition which played such a crucial role in the
computation at strong coupling. In this companion paper, we shall extend our
study to the entire sector and obtain several important
generalizations. They include in particular (i) the manifestly conformally
covariant construction, from the basic principle, of the singlet-projection
operator for performing the Wick contraction and (ii) the derivation of the
monodromy relation for the case of the so-called "harmonic R-matrix", as well
as for the usual fundamental R-matrtix. The former case, which is new and has
features rather different from the latter, is expected to have important
applications. We also describe how the form of the monodromy relation is
modified as is reduced to its subsectors.Comment: 49+10 pages;v3 Published version. Typos corrected. Explicit form of
the monodromy relations for the three-point functions displaye
Charmonium-nucleon interactions from the time-dependent HAL QCD method
The charmonium-nucleon effective central interactions have been computed by
the time-dependent HAL QCD method. This gives an updated result of a previous
study based on the time-independent method, which is now known to be
problematic because of the difficulty in achieving the ground-state saturation.
We discuss that the result is consistent with the heavy quark symmetry. No
bound state is observed from the analysis of the scattering phase shift;
however, this shall lead to a future search of the hidden-charm pentaquarks by
considering channel-coupling effects.Comment: 8 pages, 8 figure
Lattice QCD Study of the Nucleon-Charmonium Interaction
The -nucleon interaction is studied by lattice QCD calculations. At
the leading order of the derivative expansion, the interaction consists of four
terms: the central, the spin-spin, and two types of tensor forces. We determine
these spin-dependent forces quantitatively by using the time-dependent HAL QCD
method. We find that the spin-spin force is the main cause of the hyperfine
splitting between the and the states, while the two tensor
forces have much smaller effects on the S-wave scattering processes.Comment: 5 pages, 4 figure
Novel construction and the monodromy relation for three-point functions at weak coupling
In this article, we shall develop and formulate two novel viewpoints and
properties concerning the three-point functions at weak coupling in the SU(2)
sector of the N = 4 super Yang-Mills theory. One is a double spin-chain
formulation of the spin-chain and the associated new interpretation of the
operation of Wick contraction. It will be regarded as a skew symmetric pairing
which acts as a projection onto a singlet in the entire SO(4) sector, instead
of an inner product in the spin-chain Hilbert space. This formalism allows us
to study a class of three-point functions of operators built upon more general
spin-chain vacua than the special configuration discussed so far in the
literature. Furthermore, this new viewpoint has the signicant advantage over
the conventional method: In the usual "tailoring" operation, the Wick
contraction produces inner products between off-shell Bethe states, which
cannot be in general converted into simple expressions. In contrast, our
procedure directly produces the so-called partial domain wall partition
functions, which can be expressed as determinants. Using this property, we
derive simple determinantal representation for a broader class of three-point
functions. The second new property uncovered in this work is the non-trivial
identity satisfied by the three-point functions with monodromy operators
inserted. Generically this relation connects three-point functions of different
operators and can be regarded as a kind of Schwinger-Dyson equation. In
particular, this identity reduces in the semiclassical limit to the triviality
of the product of local monodromies around the vertex operators, which played a
crucial role in providing all important global information on the three-point
function in the strong coupling regime. This structure may provide a key to the
understanding of the notion of "integrability" beyond the spectral level.Comment: 35 pages;v2 Minor corrections made. An appendix and references
added;v3 Typos correcte
Branch-and-Reduce Exponential/FPT Algorithms in Practice: A Case Study of Vertex Cover
We investigate the gap between theory and practice for exact branching
algorithms. In theory, branch-and-reduce algorithms currently have the best
time complexity for numerous important problems. On the other hand, in
practice, state-of-the-art methods are based on different approaches, and the
empirical efficiency of such theoretical algorithms have seldom been
investigated probably because they are seemingly inefficient because of the
plethora of complex reduction rules. In this paper, we design a
branch-and-reduce algorithm for the vertex cover problem using the techniques
developed for theoretical algorithms and compare its practical performance with
other state-of-the-art empirical methods. The results indicate that
branch-and-reduce algorithms are actually quite practical and competitive with
other state-of-the-art approaches for several kinds of instances, thus showing
the practical impact of theoretical research on branching algorithms.Comment: To appear in ALENEX 201
Cut Tree Construction from Massive Graphs
The construction of cut trees (also known as Gomory-Hu trees) for a given
graph enables the minimum-cut size of the original graph to be obtained for any
pair of vertices. Cut trees are a powerful back-end for graph management and
mining, as they support various procedures related to the minimum cut, maximum
flow, and connectivity. However, the crucial drawback with cut trees is the
computational cost of their construction. In theory, a cut tree is built by
applying a maximum flow algorithm for times, where is the number of
vertices. Therefore, naive implementations of this approach result in cubic
time complexity, which is obviously too slow for today's large-scale graphs. To
address this issue, in the present study, we propose a new cut-tree
construction algorithm tailored to real-world networks. Using a series of
experiments, we demonstrate that the proposed algorithm is several orders of
magnitude faster than previous algorithms and it can construct cut trees for
billion-scale graphs.Comment: Short version will appear at ICDM'1
Fast Exact Shortest-Path Distance Queries on Large Networks by Pruned Landmark Labeling
We propose a new exact method for shortest-path distance queries on
large-scale networks. Our method precomputes distance labels for vertices by
performing a breadth-first search from every vertex. Seemingly too obvious and
too inefficient at first glance, the key ingredient introduced here is pruning
during breadth-first searches. While we can still answer the correct distance
for any pair of vertices from the labels, it surprisingly reduces the search
space and sizes of labels. Moreover, we show that we can perform 32 or 64
breadth-first searches simultaneously exploiting bitwise operations. We
experimentally demonstrate that the combination of these two techniques is
efficient and robust on various kinds of large-scale real-world networks. In
particular, our method can handle social networks and web graphs with hundreds
of millions of edges, which are two orders of magnitude larger than the limits
of previous exact methods, with comparable query time to those of previous
methods.Comment: To appear in SIGMOD 201
- …