38,750 research outputs found
Finite Factorization equations and Sum Rules for BPS correlators in N=4 SYM theory
A class of exact non-renormalized extremal correlators of half-BPS operators
in N=4 SYM, with U(N) gauge group, is shown to satisfy finite factorization
equations reminiscent of topological gauge theories. The finite factorization
equations can be generalized, beyond the extremal case, to a class of
correlators involving observables with a simple pattern of SO(6) charges. The
simple group theoretic form of the correlators allows equalities between ratios
of correlators in N=4 SYM and Wilson loops in Chern-Simons theories at
k=\infty, correlators of appropriate observables in topological G/G models and
Wilson loops in two-dimensional Yang-Mills theories. The correlators also obey
sum rules which can be generalized to off-extremal correlators. The simplest
sum rules can be viewed as large k limits of the Verlinde formula using the
Chern-Simons correspondence. For special classes of correlators, the saturation
of the factorization equations by a small subset of the operators in the large
N theory is related to the emergence of semiclassical objects like KK modes and
giant gravitons in the dual ADS \times S background. We comment on an
intriguing symmetry between KK modes and giant gravitons.Comment: 1+69 pages, harvmac, 38 figures; v2: references added, comment added
on next-to-extremal correlator
Semi-naive dimensional renormalization
We propose a treatment of in dimensional regularization which is
based on an algebraically consistent extension of the Breitenlohner-Maison-'t
Hooft-Veltman (BMHV) scheme; we define the corresponding minimal
renormalization scheme and show its equivalence with a non-minimal BMHV scheme.
The restoration of the chiral Ward identities requires the introduction of
considerably fewer finite counterterms than in the BMHV scheme. This scheme is
the same as the minimal naive dimensional renormalization in the case of
diagrams not involving fermionic traces with an odd number of , but
unlike the latter it is a consistent scheme. As a simple example we apply our
minimal subtraction scheme to the Yukawa model at two loops in presence of
external gauge fields.Comment: 28 pages, 3 figure
A Generic Framework for Engineering Graph Canonization Algorithms
The state-of-the-art tools for practical graph canonization are all based on
the individualization-refinement paradigm, and their difference is primarily in
the choice of heuristics they include and in the actual tool implementation. It
is thus not possible to make a direct comparison of how individual algorithmic
ideas affect the performance on different graph classes.
We present an algorithmic software framework that facilitates implementation
of heuristics as independent extensions to a common core algorithm. It
therefore becomes easy to perform a detailed comparison of the performance and
behaviour of different algorithmic ideas. Implementations are provided of a
range of algorithms for tree traversal, target cell selection, and node
invariant, including choices from the literature and new variations. The
framework readily supports extraction and visualization of detailed data from
separate algorithm executions for subsequent analysis and development of new
heuristics.
Using collections of different graph classes we investigate the effect of
varying the selections of heuristics, often revealing exactly which individual
algorithmic choice is responsible for particularly good or bad performance. On
several benchmark collections, including a newly proposed class of difficult
instances, we additionally find that our implementation performs better than
the current state-of-the-art tools
The submonoid and rational subset membership problems for graph groups
We show that the membership problem in a finitely generated submonoid of a
graph group (also called a right-angled Artin group or a free partially
commutative group) is decidable if and only if the independence graph
(commutation graph) is a transitive forest. As a consequence we obtain the
first example of a finitely presented group with a decidable generalized word
problem that does not have a decidable membership problem for finitely
generated submonoids. We also show that the rational subset membership problem
is decidable for a graph group if and only if the independence graph is a
transitive forest, answering a question of Kambites, Silva, and the second
author. Finally we prove that for certain amalgamated free products and
HNN-extensions the rational subset and submonoid membership problems are
recursively equivalent. In particular, this applies to finitely generated
groups with two or more ends that are either torsion-free or residually finite
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