57,341 research outputs found
Gauge Threshold Corrections for Local String Models
We study gauge threshold corrections for local brane models embedded in a
large compact space. A large bulk volume gives important contributions to the
Konishi and super-Weyl anomalies and the effective field theory analysis
implies the unification scale should be enhanced in a model-independent way
from M_s to R M_s. For local D3/D3 models this result is supported by the
explicit string computations. In this case the scale R M_s comes from the
necessity of global cancellation of RR tadpoles sourced by the local model. We
also study D3/D7 models and discuss discrepancies with the effective field
theory analysis. We comment on phenomenological implications for gauge coupling
unification and for the GUT scale.Comment: 30 pages; v2: references added, minor typos correcte
Comparative Evaluation of Community Detection Algorithms: A Topological Approach
Community detection is one of the most active fields in complex networks
analysis, due to its potential value in practical applications. Many works
inspired by different paradigms are devoted to the development of algorithmic
solutions allowing to reveal the network structure in such cohesive subgroups.
Comparative studies reported in the literature usually rely on a performance
measure considering the community structure as a partition (Rand Index,
Normalized Mutual information, etc.). However, this type of comparison neglects
the topological properties of the communities. In this article, we present a
comprehensive comparative study of a representative set of community detection
methods, in which we adopt both types of evaluation. Community-oriented
topological measures are used to qualify the communities and evaluate their
deviation from the reference structure. In order to mimic real-world systems,
we use artificially generated realistic networks. It turns out there is no
equivalence between both approaches: a high performance does not necessarily
correspond to correct topological properties, and vice-versa. They can
therefore be considered as complementary, and we recommend applying both of
them in order to perform a complete and accurate assessment
Deformed N=2 theories, generalized recursion relations and S-duality
We study the non-perturbative properties of N=2 super conformal field
theories in four dimensions using localization techniques. In particular we
consider SU(2) gauge theories, deformed by a generic epsilon-background, with
four fundamental flavors or with one adjoint hypermultiplet. In both cases we
explicitly compute the first few instanton corrections to the partition
function and the prepotential using Nekrasov's approach. These results allow to
reconstruct exact expressions involving quasi-modular functions of the bare
gauge coupling constant and to show that the prepotential terms satisfy a
modular anomaly equation that takes the form of a recursion relation with an
explicitly epsilon-dependent term. We then investigate the implications of this
recursion relation on the modular properties of the effective theory and find
that with a suitable redefinition of the prepotential and of the effective
coupling it is possible, at least up to the third order in the deformation
parameters, to cast the S-duality relations in the same form as they appear in
the Seiberg-Witten solution of the undeformed theory.Comment: 33 pages, no figures, LaTeX2
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