19,379 research outputs found
Supersymmetrizing 5d instanton operators
We construct a supersymmetric version of instanton operators in
five-dimensional Yang-Mills theories. This is possible by considering a
five-dimensional generalization of the familiar four-dimensional topologically
twisted theory, where the gauge configurations corresponding to instanton
operators are supersymmetric.Comment: 8 pages; v2: additional references added, typos correcte
Modeling Adoption and Usage of Competing Products
The emergence and wide-spread use of online social networks has led to a
dramatic increase on the availability of social activity data. Importantly,
this data can be exploited to investigate, at a microscopic level, some of the
problems that have captured the attention of economists, marketers and
sociologists for decades, such as, e.g., product adoption, usage and
competition.
In this paper, we propose a continuous-time probabilistic model, based on
temporal point processes, for the adoption and frequency of use of competing
products, where the frequency of use of one product can be modulated by those
of others. This model allows us to efficiently simulate the adoption and
recurrent usages of competing products, and generate traces in which we can
easily recognize the effect of social influence, recency and competition. We
then develop an inference method to efficiently fit the model parameters by
solving a convex program. The problem decouples into a collection of smaller
subproblems, thus scaling easily to networks with hundred of thousands of
nodes. We validate our model over synthetic and real diffusion data gathered
from Twitter, and show that the proposed model does not only provides a good
fit to the data and more accurate predictions than alternatives but also
provides interpretable model parameters, which allow us to gain insights into
some of the factors driving product adoption and frequency of use
Aspects of the moduli space of instantons on and its orbifolds
We study the moduli space of self-dual instantons on . These
are described by an ADHM-like construction which allows to compute the Hilbert
series of the moduli space. The latter has been found to be blind to certain
compact directions. In this paper we probe these, finding them to correspond to
a Grassmanian, upon considering appropriate ungaugings. Moreover, the ADHM-like
construction can be embedded into a gauge theory with a known gravity
dual. Using this, we realize in (part of) the instanton moduli
space providing at the same time further evidence supporting the
duality. Moreover, upon orbifolding, we provide the ADHM-like construction of
instantons on as well as compute its Hilbert
series. As in the unorbifolded case, these turn out to coincide with those for
instantons on .Comment: 65 page
5d gauge theories on orbifolds and 4d 't Hooft line indices
We study indices for 5d gauge theories on S^1 \times S^4/Z_n. In the large
orbifold limit, n \rightarrow \infty, we find evidence that the indices become
4d indices in the presence of a 't Hooft line operator. The non-perturbative
part of the index poses some subtleties when being compared to the 4d monopole
bubbling which happens in the presence of 't Hooft line operators. We study
such monopole bubbling indices and find an interesting connection to the
Hilbert series of the moduli space of instantons on an auxiliary ALE space.Comment: 43 page
On the 5d instanton index as a Hilbert series
The superconformal index for N=2 5d theories contains a non-perturbative part
arising from 5d instantonic operators which coincides with the Nekrasov
instanton partition function. In this note, for pure gauge theories, we
elaborate on the relation between such instanton index and the Hilbert series
of the instanton moduli space. We propose a non-trivial identification of
fugacities allowing the computation of the instanton index through the Hilbert
series. We show the agreement of our proposal with existing results in the
literature, as well as use it to compute the exact index for a pure U(1) gauge
theory.Comment: 13 pages, 2 figure
The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
We study the moduli spaces of self-dual instantons on CP^2 in a simple group
G. When G is a classical group, these instanton solutions can be realised using
ADHM-like constructions which can be naturally embedded into certain three
dimensional quiver gauge theories with 4 supercharges. The topological data for
such instanton bundles and their relations to the quiver gauge theories are
described. Based on such gauge theory constructions, we compute the Hilbert
series of the moduli spaces of instantons that correspond to various
configurations. The results turn out to be equal to the Hilbert series of their
counterparts on C^2 upon an appropriate mapping, in agreement with the result
of [arXiv:0802.3120]. We check the former against the Hilbert series derived
from the blowup formula for the Hirzebruch surface F_1 and find an agreement.
The connection between the moduli spaces of instantons on such two spaces is
explained in detail.Comment: 40 pages; v2: references edite
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