A tale of exceptional 3d dualities Benvenuti, Sergio
The journal of high energy physics,
03/2019, Letnik:
2019, Številka:
3
Journal Article
Recenzirano
Odprti dostop
A
bstract
We consider interesting Seiberg dualities for Usp gauge theories with an antisymmetric, 8 fundamentals and no superpotential. We reduce to three dimensions and systematically analyze ...deformations triggered by real and complex masses, reaching a plethora of
N
= 2 dualities for U(
N
) and Usp(2
N
) gauge theories, possibly with monopole superpotentials and Chern-Simons interactions. Special cases of these “exceptional dualities” are: supersymmetry enhancement dualities, “duality appetizers” and many known dualities relating rank-1 gauge groups. The 4
d
N
= 1 Usp dualities provide a unified perspective on many curious phenomena of 3
d
and 4
d
gauge theories with four supercharges.
Finally, we propose a free mirror for
A
2
N
Argyres-Douglas, with its related adjoint-Usp(2
N
) duality, and we construct a mirror for adjoint-U(
N
), with an arbitrary number flavors and zero superpotential.
This survey aims to present a comprehensive and systematic synthesis of concepts and results on the minimal state space realization problem for positive, linear, time-invariant systems. Positive ...systems are systems for which the state and the output are always non-negative for any non-negative initial state and input. They are used to model phenomena in which the variables must take non-negative values due to the nature of the underlying physical system. Restricting the state–space realization to positive systems makes the problem extremely different and much more difficult than that for ordinary systems. Indeed, a minimal positive realization may have a dimension even much greater than the order of the transfer function it realizes. Although the problem of finding a finite-dimensional positive state–space realization of a given transfer function has been solved, the characterization of minimality for positive systems is still an open problem. This survey introduces the reader to different aspects of the problem and presents the mathematical approaches used to tackle it as well as some relevant related problems. Moreover, some partial results are presented. Finally, a comprehensive bibliography on positive systems, organized by topics, is provided.
We propose a general way to complete supersymmetric theories with operators below the unitarity bound, adding gauge-singlet fields that enforce the decoupling of such operators. This makes it ...possible to perform all usual computations, and to compactify on a circle. We concentrate on a duality between an N=1 SU(2) gauge theory and the N=2 A_{3} Argyres-Douglas theory, mapping the moduli space and chiral ring of the completed N=1 theory to those of the A_{3} model. We reduce the completed gauge theory to 3D, finding a 3D duality with N=4 supersymmetric QED (SQED) with two flavors. The naive dimensional reduction is instead N=2 SQED. Crucial is a concept of chiral ring stability, which modifies the superpotential and allows for a 3D emergent global symmetry.
•The wildflower diversity promotes the diversity of pollinators.•The dominance of a few wildflowers increases pollinators characterized by constancy.•There is no close relationship between wildflower ...biodiversity and rates of pollinator visits.•Crab spiders are more abundant in less biodiverse wildflower communities.•Crab spiders appear to provide an ecosystem service that reduces the seed-set of dominant species, thus maintaining biodiversity.
Wildflowers play a crucial role in the functionality of the agroecosystem food chain. In order to investigate the role of biodiversity in the relationships between wildflowers, relative pollinators and their crab spider predators, six wildflower communities, characterized by a different botanical complexity, were sown in a two-year experiment. The selected Mediterranean species flowered between March and September, with a peak during May. The indices of dominance (D) and biodiversity (H ') of the wildflower communities confirmed two expected levels of floristic complexity of the oligo-specific plant communities (only three species) in comparison to the poly-specific wildflower communities (a further 20 species for each oligo-specific plant community). The greater floristic biodiversity facilitated a greater pollinator biodiversity (bees, solitary bees, bumblebees, lepidoptera, diptera syrphidae and bombyliidae) but the respective total visitation rate was unchanged. In the case of the lower floristic complexity (oligo-specific plant communities), the dominance of bees increased, confirming their tendency to always choose the same wildflower species to visit. The evaluation of the crab spiders detected on flowers, waiting for pollinators, showed a significant reduction in the case of additional botanical complexity. Indeed, significant linear regressions (p < 0.05) showed a direct relationship between the number of crab spiders observed and the dominance indices of the various wildflower communities. The paper also discusses the possible ecological role of crab spiders in the biodiversity sustainability of the various wildflower communities.
The biodiversity restoration of the agroecosystem through wildflower strips is one of the most important agronomic strategies of the last few decades. However, poor knowledge of the bio-agronomic ...characteristics of the various wildflower species often leads to suboptimal performances especially as a result of their poor seed germination and poor seedling emergence due to the erratic soil texture. A two-year experiment involving the sowing of eighteen wildflower species in different texture conditions highlighted how some species emerged earlier or more effectively than others and verifying the consequent ecosystem service provided to pollinators. Species with smaller seeds were more inhibited by sowing in soil with high content of clay. Additionally, an inverse relationship (Boltzmann's sigmoidal regression) was found between seed weight and soil-mediated inhibition. This soil-mediated inhibition was higher in the clayey textured soil, showing that this inhibition was mediated both by seed weight and by the clay particles of the soil. The reciprocal interference between the emerged seedlings also determined a further decline in the wildflower species with small seeds. This differing agronomic performance, after sowing in the two different soil textures, did not affect the number of pollinator visits. Performance differed both in terms of floristic biodiversity and pollinator biodiversity. Finally, the experiment highlighted the importance of the appropriate selection of the wildflower species for biodiversity restoration - not only in terms of pollen and nectar availability for pollinators, but also in terms of compatibility with the soil texture in which the wildflower seeds are sown.
•The sowing of wildflower strips is effective in enhancing agroecosystem biodiversity.•Soil texture strongly affects the agronomic performance of the selected wildflower mixtures.•Clay hinders germination and seedling emergence of species with small and light seeds.•Clay soils reduce the emergence of small-seed species, thus reducing the biodiversity of both plants and pollinators.•The choice of wildflower mixtures according to the soil texture will optimize biodiversity restoration.
A
bstract
We continue the study of Lagrangian descriptions of
N
=
2
Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the Lagrangians of all the ...Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional
N
=
1
quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the (
A
k
,
A
kN
+
N
−1
) models. We study in detail how the
N
=
1
chiral rings map to the Coulomb and Higgs Branches of the
N
=
2
CFT’s. The three dimensional mirror RG flows are shown to land on the
N
=
4
complete graph quivers. We also compactify to three dimensions the gauge theory dual to (
A
1
,
D
4
), and find the expected Abelianization duality with
N
=
4
SQED with 3 flavors.
Easy-plane QED3’s in the large Nf limit Benvenuti, Sergio; Khachatryan, Hrachya
The journal of high energy physics,
05/2019, Letnik:
2019, Številka:
5
Journal Article
Recenzirano
Odprti dostop
A
bstract
We consider Quantum Electrodynamics in 2 + 1 dimensions with
N
f
fermionic or bosonic flavors, allowing for interactions that respect the global symmetry U(
N
f
/2)
2
. There are four ...bosonic and four fermionic fixed points, which we analyze using the large
N
f
expansion. We systematically compute, at order
O
(1/
N
f
), the scaling dimensions of quadratic and quartic mesonic operators.
We also consider Quantum Electrodynamics with minimal supersymmetry. In this case the large
N
f
scaling dimensions, extrapolated at
N
f
= 2, agree quite well with the scaling dimensions of a dual supersymmetric Gross-Neveu-Yukawa model. This provides a quantitative check of the conjectured duality.
In some applications one is interested in having a state–space realization with nonnegative matrices (positive realization) of a given transfer function and it is known that such a realization may ...have a dimension strictly larger than the order of the transfer function itself. Moreover, in most cases, it is desirable to have a realization with minimal dimension. Unfortunately, it is not known, to date, how to determine in general the minimum dimension of a positive realization and only lower and upper bounds to it are available. This letter provides an upper bound on the dimension of a minimal positive realization for transfer functions with simple poles. This is a considerable improvement on an earlier upper bound in which only transfer functions with real poles were considered.
A
bstract
We consider the lagrangian description of Argyres-Douglas theories of type
A
2
N
−1
, which is a SU(
N
) gauge theory with an adjoint and one fundamental flavor. An appropriate ...reformulation allows us to map the moduli space of vacua across the duality, and to dimensionally reduce. Going down to three dimensions, we find that the adjoint SQCD “abelianizes”: in the infrared it is equivalent to a
N
=
4
linear quiver theory. Moreover, we study the mirror dual: using a monopole duality to “sequentially confine” quivers tails with balanced nodes, we show that the mirror RG flow lands on
N
=
4
SQED with
N
flavors. These results make the supersymmetry enhancement explicit and provide a physical derivation of previous proposals for the three dimensional mirror of AD theories.
N = 1 dualities in 2+1 dimensions Benini, Francesco; Benvenuti, Sergio
The journal of high energy physics,
11/2018, Letnik:
2018, Številka:
11
Journal Article
Recenzirano
Odprti dostop
A
bstract
We consider minimally supersymmetric QCD in 2+1 dimensions, with Chern-Simons and superpotential interactions. We propose an infrared SU(
N
) ↔ U(
k
) duality involving gauge-singlet fields ...on one of the two sides. It shares qualitative features both with 3
d
bosonization and with 4
d
Seiberg duality. We provide a few consistency checks of the proposal, mapping the structure of vacua and performing perturbative computations in the
ε
-expansion.
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