3,436 research outputs found
Superconformal indices of three-dimensional theories related by mirror symmetry
Recently, Kim and Imamura and Yokoyama derived an exact formula for
superconformal indices in three-dimensional field theories. Using their
results, we prove analytically the equality of superconformal indices in some
U(1)-gauge group theories related by the mirror symmetry. The proofs are based
on the well known identities of the theory of -special functions. We also
suggest the general index formula taking into account the global
symmetry present for abelian theories.Comment: 17 pages; minor change
Loss of spiritual and moral values
В работе была рассмотрена проблема духовно-нравственного воспитания молодежи Российского общества. В процессе изучения были выявлены проблемы, которые были связаны с утратой духовных и нравственных ценностей, перед нами стояла задача выявить пути и методы решения этой проблемы.In this study we consider the problem of spiritual and moral education of the youth of the Russian society. In the course of studying the problems were identified that were associated with the loss of spiritual and moral values, our task was to identify ways and means of solving this problem
Relation between the 4d superconformal index and the S^3 partition function
A relation between the 4d superconformal index and the S^3 partition function
is studied with focus on the 4d and 3d actions used in localization. In the
case of vanishing Chern-Simons levels and round S^3 we explicitly show that the
3d action is obtained from the 4d action by dimensional reduction up to terms
which do not affect the exact results. By combining this fact and a recent
proposal concerning a squashing of S^3 and SU(2) Wilson line, we obtain a
formula which gives the partition function depending on the Weyl weight of
chiral multiplets, real mass parameters, FI parameters, and a squashing
parameter as a limit of the index of a parent 4d theory.Comment: 20 pages, LaTeX; v2: comments added; v3: minor corrections, version
published in JHE
S-duality and 2d Topological QFT
We study the superconformal index for the class of N=2 4d superconformal
field theories recently introduced by Gaiotto. These theories are defined by
compactifying the (2,0) 6d theory on a Riemann surface with punctures. We
interpret the index of the 4d theory associated to an n-punctured Riemann
surface as the n-point correlation function of a 2d topological QFT living on
the surface. Invariance of the index under generalized S-duality
transformations (the mapping class group of the Riemann surface) translates
into associativity of the operator algebra of the 2d TQFT. In the A_1 case, for
which the 4d SCFTs have a Lagrangian realization, the structure constants and
metric of the 2d TQFT can be calculated explicitly in terms of elliptic gamma
functions. Associativity then holds thanks to a remarkable symmetry of an
elliptic hypergeometric beta integral, proved very recently by van de Bult.Comment: 25 pages, 11 figure
q-Ultraspherical polynomials for q a root of unity
Properties of the -ultraspherical polynomials for being a primitive
root of unity are derived using a formalism of the algebra. The
orthogonality condition for these polynomials provides a new class of
trigonometric identities representing discrete finite-dimensional analogs of
-beta integrals of Ramanujan.Comment: 7 pages, LATE
Distinct Patterns of Expression and Evolution of Intronless and Intron-Containing Mammalian Genes
Comparison of expression levels and breadth and evolutionary rates of intronless and intron-containing mammalian genes shows that intronless genes are expressed at lower levels, tend to be tissue specific, and evolve significantly faster than spliced genes. By contrast, monomorphic spliced genes that are not subject to detectable alternative splicing and polymorphic alternatively spliced genes show similar statistically indistinguishable patterns of expression and evolution. Alternative splicing is most common in ancient genes, whereas intronless genes appear to have relatively recent origins. These results imply tight coupling between different stages of gene expression, in particular, transcription, splicing, and nucleocytosolic transport of transcripts, and suggest that formation of intronless genes is an important route of evolution of novel tissue-specific functions in animals
An E7 Surprise
We explore some curious implications of Seiberg duality for an SU(2)
four-dimensional gauge theory with eight chiral doublets. We argue that two
copies of the theory can be deformed by an exactly marginal quartic
superpotential so that they acquire an enhanced E7 flavor symmetry. We argue
that a single copy of the theory can be used to define an E7-invariant
superconformal boundary condition for a theory of 28 five-dimensional free
hypermultiplets. Finally, we derive similar statements for three-dimensional
gauge theories such as an SU(2) gauge theory with six chiral doublets or Nf=4
SQED.Comment: 27 page
Rigid Supersymmetric Theories in Curved Superspace
We present a uniform treatment of rigid supersymmetric field theories in a
curved spacetime , focusing on four-dimensional theories with four
supercharges. Our discussion is significantly simpler than earlier treatments,
because we use classical background values of the auxiliary fields in the
supergravity multiplet. We demonstrate our procedure using several examples.
For we reproduce the known results in the literature. A
supersymmetric Lagrangian for exists, but unless the
field theory is conformal, it is not reflection positive. We derive the
Lagrangian for and note that the
time direction can be rotated to Euclidean signature and be
compactified to only when the theory has a continuous R-symmetry. The
partition function on is independent of
the parameters of the flat space theory and depends holomorphically on some
complex background gauge fields. We also consider R-invariant
theories on and clarify a few points about them.Comment: 26 pages, uses harvmac; v2 with added reference
Bipartite quantum states and random complex networks
We introduce a mapping between graphs and pure quantum bipartite states and
show that the associated entanglement entropy conveys non-trivial information
about the structure of the graph. Our primary goal is to investigate the family
of random graphs known as complex networks. In the case of classical random
graphs we derive an analytic expression for the averaged entanglement entropy
while for general complex networks we rely on numerics. For large
number of nodes we find a scaling where both
the prefactor and the sub-leading O(1) term are a characteristic of
the different classes of complex networks. In particular, encodes
topological features of the graphs and is named network topological entropy.
Our results suggest that quantum entanglement may provide a powerful tool in
the analysis of large complex networks with non-trivial topological properties.Comment: 4 pages, 3 figure
Bootstrapping the superconformal index with surface defects
The analytic properties of the N = 2 superconformal index are given a
physical interpretation in terms of certain BPS surface defects, which arise as
the IR limit of supersymmetric vortices. The residue of the index at a pole in
flavor fugacity is interpreted as the index of a superconformal field theory
without this flavor symmetry, but endowed with an additional surface defect.
The residue can be efficiently extracted by acting on the index with a
difference operator of Ruijsenaars-Schneider type. By imposing the
associativity constraints of S-duality, we are then able to evaluate the index
of all generalized quiver theories of type A, for generic values of the three
superconformal fugacities, with or without surface defects.Comment: 60 pages, 7 figure
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