3,223 research outputs found
Reconstruction of dielectric constants of multi-layered optical fibers using propagation constants measurements
We present new method for the numerical reconstruction of the variable
refractive index of multi-layered circular weakly guiding dielectric waveguides
using the measurements of the propagation constants of their eigenwaves. Our
numerical examples show stable reconstruction of the dielectric permittivity
function for random noise level using these measurements
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
Новые находки кремневой пластики в горно-лесном Зауралье
The paper introduces two flint figurines into scientific discourse, they were found during excavations of the multilayer Shaitanskoye 4-6 site in the Sverdlovsk region. Analysis of the contexts and analogies helps attribute these figurines to the Ayat culture of the Eneolithic with a high degree of certainty and consider them to be an evidence of symbolic activities of the local population in IV-III mill. BC. © 2021 Russian Academy of Sciences, Institute of Archaeology. All rights reserved.Работа выполнена при поддержке гранта РФФИ 18-09-40011 и Госзадания FEUZ-2020-0056
Exceptional Indices
Recently a prescription to compute the superconformal index for all theories
of class S was proposed. In this paper we discuss some of the physical
information which can be extracted from this index. We derive a simple
criterion for the given theory of class S to have a decoupled free component
and for it to have enhanced flavor symmetry. Furthermore, we establish a
criterion for the "good", the "bad", and the "ugly" trichotomy of the theories.
After interpreting the prescription to compute the index with non-maximal
flavor symmetry as a residue calculus we address the computation of the index
of the bad theories. In particular we suggest explicit expressions for the
superconformal index of higher rank theories with E_n flavor symmetry, i.e. for
the Hilbert series of the multi-instanton moduli space of E_n.Comment: 33 pages, 11 figures, v2: minor correction
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
Index for Three Dimensional Superconformal Field Theories and Its Applications
We review aspects of superconformal indices in three dimension. Three
dimensional superconformal indices can be exactly computed by using
localization method including monopole contribution, and can be applied to
provide evidences for mirror duality, AdS_4/CFT_3 correspondence and global
symmetry enhancement of strongly coupled gauge theories. After reviewing, we
discuss the possibility of global symmetry enhancement in a finite rank of
gauge group.Comment: 14 pages, Proceedings of the Seventh International Conference Quantum
Theory and Symmetries (QTS-7) in Prague, Czech Republic, August, 2011; v2:
minor modifications, discussion of supersymmetry enhancement of abelian ABJM
theory by using an index were adde
Charging the Superconformal Index
The superconformal index is an important invariant of superconformal field
theories. In this note we refine the superconformal index by inserting the
charge conjugation operator C. We construct a matrix integral for this charged
index for N=4 SYM with SU(N) gauge group. The key ingredient for the
construction is a "charged character," which reduces to Tr(C) for singlet
representations of the gauge group. For each irreducible real SU(N)
representation, we conjecture that this charged character is equal to the
standard character for a corresponding representation of SO(N+1) or SP(N-1),
for N even or odd respectively. The matrix integral for the charged index
passes tests for small N and for N -> infinity. Like the ordinary
superconformal index, for N=4 SYM the charged index is independent of N in the
large-N limit.Comment: 31 pages, v2: minor changes, published versio
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
Lagrangian Sp(3) BRST symmetry for irreducible gauge theories
The Lagrangian Sp(3) BRST symmetry for irreducible gauge theories is
constructed in the framework of homological perturbation theory. The canonical
generator of this extended symmetry is shown to exist. A gauge-fixing procedure
specific to the standard antibracket-antifield formalism, that leads to an
effective action, which is invariant under all the three differentials of the
Sp(3) algebra, is given.Comment: LaTeX 2e, 42 pages, to appear in Int. J. Mod. Phys.
On Paragrassmann Differential Calculus
Explicit general constructions of paragrassmann calculus with one and many
variables are given. Relations of the paragrassmann calculus to quantum groups
are outlined and possible physics applications are briefly discussed. This
paper is the same as the original 9210075 except added Appendix and minor
changes in Acknowledgements and References. IMPORTANT NOTE: This paper bears
the same title as the Dubna preprint E5-92-392 but is NOT identical to it,
containing new results, extended discussions, and references.Comment: 19p
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