5,191 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
Discrete Darboux transformation for discrete polynomials of hypergeometric type
Darboux Transformation, well known in second order differential operator
theory, is applied here to the difference equation satisfied by the discrete
hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)
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
On the structure of the top homology group of the Johnson kernel
The Johnson kernel is the subgroup of the mapping class group
of a genus oriented closed surface
generated by all Dehn twists about separating curves. In this paper we study
the structure of the top homology group . For any collection of disjoint separating curves on
one can construct the corresponding abelian cycle in the group
; such abelian cycles will be called
simplest. In this paper we describe the structure of -module on the subgroup of generated by all simplest abelian cycles
and find all relations between them.Comment: 22 page
The top homology group of the genus 3 Torelli group
The Torelli group of a genus oriented surface is the subgroup
of the mapping class group consisting of
all mapping classes that act trivially on .
The quotient group is isomorphic to the
symplectic group . The cohomological dimension of the
group equals to . The main goal of the present paper is
to compute the top homology group of the Torelli group in the case as
-module. We prove an isomorphism
where is the quotient of by its diagonal subgroup
with the natural action of the permutation group (the action
of is trivial). We also construct an
explicit set of generators and relations for the group .Comment: 35 pages, minor correction
On a modular property of N=2 superconformal theories in four dimensions
In this note we discuss several properties of the Schur index of N=2
superconformal theories in four dimensions. In particular, we study modular
properties of this index under SL(2,Z) transformations of its parameters.Comment: 23 page, 2 figure
Driving Operators Relevant: A Feature of Chern-Simons Interaction
By computing anomalous dimensions of gauge invariant composite operators
and in Chern-Simons fermion and boson
models, we address that Chern-Simons interactions make these operators more
relevant or less irrelevant in the low energy region. We obtain a critical
Chern-Simons fermion coupling, , for a phase
transition at which the leading irrelevant four-fermion operator
becomes marginal, and a critical Chern-Simons boson
coupling, , for a similar phase transition
for the leading irrelevant operator . We see this phenomenon
also in the expansion.Comment: (ten pages, latex, figures included
Self-Similar Potentials and the q-Oscillator Algebra at Roots of Unity
Properties of the simplest class of self-similar potentials are analyzed.
Wave functions of the corresponding Schr\"odinger equation provide bases of
representations of the -deformed Heisenberg-Weyl algebra. When the parameter
is a root of unity the functional form of the potentials can be found
explicitly. The general and the particular potentials are given
by the equianharmonic and (pseudo)lemniscatic Weierstrass functions
respectively.Comment: 15 pp, Latex, to appear in Lett.Math.Phy
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
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