3,994 research outputs found
Exact Propagators for Soliton Potentials
Using the method of Darboux transformations (or equivalently supersymmetric
quantum mechanics) we obtain an explicit expression for the propagator for the
one-dimensional Schr\"odinger equation with a multi-soliton potential.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Classical quasi-trigonometric matrices of Cremmer-Gervais type and their quantization
We propose a method of quantization of certain Lie bialgebra structures on
the polynomial Lie algebras related to quasi-trigonometric solutions of the
classical Yang-Baxter equation. The method is based on so-called affinization
of certain seaweed algebras and their quantum analogues.Comment: 9 pages, LaTe
SUSY transformations with complex factorization constants. Application to spectral singularities
Supersymmetric (SUSY) transformation operators corresponding to complex
factorization constants are analyzed as operators acting in the Hilbert space
of functions square integrable on the positive semiaxis. Obtained results are
applied to Hamiltonians possessing spectral singularities which are
non-Hermitian SUSY partners of selfadjoint operators. A new regularization
procedure for the resolution of the identity operator in terms of continuous
biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed.
It is also shown that the continuous spectrum eigenfunction has zero binorm (in
the sense of distributions) at the singular point.Comment: Thanks to A. Sokolov a number of inaccuracies are correcte
The anomalous current multiplet in 6D minimal supersymmetry
For supersymmetric gauge theories with eight supercharges in four, five and
six dimensions, a conserved current belongs to the linear multiplet. In the
case of six-dimensional Poincar\'e supersymmetry, we present a
consistent deformation of the linear multiplet which describes chiral
anomalies. This is achieved by developing a superform formulation for the
deformed linear multiplet. In the abelian case, we compute a nonlocal effective
action generating the gauge anomaly.Comment: 27 pages; V2: published versio
Chiral anomalies in six dimensions from harmonic superspace
We develop a superfield approach to compute chiral anomalies in general
supersymmetric gauge theories in six dimensions. Within the
harmonic-superspace formulation for these gauge theories, the anomalous
contributions to the effective action only come from matter and ghost
hypermultiplets. By studying the short-distance behaviour of the propagator for
the hypermultiplet coupled to a background vector multiplet, we compute the
covariant and consistent chiral anomalies. We also provide a superform
formulation for the non-abelian anomalous current multiplet in general supersymmetric gauge theories.Comment: 33 page
Superconformal field theory in three dimensions: Correlation functions of conserved currents
For N-extended superconformal field theories in three spacetime dimensions
(3D), with N=1,2,3, we compute the two- and three-point correlation functions
of the supercurrent and the flavour current multiplets. We demonstrate that
supersymmetry imposes additional restrictions on the correlators of conserved
currents as compared with the non-supersymmetric case studied by Osborn and
Petkou in hep-th/9307010. It is shown that the three-point function of the
supercurrent is determined by a single functional form consistent with the
conservation equation and all the symmetry properties. Similarly, the
three-point function of the flavour current multiplets is also determined by a
single functional form in the N=1 and N=3 cases. The specific feature of the
N=2 case is that two independent structures are allowed for the three-point
function of flavour current multiplets, but only one of them contributes to the
three-point function of the conserved currents contained in these multiplets.
Since the supergravity and super-Yang-Mills Ward identities are expected to
relate the coefficients of the two- and three-point functions under
consideration, the results obtained for 3D superconformal field theory are
analogous to those in 2D conformal field theory.
In addition, we present a new supertwistor construction for compactified
Minkowski superspace. It is suitable for developing superconformal field theory
on 3D spacetimes other than Minkowski space, such as S^1 x S^2 and its
universal covering space R x S^2.Comment: 81 pages; v2: reference added, typos correcte
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