Types of N=2 Superconformal Transformations (original) (raw)
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Superconformal-like transformations and nonlinear realizations
1998
We consider various properties of N = 1 superconformal-like transformations which generalize conformal transformations to supersymmetric and noninvertible case. Alternative tangent space reduction in N = 1 superspace leads to some new transformations which are similar to the anti-holomorphic ones of the complex function theory, which g i v es new odd N = 1 superanalog of complex structure. They are dual to the ordinary superconformal transformations subject to the Berezinian addition formula presented, noninvertible, highly degenerated and twist parity of the tangent space in the standard basis, and they also lead to some "mixed cocycle condition". A new parametrization for the superconformal group is presented which allows us to extend it to a semigroup and to unify the description of old and new transformations. The nonlinear realization of invertible and noninvertible N = 1 superconformal-like transformations is studied by means of the odd curve motion technique and introduced clear diagrammatic method. 1991 A.M.S. Subject Classi cation Codes.
Superconformal mechanics and nonlinear supersymmetry
Journal of High Energy Physics, 2003
We show that a simple change of the classical boson-fermion coupling constant, 2alphato2alphan2\alpha \to 2\alpha n 2alphato2alphan, ninNn\in \NninN, in the superconformal mechanics model gives rise to a radical change of a symmetry: the modified classical and quantum systems are characterized by the nonlinear superconformal symmetry. It is generated by the four bosonic integrals which form the so(1,2) x u(1) subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2 so(1,2)-representations and anticommuting for the order n polynomials of the even generators. We find that the modified quantum system with an integer value of the parameter alpha\alphaalpha is described simultaneously by the two nonlinear superconformal symmetries of the orders relatively shifted in odd number. For the original quantum model with ∣alpha∣=p|\alpha|=p∣alpha∣=p, pinNp\in \NpinN, this means the presence of the order 2p nonlinear superconformal symmetry in addition to the osp(2|2) supersymmetry.
Journal of Physics A: Mathematical and Theoretical, 2012
We survey the salient features and problems of conformal and superconformal mechanics and portray some of its developments over the past decade. Both classical and quantum issues of single-and multiparticle systems are covered. ⋆ Invited review by Journal of Physics A: Mathematical and Theoretical × On leave of absence from V.N. Karazin Kharkov National University, Ukraine N =0 , N =2 [61] and N = 4 [9] superconformal mechanics.
On the semigroup nature of superconformal symmetry
Journal of Mathematical Physics, 1991
A semigroup of N = 1 superconformal transformations is introduced and analyzed. Noninvertible ones can describe transitions from body to soul and form a proper ideal containing a set of nilpotent transformations. The projective superspace is also considered. Transformations twisting the parity of a tangent space are brought in. They can be a nonsuperconformal "square root" of noninvertible superconformal transformations and the analogs of the Poincare metric and conformal invariance are suggested for them.
Conformal bridge transformation, 𝒫𝒯- and super- symmetry
2021
Supersymmetric extensions of the 1D and 2D Swanson models are investigated by using the conformal bridge transformation. The latter plays the role of the Dyson map that transforms the models into supersymmetric generalizations of the 1D and 2D harmonic oscillator systems, allowing us to define pseudo-Hermitian conjugation and a suitable inner product. In the 1D case, we construct a 𝒫𝒯-invariant supersymmetric model with N subsystems by using the conformal generators of supersymmetric free particle, and identify its complete set of the true bosonic and fermionic integrals of motion. We also investigate an exotic N=2 supersymmetric generalization, in which the higher order supercharges generate nonlinear superalgebras. We generalize the construction for the 2D case to obtain the 𝒫𝒯-invariant supersymmetric systems that transform into the spin-1/2 Landau problem with and without an additional Aharonov-Bohm flux, where in the latter case, the well-defined integrals of motion appear only...
Second N=1 Superanalog of Complex Structure
We found another N = 1 odd superanalog of complex structure (the even one is widely used in the theory of super Riemann surfaces). New N = 1 superconformal-like transformations are similar to anti-holomorphic ones of nonsupersymmetric complex function theory. They are dual to the ordinary superconformal transformations subject to the Berezinian addition formula presented, noninvertible, highly degenerated and twist parity of the tangent space in the standard basis. They also lead to the "mixed cocycle condition" which can be used in building noninvertible objects analogous to super Riemann surfaces. A new parametrization for the superconformal group is presented which allows us to extend it to a semigroup and to unify the description of old and new transformations.
Noninvertible N=1 superanalog of complex structure
Journal of Mathematical Physics, 1997
We found another N = 1 odd superanalog of complex structure (the even one is widely used in the theory of super Riemann surfaces). New N = 1 superconformal-like transformations are similar to anti-holomorphic ones of nonsupersymmetric complex function theory. They are dual to the ordinary superconformal transformations subject to the Berezinian addition formula presented, noninvertible, highly degenerated and twist parity of the tangent space in the standard basis. They also lead to the "mixed cocycle condition" which can be used in building noninvertible objects analogous to super Riemann surfaces. A new parametrization for the superconformal group is presented which allows us to extend it to a semigroup and to unify the description of old and new transformations.
Some Algebraic Symmetries of (2, 2)-SUPERSYMMETRIC Systems
Modern Physics Letters A, 2001
The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2, 2)-supersymmetric systems in two-dimensional space–time which are closely related to superstring models. They all turn out to possess some hitherto unexploited and geometrically and topologically unobstructed symmetries, providing new tools for studying the topology and geometry of superstring target space–times, and so the dynamics of the effective field theory in these.
Comments on the N= 2, 3, 4 superconformal algebras in two dimensions
Physics Letters B, 1987
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Nonlinear superconformal symmetry
We discuss two different nonlinear generalizations of the osp(2|2) supersymmetry which arise in superconformal mechanics and fermion-monopole models.