Geometric superfield approach to superconformal mechanics

Ivanov, E.; Krivonos, S.; Leviant, V. M.

doi:10.1088/0305-4470/22/19/015

Cited by 133 publications

(348 citation statements)

References 17 publications

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“…It follows from the requirement of the κ-symmetry. By imposing the gauge fixing condition, we demonstrate that the model is canonically related to the SU(1, 1|N ) superparticle models constructed earlier in [35,37]. Section 3 contains the discussion of generalized Gell-Mann matrices and su(N ) algebra.…”

Section: Jhep04(2018)009mentioning

confidence: 85%

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SU(1, 1|N) superconformal mechanics with fermionic gauge symmetry

Chernyavsky

2018

J. High Energ. Phys.

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Abstract:We study superpaticle models with fermionic gauge symmetry on the coset spaces of the SU(1, 1|N ) supergroup. We first construct SU(1, 1|N ) supersymmetric extension of a particle on AdS 2 possessing the κ-symmetry. Including angular degrees of freedom and extending this model to a superparticle on the AdS 2 × CP N −1 background with two-form flux, one breaks the κ-symmetry down to a fermionic gauge symmetry with one parameter. A link of the background field configuration to the near horizon black hole geometries is discussed.

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Section: Jhep04(2018)009mentioning

confidence: 85%

“…There are several competing approaches to the construction of superconformal mechanics: the superfield approach [10,14,[16][17][18][19][20][21][22]35], the method of nonlinear realizations [5,9,25,34], and the canonical formalism (e.g. [29,37,45]).…”

Section: Introductionmentioning

confidence: 99%

SU(1, 1|N) superconformal mechanics with fermionic gauge symmetry

Chernyavsky

2018

J. High Energ. Phys.

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“…These constraints define standard and twisted N =4 supermultiplets, respectively [15,16]. From (2.1a) it immediately follows that…”

Section: Introductionmentioning

confidence: 98%

“…This is what we present in the current paper. We profit from the fact that N =4, d=1 superspace is well developed [15,16,17,18,19]. Our goal is to construct an N =4 superconformally invariant one-dimensional system for n bosonic and 4n fermionic physical components.…”

Section: Introductionmentioning

confidence: 99%

“…Hence we need n copies of an N =4 superfield of type (1,4,3), containing 1 physical bosonic, 4 fermionic and 3 auxiliary bosonic degrees of freedom. Such a supermultiplet is known for a long time [15], and its general action in superfields as well as in components was constructed in [1]. Everything in this action depends on a single bosonic function G of the n superfields, namely the superpotential.…”

Section: Introductionmentioning

confidence: 99%

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N=4 superconformal n-particle mechanics via superspace

Krivonos¹,

Lechtenfeld

Polovnikov

2009

Nuclear Physics B

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We revisit the (untwisted) superfield approach to one-dimensional multi-particle systems with N =4 superconformal invariance. The requirement of a standard (flat) bosonic kinetic energy implies the existence of inertial (super-)coordinates, which is nontrivial beyond three particles. We formulate the corresponding integrability conditions, whose solution directly yields the superpotential, the two prepotentials and the bosonic potential. The structure equations for the two prepotentials, including the WDVV equation, follow automatically. The general solution for translation-invariant three-particle models is presented and illustrated with examples. For the four-particle case, we take advantage of known WDVV solutions to construct a D3 and a B3 model, thus overcoming a previously-found barrier regarding the bosonic potential. The general solution and classification remain a challenge.

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Supersymmetric Mechanics in Superspace

Bellucci

Krivonos

Supersymmetric Mechanics – Vol. 1

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These Lectures have been given at Laboratori Nazionali di Frascati in the month of March, 2005. The main idea was to provide our young collegues, who joined us in our attempts to understand the structure of $N$-extended supersymmetric one-dimensional systems, with short descriptions of the methods and techniques we use. This was reflected in the choice of material and in the style of presentation. We base our treatment mainly on the superfield point of view. Moreover, we prefer to deal with N=4 and N=8 superfields. At present, the exists an extensive literature on the components approach to extended supersymmetric theories in $d=1$ while the manifestly supersymmetric formulation in terms of properly constrained superfields is much less known. Nevertheless, we believe that just such formulations are preferable. In order to make these Lectures more or less self-consistent, we started from the simplest examples of one-dimensional supersymmetric theories and paid a lot of attention to the peculiarities of $d=1$ supersymmetry. From time to time we presented the calculations in a very detailed way. In other cases we omitted the details and gave only the final answers. In any case these Lectures cannot be considered as a textbook in any respect. They can be considered as our personal point of view on the one-dimensional superfield theories and on the methods and techniques we believe to be important. Especially, all this concerns Section 3, were we discuss the nonlinear realizations method. We did not present any proofs in this Section. Instead we focused on the details of calculations. Finally, we apologize for the absolutely incomplete list of References

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Geometric superfield approach to superconformal mechanics

Cited by 133 publications

References 17 publications

SU(1, 1|N) superconformal mechanics with fermionic gauge symmetry

SU(1, 1|N) superconformal mechanics with fermionic gauge symmetry

N=4 superconformal n-particle mechanics via superspace

Supersymmetric Mechanics in Superspace

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