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New supersymmetric sigma-model duality

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Sergei M. Kuzenko, Ulf Lindstrom, Rikard von Unge

High Energy Physics - Theory · Submitted 11 Jun 2010

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The authors' main claim We demonstrate that the dual of any superconformal sigma-model is superconformal.

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arXiv ID1006.2299 (version 3)
Pith IDWCJFGRAT, Pith's permanent record of this paper and its review
CitationRikard von Unge, Sergei M. Kuzenko, Ulf Lindstrom. "New supersymmetric sigma-model duality." arXiv:1006.2299 (2010). https://pith.science/paper/WCJFGRAT
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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.08 · mentions code or data availability 0.01.

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arXiv listing abstract v3. Results and the main claim are underlined; .

We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any superconformal sigma-model is superconformal. Since N = 2 superconformal sigma-models (for which target spaces are hyperkahler cones) formulated in terms of polar multiplets are naturally associated with Kahler cones (which are target spaces for N = 1 superconformal sigma-models), polar-polar duality generates a transformation between different Kahler cones. In the non-superconformal case, we study implications of polar-polar duality for the sigma-model formulation in terms of N = 1 chiral superfields. In particular, we find the relation between the original hyperkahler potential and its dual. As an application of polar-polar duality, we study self-dual models.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. contribution 0.91 0.93 0.05 asserted 0.87
s1 These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. contribution 0.76 0.41 0.09 asserted 0.99
s2 We demonstrate that the dual of any superconformal sigma-model is superconformal. result 0.99 0.94 0.38 asserted 1.00
s3 Since N = 2 superconformal sigma-models (for which target spaces are hyperkahler cones) formulated in terms of polar multiplets are naturally associated with Kahler cones (which are target spaces for N = 1 superconformal sigma-models), polar-polar duality generates a transformation between different Kahler cones. interpretation 0.89 0.37 0.18 asserted 1.00
s4 In the non-superconformal case, we study implications of polar-polar duality for the sigma-model formulation in terms of N = 1 chiral superfields. contribution 1.00 0.88 0.04 asserted 0.59
s5 In particular, we find the relation between the original hyperkahler potential and its dual. result 0.99 0.95 0.14 asserted 1.00
s6 As an application of polar-polar duality, we study self-dual models. contribution 0.99 0.93 0.10 asserted 0.85

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The paper
Original abstract

We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any superconformal sigma-model is superconformal. Since N = 2 superconformal sigma-models (for which target spaces are hyperkahler cones) formulated in terms of polar multiplets are naturally associated with Kahler cones (which are target spaces for N = 1 superconformal sigma-models), polar-polar duality generates a transformation between different Kahler cones. In the non-superconformal case, we study implications of polar-polar duality for the sigma-model formulation in terms of N = 1 chiral superfields. In particular, we find the relation between the original hyperkahler potential and its dual. As an application of polar-polar duality, we study self-dual models.

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6 arXiv papers cite this in 7 sentences

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Papers citing it · 5 sentences without a confident label

Uses its method or tool 1 paper
  • This requires implementing the following steps: (i) pick out a complex structure $J_3$ to realize $$ as the Kähler manifold with respect to $J_3$; (ii) introduce Darboux coordinates for $ø^(2,0)$ and then construct the $$-model ([ref]); (iii) perform the inverse Legendre transformation (or the chiral-linear duality, following the terminology of [ref] ) with respect to the variables $_I$ and their conjugates.

    Comments on N = 2 supersymmetric sigma models in projective superspace · Introduction · 0.80

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  • To work out the geometry of this self-dual model one could use that models with this particular dependence on the polar multiplet can be dualized to an $(2)$ multiplet $η$ as _2(η) =-2/g^2 + η+ √(η^2+4/g^4) -ηln(g^2η^2/2+√(η^2+g^4η^4/4)) , although there may appear contour ambiguities [ref] .

    Properties of hyperkahler manifolds and their twistor spaces · Self-duality equation · 0.82

Uses data or values from 1 paper
Compares with 4 papers
Cites as background 20 papers
  • In the projective superspace approach, general off-shell $=2$ superconformal $$-models were studied in [ref] , while the superconformal couplings of $=2$ tensor multiplets had appeared already in [ref] without a discussion of the conformal properties.

    N = 2 supersymmetric sigma-models and duality · Introduction · 0.94

  • In the projective superspace approach, general off-shell $=2$ superconformal $$-models were studied in [ref] , while the superconformal couplings of $=2$ tensor multiplets had appeared already in [ref] without a discussion of the conformal properties.

    On superconformal projective hypermultiplets · Introduction · 0.94

  • In the projective superspace approach, general off-shell $=2$ superconformal $$-models were studied in [ref] , while the superconformal couplings of $=2$ tensor multiplets had appeared already in [ref] without a discussion of the conformal properties.

    New extended superconformal sigma models and Quaternion Kahler manifolds · Introduction · 0.94

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