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Self-dual supersymmetric nonlinear sigma models
High Energy Physics - Theory · Submitted 14 Jun 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one.
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The abstract, sentence by sentence
In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar and their conjugate superfields. Here we introduce CCL sigma models that are invariant under U(1) "duality rotations" exchanging the dynamical variables and their equations of motion. The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. The target space isometry group for these sigma models contains a subgroup U(1) x U(1).
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar and their conjugate superfields. | background 1.00 | 0.14 | 0.04 | hedged possibility 0.99 |
| s1 | Here we introduce CCL sigma models that are invariant under U(1) "duality rotations" exchanging the dynamical variables and their equations of motion. | contribution 1.00 | 0.92 | 0.18 | asserted 1.00 |
| s2 | The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. | result 0.98 | 0.85 | 0.25 | asserted 1.00 |
| s3 | These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. | result 0.95 | 0.82 | 0.36 | asserted 1.00 |
| s4 | Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. | result 0.98 | 0.82 | 0.18 | asserted 0.99 |
| s5 | The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. | result 0.88 | 0.89 | 0.12 | asserted 1.00 |
| s6 | Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. | result 0.92 | 0.70 | 0.07 | asserted 0.98 |
| s7 | The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. | result 0.96 | 0.76 | 0.12 | asserted 0.96 |
| s8 | Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. | result 0.95 | 0.73 | 0.08 | asserted 1.00 |
| s9 | In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. | result 0.96 | 0.80 | 0.08 | asserted 0.85 |
| s10 | We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. | result 0.87 | 0.90 | 0.14 | asserted 1.00 |
| s11 | The target space isometry group for these sigma models contains a subgroup U(1) x U(1). | result 1.00 | 0.74 | 0.07 | asserted 1.00 |
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Original abstract
In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar and their conjugate superfields. Here we introduce CCL sigma models that are invariant under U(1) "duality rotations" exchanging the dynamical variables and their equations of motion. The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. The target space isometry group for these sigma models contains a subgroup U(1) x U(1).
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How the literature uses it
3 arXiv papers cite this in 7 sentences
Papers citing it · 5 sentences without a confident label
Builds on it 1 paper
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The formalism of [ref] admits a natural extension to $=1$ supergravity.
A supersymmetric nonlinear sigma model analogue of the ModMax theory · Chiral formulation · 0.96
Cites it as background 1 paper
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In [ref] , sigma models were introduced that are invariant under U(1) "duality rotations," which exchange the dynamical variables and their equations of motion.
Generalized $T\bar{T}$-like flows for scalar theories in two dimensions · Introduction · 0.91
What it cites · 38 sentences without a confident label
Uses the method or tool of 1 paper
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The implications of this condition are derived in the Appendix, mimicking standard constructions in nonlinear electrodynamics (see, for example, the Appendix in [ref] ).
Nonlinear Self-Duality and Supersymmetry · Duality invariant sigma models · 0.92
Cites as background 7 papers
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Within the framework of four-dimensional $=2$ Poincaré supersymmetry, the most general nonlinear $$-model can be formulated using off-shell polar supermultiplets [ref] (see [ref] for reviews).
Properties of hyperkahler manifolds and their twistor spaces · Introduction · 0.98
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Within the framework of four-dimensional $=2$ Poincaré supersymmetry, the most general nonlinear $$-model can be formulated using off-shell polar supermultiplets [ref] (see [ref] for reviews).
Lectures on nonlinear sigma-models in projective superspace · Introduction · 0.98
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Chiral and complex linear superfields are known to provide dual off-shell descriptions of the massless scalar supermultiplet [ref] .
Superspace, or One thousand and one lessons in supersymmetry · Introduction · 0.90
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