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Boundary Spectra in Superspace Sigma-Models
High Energy Physics - Theory · Submitted 20 Dec 2007
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this note we compute exact boundary spectra for D-instantons in sigma-models on the supergroup PSL(2|2).
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The abstract, sentence by sentence
In this note we compute exact boundary spectra for D-instantons in sigma-models on the supergroup PSL(2|2). Our results are obtained through an explicit summation of the perturbative expansion for conformal dimensions to all orders in the curvature radius. The analysis exploits several remarkable properties of the perturbation series that arises from rescalings of the metric on PSL(2|2) relative to a fixed Wess-Zumino term. According to Berkovits, Vafa and Witten, the models are relevant in the context of string theory on AdS3 with non-vanishing RR-flux. The note concludes with a number of comments on various possible generalizations to other supergroups and higher dimensional supercoset theories.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this note we compute exact boundary spectra for D-instantons in sigma-models on the supergroup PSL(2|2). | contribution 0.93 | 0.96 | 0.76 | asserted 1.00 |
| s1 | Our results are obtained through an explicit summation of the perturbative expansion for conformal dimensions to all orders in the curvature radius. | method 1.00 | 0.96 | 0.15 | asserted 1.00 |
| s2 | The analysis exploits several remarkable properties of the perturbation series that arises from rescalings of the metric on PSL(2|2) relative to a fixed Wess-Zumino term. | method 0.99 | 0.70 | 0.05 | asserted 1.00 |
| s3 | According to Berkovits, Vafa and Witten, the models are relevant in the context of string theory on AdS3 with non-vanishing RR-flux. | background 0.98 | 0.04 | 0.04 | asserted 0.96 |
| s4 | The note concludes with a number of comments on various possible generalizations to other supergroups and higher dimensional supercoset theories. | future work 1.00 | 0.54 | 0.06 | asserted 0.53 |
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The paper
Original abstract
In this note we compute exact boundary spectra for D-instantons in sigma-models on the supergroup PSL(2|2). Our results are obtained through an explicit summation of the perturbative expansion for conformal dimensions to all orders in the curvature radius. The analysis exploits several remarkable properties of the perturbation series that arises from rescalings of the metric on PSL(2|2) relative to a fixed Wess-Zumino term. According to Berkovits, Vafa and Witten, the models are relevant in the context of string theory on AdS3 with non-vanishing RR-flux. The note concludes with a number of comments on various possible generalizations to other supergroups and higher dimensional supercoset theories.
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References
How the literature uses it
28 arXiv papers cite this in 57 sentences
Papers citing it · 35 sentences without a confident label
Builds on it 4 papers
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Many of the central results of [ref] , however, hold much more generally for models whose symmetries are described by an affine Lie superalgebra with vanishing dual Coxeter number.
Principal Chiral Model on Superspheres · Deformation from free GN model to free PCM · 0.88
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Our result generalizes previous findings [ref] for Wess-Zumino-Witten (WZW) models on supergroups with vanishing dual Coxeter number.
Superspace Parafermions · Introduction · 0.98
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Generalizing classification of integrable boundary conditions for the $Z_4$ cosets [ref] to include the WZ coupling should be really helpful in this respect, as it may provide a direct link to the boundary conformal perturbation theory of [ref] .
B-field in AdS(3)/CFT(2) Correspondence and Integrability · Discussion · 0.80
Uses its method or tool 2 papers
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To this end we shall employ some recent results of [ref] that are designed to compute exact spectra in models with a special class of target space supersymmetries, including the two series psl(N$|$N) and .
Principal Chiral Model on Superspheres · Introduction · 0.96
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Our strategy then was to calculate the spectrum at finite coupling by assuming so-called Casimir evolution of conformal weights [ref] .
Cohomological Reduction of Sigma Models · Conclusion and Outlook · 0.95
Compares with it 1 paper
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While [ref] focused on a bulk deformation preserving global left and right transformations simultaneously, the current-current perturbation [ref] considered here is of a very different type.
Principal Chiral Model on Superspheres · Conclusions, open questions and outlook · 0.99
Cites it as background 9 papers
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In order to fully appreciate its content, let us review a few results from [ref] .
Principal Chiral Model on Superspheres · Deformation from free GN model to free PCM · 0.91
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A more detailed discussion of these issues can be found in [ref] .
Conformal superspace sigma-models · Anomalous dimensions · 0.95
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One can think of this theory as a perturbation of the rather well understood [ref] Kac-Moody (KM) point characterized by the condition $f^-2 = k$, perturbed by a term in the action of the form [ref] $δS = (λ/k^2) ∫d^2 z ϕ_ab(z,z̅) J^a(z) J̅^b(z̅)$, where $λ= f^-2 - k$.
Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory · Introduction · 0.97
What it cites · 42 sentences without a confident label
Contests 1 paper
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We use this opportunity to clarify a few unsatisfactory issues in the original argument [ref] .
$PSL(n|n)$ Sigma Model as a Conformal Field Theory · Derivation of the main vanishing lemma · contest 0.81
Builds on 2 papers
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We start with a few comments on brane geometries in WZNW models on $$, extending our previous analysis of branes in the gl(1$|$1) WZNW model [ref] .[This first subsection is based on unpublished notes of TC on branes in supergroup WZNW models.] One of the instantonic D-branes we find, possesses exactly the spectrum that was anticipated in [ref] .
Branes in the GL(1|1) WZNW-Model · Collection of background material · 0.89
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We start with a few comments on brane geometries in WZNW models on $$, extending our previous analysis of branes in the gl(1$|$1) WZNW model [ref] .[This first subsection is based on unpublished notes of TC on branes in supergroup WZNW models.] One of the instantonic D-branes we find, possesses exactly the spectrum that was anticipated in [ref] .
The WZNW model on PSU(1,1|2) · Collection of background material · 0.89
Uses the method or tool of 1 paper
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Finally, all the pieces are collected and the conformal weights of boundary fields are computed explicitly, following a closely related computation in [ref] .
D-branes and Deformation Quantization · Deformation of the boundary partition function · 0.86
Compares with 2 papers
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While in [ref] the effective perturbation was used to compute both the change of conformal weights and of 3-point couplings, our entire derivation here was restricted to conformal weights!
D-branes and Deformation Quantization · Computation of boundary conformal weights · 0.97
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Similar phenomena have been encountered in recent work of Read and Saleur [ref] .
Associative-algebraic approach to logarithmic conformal field theories · Conclusions and outlook · 0.88
Cites as background 39 papers
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In the next section we collect some background material, partly from our earlier paper [ref] .
The WZNW model on PSU(1,1|2) · Introduction · 0.97
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At the WZ point, maximally symmetric boundary conditions are associated with so-called twisted conjugacy classes (see [ref] and [ref] for the supersymmetric case).
Branes in the GL(1|1) WZNW-Model · Branes at the WZ point: gluing conditions and geometry · 0.89
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At the WZ point, maximally symmetric boundary conditions are associated with so-called twisted conjugacy classes (see [ref] and [ref] for the supersymmetric case).
D-branes in the WZW model · Branes at the WZ point: gluing conditions and geometry · 0.89
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