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Semi-classical scalar products in the generalised SU(2) model
Mathematical Physics · Submitted 1 Apr 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We formulate a systematic procedure for computing the 1/M expansion of the on-shell/off-shell scalar product of M-magnon states in the generalised integrable model with SU(2)-invariant rational R-matrix.
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The abstract, sentence by sentence
In these notes we review the field-theoretical approach to the computation of the scalar product of multi-magnon states in the Sutherland limit where the magnon rapidities condense into one or several macroscopic arrays. We formulate a systematic procedure for computing the 1/M expansion of the on-shell/off-shell scalar product of M-magnon states in the generalised integrable model with SU(2)-invariant rational R-matrix. The coefficients of the expansion are obtained as multiple contour integrals in the rapidity plane.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In these notes we review the field-theoretical approach to the computation of the scalar product of multi-magnon states in the Sutherland limit where the magnon rapidities condense into one or several macroscopic arrays. | background 0.66 | 0.28 | 0.09 | asserted 0.86 |
| s1 | We formulate a systematic procedure for computing the 1/M expansion of the on-shell/off-shell scalar product of M-magnon states in the generalised integrable model with SU(2)-invariant rational R-matrix. | contribution 0.54 | 0.92 | 0.34 | asserted 1.00 |
| s2 | The coefficients of the expansion are obtained as multiple contour integrals in the rapidity plane. | method 0.84 | 0.84 | 0.17 | asserted 1.00 |
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The paper
Original abstract
In these notes we review the field-theoretical approach to the computation of the scalar product of multi-magnon states in the Sutherland limit where the magnon rapidities condense into one or several macroscopic arrays. We formulate a systematic procedure for computing the 1/M expansion of the on-shell/off-shell scalar product of M-magnon states in the generalised integrable model with SU(2)-invariant rational R-matrix. The coefficients of the expansion are obtained as multiple contour integrals in the rapidity plane.
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How the literature uses it
4 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 2 papers
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The three-point functions in the $𝒩=4$ SYM at weak coupling can be expressed as generalized overlaps of Bethe states [ref] and can be rendered into a compact determinant form [ref] , which is particularly useful in the semiclassical thermodynamic limit [ref] .
One-point Functions in Defect CFT and Integrability · Domain wall and spin chains · 0.91
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For large operators there could be interesting semi-classical limits [ref] where one might be able to make progress; for small operators we know very little about what to expect for the Baxter functions and we have nothing intelligent to say.
Structure Constants in $\mathcal{N} = 4$ SYM and Separation of Variables · Discussion · 0.88
What it cites · 54 sentences without a confident label
Uses the method or tool of 1 paper
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Bettelheim and the author [ref] , which leads to a systematical semi-classical expansion of the on-shell/off-shell scalar product.
Semi-classical analysis of the inner product of Bethe states · Introduction · 0.86
Compares with 4 papers
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The comparison with the recent computation in [ref] looks very encouraging.
Three-point functions in the SU(2) sector at strong coupling · Discussion · 1.00
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The problem considered here is formally similar to the problem of computing the instanton partition functions in $=1$ and $=2$ SYM [ref] .
Quantization of Integrable Systems and Four Dimensional Gauge Theories · Discussion · 0.83
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The problem considered here is formally similar to the problem of computing the instanton partition functions in $=1$ and $=2$ SYM [ref] .
Integrating Over Higgs Branches · Discussion · 0.83
Cites as background 3 papers
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Sum formulas for the scalar product between two generic Bethe states were obtained by by Izergin and Korepin [ref] .
Norm of Bethe Wave Function as a Determinant · Introduction · 0.93
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In the last years the thermodynamical limit attracted much attention in the context of the integrability in AdS/CFT [ref] , where it describes “heavy” operators in the $=4$ supersymmetric Yang-Mills theory (SYM), dual to classical strings embedded in the curved $AdS_5×S^5$ space-time [ref] .
Stringing Spins and Spinning Strings · Introduction · 0.92
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In the last years the thermodynamical limit attracted much attention in the context of the integrability in AdS/CFT [ref] , where it describes “heavy” operators in the $=4$ supersymmetric Yang-Mills theory (SYM), dual to classical strings embedded in the curved $AdS_5×S^5$ space-time [ref] .
Classical/quantum integrability in AdS/CFT · Introduction · 0.92
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