The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation

Michael C. Abbott (UCT)

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The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation

Michael C. Abbott (UCT)

High Energy Physics - Theory · Submitted 21 Jun 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 x S3 x T4 case, and exactly 1/2 this in the general case AdS3 x S3 x S3 x S1 for any \alpha\ and any (light) polarisations.

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This note calculates the Hernandez-Lopez phases for strings in AdS3 x S3 x S3 x S1 by semiclassical methods using the d(2,1;\alpha)^2 algebraic curve. By working at general \alpha\ we include modes absent from previous semiclassical calculations of this phase in AdS3 x S3 x T4, and in particular can study the scattering of particles of different mass. By carefully re-deriving the semiclassical formula we clarify some issues of antisymmetrisation, cutoffs and surface terms which could safely be ignored in AdS5 x S5, and some issues about the terms c_1,s which were absent there. As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 x S3 x T4 case, and exactly 1/2 this in the general case AdS3 x S3 x S3 x S1 for any \alpha\ and any (light) polarisations.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This note calculates the Hernandez-Lopez phases for strings in AdS3 x S3 x S3 x S1 by semiclassical methods using the d(2,1;\alpha)^2 algebraic curve.	contribution 0.99	0.96	0.08	asserted 1.00
s1	By working at general \alpha\ we include modes absent from previous semiclassical calculations of this phase in AdS3 x S3 x T4, and in particular can study the scattering of particles of different mass.	contribution 0.85	0.91	0.05	asserted 0.89
s2	By carefully re-deriving the semiclassical formula we clarify some issues of antisymmetrisation, cutoffs and surface terms which could safely be ignored in AdS5 x S5, and some issues about the terms c_1,s which were absent there.	contribution 0.63	0.92	0.06	asserted 0.83
s3	As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 x S3 x T4 case, and exactly 1/2 this in the general case AdS3 x S3 x S3 x S1 for any \alpha\ and any (light) polarisations.	result 1.00	0.92	0.87	asserted 1.00

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Original abstract

This note calculates the Hernandez-Lopez phases for strings in AdS3 x S3 x S3 x S1 by semiclassical methods using the d(2,1;\alpha)^2 algebraic curve. By working at general \alpha\ we include modes absent from previous semiclassical calculations of this phase in AdS3 x S3 x T4, and in particular can study the scattering of particles of different mass. By carefully re-deriving the semiclassical formula we clarify some issues of antisymmetrisation, cutoffs and surface terms which could safely be ignored in AdS5 x S5, and some issues about the terms c_1,s which were absent there. As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 x S3 x T4 case, and exactly 1/2 this in the general case AdS3 x S3 x S3 x S1 for any \alpha\ and any (light) polarisations.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
hep-th 2014-06 accept novelty 7.0 of 10

The authors construct the symmetry-fixed worldsheet S-matrix for all fundamental excitations of Type IIB strings on AdS3 x S3 x T4, including massless modes, up to five undetermined dressing factors whose crossing equ...
The $\mathrm{AdS}_3\times \mathrm{S}^3\times \mathrm{S}^3\times\mathrm{S}^1$ worldsheet S matrix
hep-th 2015-05 conditional novelty 6.0 of 10

The worldsheet S matrix for type IIB strings on AdS3 x S3 x S3 x S1 with mixed R-R and NS-NS flux is fixed by the off-shell symmetry algebra up to dressing phases, and the crossing equations those phases must satisfy ...
The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
hep-th 2014-10 conditional novelty 6.0 of 10

The authors construct the worldsheet S matrix (up to dressing factors) for type IIB strings on AdS3 x S3 x T4 with mixed three-form flux, showing the mixed flux integrably deforms the pure-R-R S matrix.
Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
hep-th 2013-11 accept novelty 6.0 of 10

The exact dispersion relation for light-cone string excitations in AdS3 x S3 x T4 with mixed flux has a central charge linear in worldsheet momentum, fixed by an explicit dyonic giant magnon solution.
Dressing phases of AdS3/CFT2
hep-th 2013-06 conditional novelty 6.0 of 10

The two all-loop dressing phases of the AdS3 x S3 x T4 integrable S-matrix are determined by solving the crossing relations, yielding a BES-like phase plus a new term absent in the higher-dimensional cases.

Show 1 more citing papers

Towards integrability for AdS3/CFT2
hep-th 2014-06 accept novelty 3.0 of 10

A self-contained review that assembles, from previously published work, the symmetry-fixed all-loop S matrix and Bethe ansatz for massive AdS3 x S3 x T4 string excitations, including a crossing-symmetric proposal for ...

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21 arXiv papers cite this in 46 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 24 sentences without a confident label

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However the dressing phase constructed this way does not solve the crossing equations [ref] , nor does it agree with a construction from semiclassical magnon scattering [ref] , nor give the amplitude seen in near-BMN scattering [ref] .

Massless L\"uscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz · Introduction · contest 0.85

Uses its method or tool 2 papers

Multiplying by the relevant weight and integrating over the cut, [ref] obtained this expression in terms of resolvents:[We write tildes on quantities defined to match [ref] , which differ from those in the S-matrix and dressing phase papers [ref] by powers of $$.

Massless L\"uscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz · Bethe Ansatz calculation · 0.91
We also observe that truncating the model to just the massive modes breaks the agreement with the HL phase. * We also compute the phase semiclassically, using the coset model and the algebraic curve, following [ref] .

Scattering in AdS(2)/CFT(1) and the BES Phase · Introduction · 0.82

Compares with it 2 papers

Then we compute the correction [ref] [equation] finding the same coefficients as in [ref] : [equation] This is exactly the same result as in $AdS_5×S^5$, including the factors of 2.

Scattering in AdS(2)/CFT(1) and the BES Phase · The Semiclassical Dressing Phase · 0.97
This leads to Δϕ_1=Δϕ_2=Δϕ_5=0, Δϕ_3=Δϕ_4=-p/2, exactly the same as the results given in [ref] (see also [ref] ).

Finite-size Effect for Dyonic Giant Magnons in $CP^3_{\beta}$ · Fix the twists from orbifolding · 0.81

Cites it as background 13 papers

The dressing phase for $AdS_3$ backgrounds is different, and is now understood quite well at one loop [ref] ; see also [ref] .

An improved AFS phase for AdS3 string integrability · Introduction · 0.97
The one-loop part of the phase was first proposed in [ref] and later modified with additional terms in [ref] .

Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2) · Conclusions and summary · 0.88
Conventionally, there occur two plausible integrable set-ups in the case of $AdS_3/CFT_2$ [ref] namely the type IIB GS string construction in $AdS_3×S^3×ℳ^4$, $ℳ^4≡T^4$ [ref] or $S^3×S^1$ [ref] .

Neumann-Rosochatius system for rotating strings in $AdS_3 \times S^3\times S^3\times S^1$ with flux · Introduction · 0.96

What it cites · 96 sentences without a confident label

Uses the method or tool of 2 papers

To derive ([ref]), Chen, Dorey and Lima Matos [ref] studied a classical scattering state $φ_1,2(x,t)$ of two magnons in a box of size $L$, and calculated $1/L$ corrections to the one-loop energy correction ([ref]).

Quantum Scattering of Giant Magnons · Deriving the One-Loop Phase · 0.91
The integrals we need to do arise from sums over $n$ using the method of [ref] , which uses the poles of $(πn)$ to write a contour integral.

Exact expressions for quantum corrections to spinning strings · $AdS_3$ Magnon Scattering · 1.00

Uses data or values from 1 paper

These were calculated in [ref] for the purpose of finding energy corrections ([ref]), and they are written in terms of the spectral parameter as [equation] These are shown in table [ref]; see appendix [ref] for details.

Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop · $AdS_3$ Magnon Scattering · 0.97

Compares with 3 papers

The result, when expanded in the charges $Q_n$, is precisely one half the coefficients found by BOSST [ref] from their all-loop dressing phase for $AdS_3×S^3×T^4$.

Dressing phases of AdS3/CFT2 · Summary and Conclusions · 1.00
The near-flat-space limit calculation of [ref] found agreement with the phase given by [ref] .

Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase · Summary and Conclusions · 0.86
The near-flat-space limit calculation of [ref] found agreement with the phase given by [ref] .

Worldsheet scattering in AdS(3)/CFT(2) · Summary and Conclusions · 0.86

Cites as background 40 papers

We are mostly concerned with the light modes, $m=cos^2ϕ,sin^2ϕ$, as these are fundamental in the description of [ref] .

All-loop Bethe ansatz equations for AdS3/CFT2 · Introduction · 0.88
We are mostly concerned with the light modes, $m=cos^2ϕ,sin^2ϕ$, as these are fundamental in the description of [ref] .

A dynamic su(1|1)^2 S-matrix for AdS3/CFT2 · Introduction · 0.88
The dressing phase was first introduced by Arutyunov, Frolov and Staudacher (AFS) [ref] for classical strings (large $λ$), and the extension of this to one loop by Hernández and López [ref] (see also [ref] ) was an important step towards the all-$λ$ phase, conventionally $(σ_BES)^2$.

On Quantum Corrections to Spinning Strings and Bethe Equations · Introduction · 0.96

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