Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop

Michael C. Abbott

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Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop

Michael C. Abbott

High Energy Physics - Theory · Submitted 23 Nov 2012

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

The authors' main claim Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f_1 in the expansion of the cusp anomalous dimension f(h), for all \alpha (where \alpha --> 1 is the AdS3 x S3 x T4 limit).

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.61 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.94 · mentions code or data availability 0.02.

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This paper studies semiclassical strings in AdS3 x S3 x S3 x S1 using the algebraic curve. Calculating one-loop corrections to the energy of the giant magnon fixes the constant term c in the expansion of the coupling h(\lambda). Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f_1 in the expansion of the cusp anomalous dimension f(h), for all \alpha (where \alpha --> 1 is the AdS3 x S3 x T4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS4 x CP3. However at \alpha \neq 1/2 they lead to different values of f_1 and are therefore not related by a simple change of the coupling. The algebraic curve is also used to calculate various finite-size corrections for giant magnons, which are well-behaved as \alpha --> 1, and can be compared to the recently published S-matrices.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This paper studies semiclassical strings in AdS3 x S3 x S3 x S1 using the algebraic curve.	contribution 0.95	0.89	0.05	asserted 0.99
s1	Calculating one-loop corrections to the energy of the giant magnon fixes the constant term c in the expansion of the coupling h(\lambda).	result 0.90	0.81	0.39	asserted 1.00
s2	Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f_1 in the expansion of the cusp anomalous dimension f(h), for all \alpha (where \alpha --> 1 is the AdS3 x S3 x T4 limit).	result 0.87	0.81	0.50	asserted 0.89
s3	For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS4 x CP3.	background 0.49	0.39	0.03	asserted 0.99
s4	However at \alpha \neq 1/2 they lead to different values of f_1 and are therefore not related by a simple change of the coupling.	result 0.83	0.76	0.25	asserted 1.00
s5	The algebraic curve is also used to calculate various finite-size corrections for giant magnons, which are well-behaved as \alpha --> 1, and can be compared to the recently published S-matrices.	contribution 0.49	0.90	0.10	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.69 · evidence from proof or derivation 0.98.

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Original abstract

This paper studies semiclassical strings in AdS3 x S3 x S3 x S1 using the algebraic curve. Calculating one-loop corrections to the energy of the giant magnon fixes the constant term c in the expansion of the coupling h(\lambda). Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f_1 in the expansion of the cusp anomalous dimension f(h), for all \alpha (where \alpha --> 1 is the AdS3 x S3 x T4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS4 x CP3. However at \alpha \neq 1/2 they lead to different values of f_1 and are therefore not related by a simple change of the coupling. The algebraic curve is also used to calculate various finite-size corrections for giant magnons, which are well-behaved as \alpha --> 1, and can be compared to the recently published S-matrices.

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Cited by 8 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...
On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
hep-th 2013-03 conditional novelty 7.0 of 10

The tree-level scattering matrix for massive string excitations on AdS3 x S3 x T4 with mixed RR and NSNS flux depends on the flux-mixing parameter q only through a shifted dispersion relation, e^2 = (p +/- q)^2 + 1 - q^2.
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.

Show 3 more citing papers

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.
The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
hep-th 2013-03 conditional novelty 6.0 of 10

A symmetry-based bootstrap fixes the all-loop S-matrix of the psu(1,1|2)^2 spin chain up to two dressing phases, yields new Bethe equations, and states the crossing equations those phases must obey.
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 ...

How the literature uses it

21 arXiv papers cite this in 48 sentences

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Papers citing it · 25 sentences without a confident label

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At the one-loop level we also find that the two modified phases of [ref] (one of the phases was first derived in [ref] and agrees at least to lowest order) reproduce the correct answer while the standard Hernandez-Lopez phase [ref] does not, see also [ref] .

Worldsheet scattering in AdS(3)/CFT(2) · Introduction · contest 0.85
For the shifts in energy, note that we are still missing the massless bosons, and see discussion in [ref] . * One surprising feature is that the “efficient” method [ref] of constructing heavy modes off-shell by addition given by [ref] fails here.

Macroscopic (and Microscopic) Massless Modes · The Circular String · contest 0.82

Uses its data or values 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.

The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation · $AdS_3$ Magnon Scattering · 0.97

Compares with it 2 papers

A similar phase was used by [ref] when comparing to tree-level amplitudes, but with the exponent of the first factor replaced by [The variables $x^±$ depend on the mass $s_x$ through [equation] where $h=√(λ)/2π+c+1/√(λ)$ is the Bethe coupling, normalised as in [ref] . ] [equation] The last term here has no effect on tree-level worldsheet scattering.

An improved AFS phase for AdS3 string integrability · Introduction · 0.87
We derive the full plane-wave spectrum on this background and, in particular, the masses of the fields in the GS-formalism agree with [ref] .

The plane-wave spectrum from the worldsheet · Introduction · 0.99

Cites it as background 13 papers

The subject of this note is IIB strings in the R-R background $3×3×3×1$, which along with the related background $AdS_3×S^3×T^4$ has been the subject of much recent work in integrability [ref] .

The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation · Introduction · 0.99
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
The Dynkin diagram is whitewhitewhite thus the Cartan matrix is the same as that for the left sector of $AdS_3×S^3$ alone: [equation] There are three quasimomenta $p_ℓ(z)$, $ℓ=1,2,3$, and the BMN vacuum is given by the same $κ=(1,0,1)$ as for $AdS_3×S^3$ i..e [equation] The list of possible modes is also like the left sector of $AdS_3×S^3$ (see for instance [ref] 's appendix), which in turn is a truncation of the list in $AdS_5×S^5$: [equation]

Scattering in AdS(2)/CFT(1) and the BES Phase · The Semiclassical Dressing Phase · 0.81

What it cites · 123 sentences without a confident label

Builds on 2 papers

The aim of this section is to do what Gromov and Mikhaylov [ref] did for $AdS_4×CP^3$, that is, to classify the modes of long spinning strings as heavy or light based on the algebraic curve description, and then to sum their frequencies using the “new” prescription suggested by this formalism.

Comment on the Scaling Function in AdS4 x CP3 · Long Spinning Strings · 0.80
The time delay for scattering solutions is defined like this (initially on a unit sphere): [equation] It is clear that embedding this solution into the $S_+^3$ sphere via [ref] will give us a time delay $Δτ=1/cos^2ϕtanp/2log(cos^2p/2)$ scaled from the usual (centre of mass frame) delay [ref] . * We can embed a different giant magnon into each sphere, and they don't talk to each other at all.

Giant Magnons · Worldsheet Theory · 0.85

Uses the method or tool of 6 papers

This is done by using [ref] 's trick to write it as a contour integral in $n$: [equation] For each $r$ we can now use the relevant equation for the position of the pole to write this as an integral in $x$, along a contour $W$ enclosing poles along the real line at $|x|>1$.

Exact expressions for quantum corrections to spinning strings · One-loop Correction · 1.00
The addition of modes used above is one half of [ref] 's efficient procedure for constructing off-shell frequencies, and these barred modes may be constructed by the other half, namely the use of the inversion symmetry.

Efficient precision quantization in AdS/CFT · Constructing Modes · 0.98
To work this out we must use a different algebraic curve solution, and following [ref] we can use the following (approximate) form for the magnon resolvent: [equation] where the branch points are [equation] and complex conjugates (with $δ$ real).

Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J · Classical $μ$-term · 0.97

Uses data or values from 1 paper

(See [ref] in appendix [ref].) For this solution Forini, Puletti and Ohlsson Sax [ref] calculated the mode frequencies from the Green–Schwartz action; these are listed in table [ref].

Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings · Long Spinning Strings · 0.96

Compares with 15 papers

The result for the physical prescription is precisely that given in [ref] .

Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings · Long Spinning Strings · 0.84
[equation] This is a solution to $Λ_ℓ·Λ_m=A_ℓm$ which reduces to the vectors [ref] gave for $α=12$ at least on the left (i.e for the unbarred $ℓ=1,2,3$).

Algebraic Curves for Integrable String Backgrounds · Algebraic Curves for AdS3 x S3 x S3 sans $S^1$ · 0.87
Comparing first to Ahn and Bombardelli's [ref] , for the modes on the left the terms of their equation (2.14) we need are [equation] where $x_p_1^±≈x$ for the virtual particle, $x_p_2^±=$ for the physical giant magnon, and the matrix part is thus [equation] For the scalar factor $S_0$, only the classical AFS [ref] term in the BES phase [ref] matters, giving [equation] Then since $X^+=1/X^-+𝒪(1/g)$ we have agreement with the first two terms of [ref] and of [ref], apart from phases $e^-ip_2/2=√(/)$ for the fermions ($1f$ and $3f$) which will arise from going to the string frame.

Transcendentality and Crossing · Comparison with S-matrices · 1.00

Cites as background 36 papers

At $α≠1$ there is much recent work on integrability [ref] perhaps the highlight of which is a conjectured all-order Bethe ansatz for all $α$ [ref] .

Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring · Introduction · 0.88
At $α≠1$ there is much recent work on integrability [ref] perhaps the highlight of which is a conjectured all-order Bethe ansatz for all $α$ [ref] .

Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings · Introduction · 0.88
At $α≠1$ there is much recent work on integrability [ref] perhaps the highlight of which is a conjectured all-order Bethe ansatz for all $α$ [ref] .

Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring · Introduction · 0.88

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