A spin chain for the symmetric product CFT2

Pakman, Ari; Rastelli, Leonardo; Razamat, Shlomo S.

doi:10.1007/jhep05(2010)099

Cited by 80 publications

(115 citation statements)

References 66 publications

(140 reference statements)

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“…However, it appears to be much harder to understand the spin-chain picture starting from the Sym N (T 4 ) orbifold point [45], though many suggestive connections seem to exist. It would be interesting to see whether it is possible to deform the spin-chain [18,22] to approach the Sym N (T 4 ) orbifold point.…”

Section: Jhep06(2015)103mentioning

confidence: 99%

Integrability and the conformal field theory of the Higgs branch

Sax

Sfondrini

Stefański

2015

J. High Energ. Phys.

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In the context of the AdS 3 /CFT 2 correspondence, we investigate the Higgs branch CFT 2 . Witten showed that states localised near the small instanton singularity can be described in terms of vector multiplet variables. This theory has a planar, weakcoupling limit, in which anomalous dimensions of single-trace composite operators can be calculated. At one loop, the calculation reduces to finding the spectrum of a spin-chain with nearest-neighbour interactions. This CFT 2 spin-chain matches precisely the one that was previously found as the weak-coupling limit of the integrable system describing the AdS 3 side of the duality. We compute the one-loop dilatation operator in a non-trivial compact subsector and show that it corresponds to an integrable spin-chain Hamiltonian. This provides the first direct evidence of integrability on the CFT 2 side of the correspondence.

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Section: Jhep06(2015)103mentioning

confidence: 99%

Integrability and the conformal field theory of the Higgs branch

Sax

Sfondrini

Stefański

2015

J. High Energ. Phys.

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“…[18] and references there) it is hard to comment on the possible meaning of (4.1) or (4.2) in the small string tension or weak coupling region h → 0. In general, the identification of the parameter h in (4.1) with the string tension √ λ 2π in (2.2) may be true only in the strong-coupling limit √ λ ≫ 1, i.e.…”

Section: General Structure and Limitsmentioning

confidence: 99%

“…Then the combination that should appear in front of log in ϑ 0 in (5.29) is 18 Note that because of the ambiguity discussed beneath eq. (5.26), to find S 2 ± we cannot use the same procedure as used for S 1 ± starting with the q = 0 expression given in [5].…”

Section: Q = 0 Casementioning

confidence: 99%

Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3

Hoare¹,

Tseytlin²

2013

Nuclear Physics B

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The type IIB supergravity AdS 3 × S 3 × T 4 background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1 and NS5-NS1 branes. The corresponding superstring world-sheet theory is expected to be integrable, opening the possibility of computing its exact spectrum for any values of the coefficient q of the NSNS flux and the string tension. In arXiv:1303.1447 we have found the treelevel S-matrix for the massive BMN excitations in this theory, which turned out to have a simple dependence on q. Here, by analyzing the constraints of symmetry and integrability, we propose an exact massive-sector dispersion relation and the exact S-matrix for this world-sheet theory. The S-matrix generalizes its recent construction in the q = 0 case in arXiv:1303.5995.

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“…The spin-chain in this case is not alternating; instead it is homogenous. It would be very interesting to see how such a spin-chain emerges from the recent analysis of the weakly-coupled CFT 2 [58]. When restricted to just the left-or right-movers this spinchain is closely related to the psu(1, 1|2) spin-chain one encounters in N = 4 SYM [59].…”

Section: Introductionmentioning

confidence: 99%

Integrability, spin-chains and the AdS3/CFT2 correspondence

Sax

Stefański

2011

J. High Energ. Phys.

146

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Building on arXiv:0912.1723 [1], in this paper we investigate the AdS 3 /CFT 2 correspondence using integrability techniques. We present an all-loop Bethe Ansatz (BA) for strings on AdS 3 × S 3 × S 3 × S 1 , with symmetry d(2, 1; α) 2 , valid for all values of α. This construction relies on a novel, α-dependent generalisation of the Zhukovsky map. We investigate the weakly-coupled limit of this BA and of the all-loop BA for strings on AdS 3 × S 3 × T 4 . We construct integrable short-range spin-chains and Hamiltonians that correspond to these weakly-coupled BAs. The spin-chains are alternating and homogenous, respectively. The alternating spinchain can be regarded as giving some of the first hints about the unknown CFT 2 dual to string theory on AdS 3 ×S 3 ×S 3 ×S 1 . We show that, in the α → 1 limit, the integrable structure of the d(2, 1; α) 2 model is non-singular and keeps track of not just massive but also massless modes. This provides a way of incorporating massless modes into the integrability machinery of the AdS 3 /CFT 2 correspondence.

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A spin chain for the symmetric product CFT2

Cited by 80 publications

References 66 publications

Integrability and the conformal field theory of the Higgs branch

Integrability and the conformal field theory of the Higgs branch

Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3

Integrability, spin-chains and the AdS3/CFT2 correspondence

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