Michael C. Abbott

The AdS3 × S3 × S3 × S1 Hernández–López phases: a semiclassical derivation

This note calculates the Hernandez–Lopez phases for strings in AdS3 × S3 × S3 × S1 by semiclassical methods using the d(2, 1; α)2 algebraic curve. By working at general α we include modes absent from previous semiclassical calculations of this phase in AdS3 × S3 × 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 antisymmetrization, cutoffs and surface terms which could safely be ignored in AdS5 × S5, and some issues about the terms c1, s which were absent there. As a result we see agreement with the recently calculated all-loop dressing phase in the AdS3 × S3 × T4 case, and exactly 1/2 this in the general case AdS3 × S3 × S3 × S1, for any α and any (light) polarizations.

Macroscopic (and microscopic) massless modes

Abstract We study certain spinning strings exploring the flat directions of AdS 3 × S 3 × S 3 × S 1 , the massless sector cousins of su ( 2 ) and s l ( 2 ) sector spinning strings. We describe these, and their vibrational modes, using the D ( 2 , 1 ; α ) 2 algebraic curve. By exploiting a discrete symmetry of this structure which reverses the direction of motion on the spheres, and alters the masses of the fermionic modes s → κ − s , we find out how to treat the massless fermions which were previously missing from this formalism. We show that folded strings behave as a special case of circular strings, in a sense which includes their mode frequencies, and we are able to recover this fact in the worldsheet formalism. We use these frequencies to calculate one-loop corrections to the energy, with a version of the Beisert–Tseytlin resummation.

Comment on strings in AdS3 × S3 × S3 × S1 at one loop

A bstractThis paper studies semiclassical strings in AdS3 × S3 × S3 × 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(λ). Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f1 in the expansion of the cusp anomalous dimension f (h), for all α (where α → 1 is the AdS3 × S3 × T4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS4 × CP3. However at

Comment on strings in AdS 3 × S 3 × S 3 × S 1 at one loop

\alpha \ne \frac{1}{2}

Massless Lüscher terms and the limitations of the AdS 3 asymptotic Bethe ansatz

they lead to different values of f1 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 α → 1, and can be compared to the recently published S-matrices.

Scattering in AdS 2 /CFT 1 and the BES phase

A bstractThis paper studies semiclassical strings in AdS3 × S3 × S3 × 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(λ). Comparing these to similar corrections for long spinning strings gives a prediction for the one-loop term f1 in the expansion of the cusp anomalous dimension f (h), for all α (where α → 1 is the AdS3 × S3 × T4 limit). For these semiclassical mode sums there is a similar choice of regularisation prescriptions to that encountered in AdS4 × CP3. However at

T-duality of Green-Schwarz superstrings on AdSd × Sd × M10−2d

\alpha \ne \frac{1}{2}

An improved AFS phase for AdS3 string integrability

they lead to different values of f1 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 α → 1, and can be compared to the recently published S-matrices.

Meromorphic functions and the topology of giant gravitons

In AdS5/CFT4 integrability the Bethe ansatz gives the spectrum of long strings, accurate up to exponentially small corrections. This is no longer true in three-dimensional anti–de Sitter (AdS3) space, as we demonstrate here by studying Luscher F-terms with a massless particle running in the loop. We apply this to the classic test of Hernandez and Lopez, in which the su(2) sector Bethe equations (including the one-loop dressing phase) should match the semiclassical string theory result for a circular spinning string. These calculations do not agree in AdS3×S3×T4, and we show that the sum of all massless Luscher F-terms can reproduce the difference.

Fermionic T-Duality of

A bstractWe study worldsheet scattering for the type IIA superstring in AdS2 ×S2 ×T6. Using the Green-Schwarz action to quartic order in fermions we take the near-BMN limit, where as in the AdS3/CFT2 case there are both massive and massless excitations. For the massive excitations we compute all possible tree-level processes, and show that these agree with a truncated version of the exact AdS5 × S5 S-matrix. We also compute several S-matrix elements involving massless excitations. At one loop we find that the dressing phase is the same Hernándes-López phase appearing in AdS5/CFT4. We see the same phase when calculating this by semiclassical means using the PSU(1, 1|2)/U(1)2 coset sigma model, for which we can also study the scattering of fermions. This supports the conjecture that the all-loop dressing phase is again the BES phase, rather than a new phase like that seen in AdS3/CFT2.