The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz

Using the quantum string Bethe ansatz we derive the one-loop energy of a folded string rotating with angular momenta (S,J) in AdS_3 x S^1 inside AdS_5 x S^5 in the limit 1 << J << S, z=\lambda^(1/2) log(S/J) /(\pi J) fixed. The one-loop energy is a sum of two contributions, one originating from the Hernandez-Lopez phase and another one being due to spin chain finite size effects. We find a result which at the functional level exactly matches the result of a string theory computation. Expanding the result for large z we obtain the strong coupling limit of the scaling function for low twist, high spin operators of the SL(2) sector of N=4 SYM. In particular we recover the famous -3 log(2)/\pi. Its appearance is a result of non-trivial cancellations between the finite size effects and the Hernandez-Lopez correction.Comment: 18 pages, one figure, v2: footnote changed, v3: reference added, typo correcte

Renormalisability of T-dualised non-homogeneous sigma-models

The quantum equivalence between $\sigma$-models and their non-abelian T-dualised partners is examined for a large class of four dimensional non-homogeneous and quasi-Einstein metrics with an isometry group $SU(2)\times U(1)$. We prove that the one-loop renormalisability of the initial torsionless $\sigma$-models does still imply the one-loop renormalisability of the T-dualised torsionful model. A kind of new ``dilaton anomaly'' appears for T-dualised quasi-Einstein metrics which never occurs in the framework of T-dualised homogeneous Einstein metrics

Quasilocality of joining/splitting strings from coherent states

Using the coherent state formalism we calculate matrix elements of the one-loop non-planar dilatation operator of ${\cal N}=4$ SYM between operators dual to folded Frolov-Tseytlin strings and observe a curious scaling behavior. We comment on the {\it qualitative} similarity of our matrix elements to the interaction vertex of a string field theory. In addition, we present a solvable toy model for string splitting and joining. The scaling behaviour of the matrix elements suggests that the contribution to the genus one energy shift coming from semi-classical string splitting and joining is small.Comment: 17 pages, 7 figures in 11 file

Spin bits at two loops

We consider the Super Yang--Mills/spin system map to construct the SU(2) spin bit model at the level of two loops in Yang--Mills perturbation theory. The model describes a spin system with chaining interaction. In the large $N$ limit the model is shown to be reduced to the two loop planar integrable spin chain.Comment: 10 pages, 3 figures, References and Acknowledgements adde

SL(2) spin chain and spinning strings on AdS_5xS^5

We derive the coherent state representation of the integrable spin chain Hamiltonian with symmetry group SL(2,R). By passing to the continuum limit, we find a spin chain sigma model describing a string moving on the hyperboloid SL(2,R)/U(1). The same sigma model is found by considering strings rotating with large angular momentum in AdS_5xS^5. The spinning strings are identified with semiclassical coherent states built out of SL(2,R) spin chain states.Comment: 18 pages, 1 fig, References added. Earlier results in [38] are pointed ou

Splitting of Folded Strings in AdS_4*CP^3

We study classically splitting of two kinds of folded string solutions in AdS_4*CP^3. Conserved charges of the produced fragments are computed for each case. We find interesting patterns among these conserved charges.Comment: minor changes, 14 pages, no figure

The Hypermultiplet with Heisenberg Isometry in N=2 Global and Local Supersymmetry

The string coupling of N=2 supersymmetric compactifications of type II string theory on a Calabi-Yau manifold belongs to the so-called universal dilaton hypermultiplet, that has four real scalars living on a quaternion-Kaehler manifold. Requiring Heisenberg symmetry, which is a maximal subgroup of perturbative isometries, reduces the possible manifolds to a one-parameter family that describes the tree-level effective action deformed by the only possible perturbative correction arising at one-loop level. A similar argument can be made at the level of global supersymmetry where the scalar manifold is hyper-Kaehler. In this work, the connection between global and local supersymmetry is explicitly constructed, providing a non-trivial gravity decoupled limit of type II strings already in perturbation theory.Comment: 24 page

Holographic 3-point function at one loop

We explore the recent weak/strong coupling match of three-point functions in the AdS/CFT correspondence for two semi-classical operators and one light chiral primary operator found by Escobedo et al. This match is between the tree-level three-point function with the two semi-classical operators described by coherent states while on the string side the three-point function is found in the Frolov-Tseytlin limit. We compute the one-loop correction to the three-point function on the gauge theory side and compare this to the corresponding correction on the string theory side. We find that the corrections do not match. Finally, we discuss the possibility of further contributions on the gauge theory side that can alter our results.Comment: 24 pages, 2 figures. v2: Typos fixed, Ref. added, figure improved. v3: Several typos and misprints fixed, Ref. updated, figures improved, new section 2.3 added on correction from spin-flipped coherent state, computations on string theory side improve

Sigma model from SU(1,1|2) spin chain

We derive the coherent state representation of the integrable spin chain Hamiltonian with supersymmetry group $SU(1,1|2)$. By the use of a projected Hamiltonian onto bosonic states, we give explicitly the action of the Hamiltonian on $SU(2)\times SL(2)$ coherent states. Passing to the continuous limit, we find that the corresponding bosonic sigma model is the sum of the known SU(2) and SL(2) ones, and thus it gives a string spinning fast on $S^1_{\phi_1}\times S^1_{\phi_1}\times S^1_{\phi_2}$ in $\rm{AdS}_5 \times S^5$. The full sigma model on the supercoset $SU(1,1|2)/SU(1|1)^2$ is given.Comment: 20 pages, no figures, 4 tables, 1 appendix; typos corrected, references adde