More on integrable structures of superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds

In this paper we continue the study, initiated in arXiv:1009.3498 and arXiv:1104.1793, of the classical integrability of Green-Schwarz superstrings in AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superbackgrounds whose spectrum contains non-supercoset worldsheet degrees of freedom corresponding to broken supersymmetries in the bulk. We derive an explicit expression, to all orders in the coset fermions and to second order in the non-coset fermions, which extends the supercoset Lax connection in these backgrounds with terms depending on the non-coset fermions. An important property of the obtained form of the Lax connection is that it is invariant under Z_4-transformations of the superisometry generators and the spectral parameter. This demonstrates that the contribution of the non-coset fermions does not spoil the Z_4-symmetry of the super-coset Lax connection which is of crucial importance for the application of Bethe-ansatz techniques. The expressions describing the AdS(4) x CP(3) and AdS(2) x S(2) x T(6) superstring sigma--models and their Lax connections have a very similar form. This is because their amount of target-space supersymmetries complement each other to 32=24+8, the maximal number of 10d type II supersymmetries. As a byproduct, this similarity has allowed us to obtain the form of the geometry of the complete type IIA AdS(2) x S(2) x T(6) superspace to all orders in the coset fermions and to the second order in the non-coset ones.Comment: 28 pages; v2: References adde

Dirichlet Branes on Orientifolds

We consider the classification of BPS and non-BPS D-branes in orientifold models. In particular we construct all stable BPS and non-BPS D-branes in the Gimon-Polchinski (GP) and Dabholkar-Park-Blum-Zaffaroni (DPBZ) orientifolds and determine their stability regions in moduli space as well as decay products. We find several kinds of integrally and torsion charged non-BPS D-branes. Certain of these are found to have projective representations of the orientifold $\times$ GSO group on the Chan-Paton factors. It is found that the GP orientifold is not described by equivariant orthogonal K-theory as may have been at first expected. Instead a twisted version of this K-theory is expected to be relevant.Comment: 33 pages, LaTeX, 5 figures. v2 typos corrected, references included, (4,s)-branes re-examine

D-brane anomaly inflow revisited

Axial and gravitational anomaly of field theories, when embedded in string theory, must be accompanied by canceling inflow. We give a self-contained overview for various world-volume theories, and clarify the role of smeared magnetic sources in I-brane/D-brane cases. The proper anomaly descent of the source, as demanded by regularity of RR field strengths H's, turns out to be an essential ingredient. We show how this allows correct inflow to be generated for all such theories, including self-dual cases, and also that the mechanism is now insensitive to the choice between the two related but inequivalent forms of D-brane Chern-Simons couplings. In particular, SO(6)_R axial anomaly of d=4 maximal SYM is canceled by the inflow onto D3-branes via the standard minimal coupling to C_4. We also propose how, for the anomaly cancelation, the four types of Orientifold planes should be coupled to the spacetime curvatures, of which conflicting claims existed previously.Comment: 41 pages, references updated; version to appear in JHE

First-principles derivation of the AdS/CFT Y-systems

We provide a first-principles, perturbative derivation of the AdS5/CFT4 Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The proof relies on the computation of quantum effects in the fusion of some loop operators, namely the transfer matrices. More precisely we show that the leading quantum corrections in the fusion of transfer matrices induce the correct shifts of the spectral parameter in the T-system. As intermediate steps we study UV divergences in line operators up to first order and compute the fusion of line operators up to second order for the pure spinor string in AdS5xS5. We also argue that the derivation can be easily extended to other integrable models, some of which describe string theory on AdS4, AdS3 and AdS2 spacetimes.Comment: 45 pages, 5 figures; v2: minor additions, JHEP versio

Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux

We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.Comment: 44 pages, 3 figures. v2: references and a discussion about perturbative results adde

The cusp anomalous dimension at three loops and beyond

We derive an analytic formula at three loops for the cusp anomalous dimension Gamma_cusp(phi) in N=4 super Yang-Mills. This is done by exploiting the relation of the latter to the Regge limit of massive amplitudes. We comment on the corresponding three loops quark anti-quark potential. Our result also determines a considerable part of the three-loop cusp anomalous dimension in QCD. Finally, we consider a limit in which only ladder diagrams contribute to physical observables. In that limit, a precise agreement with strong coupling is observed.Comment: 34 pages, 6 figures. v2: references added, typos correcte

Off-shell symmetry algebra of the AdS_4 x CP^3 superstring

By direct calculation in classical theory we derive the central extension of the off-shell symmetry algebra for the string propagating in AdS_4 x CP^3. It turns out to be the same as in the case of the AdS_5 x S^5 string. We also elaborate on the kappa-symmetry gauge and explain, how it can be chosen in a way which does not break bosonic symmetries.Comment: 23 page

The low-energy limit of AdS(3)/CFT2 and its TBA

We investigate low-energy string excitations in AdS3 × S3 × T4. When the worldsheet is decompactified, the theory has gapless modes whose spectrum at low energies is determined by massless relativistic integrable S matrices of the type introduced by Al. B. Zamolodchikov. The S matrices are non-trivial only for excitations with identical worldsheet chirality, indicating that the low-energy theory is a CFT2. We construct a Thermodynamic Bethe Ansatz (TBA) for these excitations and show how the massless modes’ wrapping effects may be incorporated into the AdS3 spectral problem. Using the TBA and its associated Y-system, we determine the central charge of the low-energy CFT2 to be c = 6 from calculating the vacuum energy for antiperiodic fermions — with the vacuum energy being zero for periodic fermions in agreement with a supersymmetric theory — and find the energies of some excited states

Integrability, spin-chains and the AdS3/CFT2 correspondence

Building on arXiv:0912.1723, in this paper we investigate the AdS3/CFT2 correspondence using integrability techniques. We present an all-loop Bethe Ansatz (BA) for strings on AdS_3 x S^3 x S^3 x S^1, with symmetry D(2,1;alpha)^2, valid for all values of alpha. This construction relies on a novel, alpha-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 x S^3 x 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 spin-chain can be regarded as giving some of the first hints about the unknown CFT2 dual to string theory on AdS_3 x S^3 x S^3 x S^1. We show that, in the alpha to 1 limit, the integrable structure of the D(2,1;alpha) 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 AdS3/CFT2 correspondence.Comment: LaTeX, 38 pages. v2: Corrected misprints in section 6.

Protected string spectrum in AdS(3)/CFT2 from worldsheet integrability

We derive the protected closed-string spectra of AdS3/CFT2 dual pairs with 16 supercharges at arbitrary values of the string tension and of the three-form fluxes. These follow immediately from the all-loop Bethe equations for the spectra of the integrable worldsheet theories. Further, representing the underlying integrable systems as spin chains, we find that their dynamics involves length-changing interactions and that protected states correspond to gapless excitations above the Berenstein-Maldacena-Nastase vacuum. In the case of AdS3 × S3 × T4 the degeneracies of such operators precisely match those of the dual CFT2 and the supergravity spectrum. On the other hand, we find that for AdS3 × S3 × S3 × S1 there are fewer protected states than previous supergravity calculations had suggested. In particular, protected states have the same su(2) charge with respect to the two three-spheres