Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix

We review the derivation of the S-matrix for planar N=4 supersymmetric Yang-Mills theory and type IIB superstring theory on an AdS5xS5 background. After deriving the S-matrix for the su(2) and su(3) sectors at the one-loop level based on coordinate Bethe ansatz, we show how su(2|2) symmetry leads to the exact asymptotic S-matrix up to an overall scalar function. We then briefly review the spectrum of bound states by relating these states to simple poles of the S-matrix. Finally, we review the derivation of the asymptotic Bethe equations, which can be used to determine the asymptotic multiparticle spectrum.Comment: 20 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated, v3: references added and minor change

TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT

The ground-state energy of integrably-twisted theories is analyzed in finite volume. We derive the leading and next-to-leading order (NLO) L\"uscher-type corrections for large volumes of the vacuum energy for integrable theories with twisted boundary conditions and twisted S-matrix. We then derive the twisted thermodynamic Bethe ansatz (TBA) equations to describe exactly the ground state, from which we obtain an untwisted Y-system. The two approaches are compared by expanding the TBA equations to NLO, and exact agreement is found. We give explicit results for the O(4) model and for the three-parameter family of $\gamma$-deformed (non-supersymmetric) planar AdS/CFT model, where the ground-state energy can be nontrivial and can acquire finite-size corrections. The NLO corrections, which correspond to double-wrapping diagrams, are explicitly evaluated for the latter model at six loops.Comment: 42 pages, 2 figures, v2: references added, v3: minor correction

Yangian symmetry and bound states in AdS/CFT boundary scattering

We consider the problem of boundary scattering for Y=0 maximal giant graviton branes. We show that the boundary S-matrix for the fundamental excitations has a Yangian symmetry. We then exploit this symmetry to determine the boundary S-matrix for two-particle bound states. We verify that this boundary S-matrix satisfies the boundary Yang-Baxter equations.Comment: 17 page

Screened hybrid functional applied to 3d^0-->3d^8 transition-metal perovskites LaMO3 (M=Sc-Cu): influence of the exchange mixing parameter on the structural, electronic and magnetic properties

We assess the performance of the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid density functional scheme applied to the perovskite family LaMO3 (M=Sc-Cu) and discuss the role of the mixing parameter alpha (which determines the fraction of exact Hartree-Fock exchange included in the density functional theory (DFT) exchange-correlation functional) on the structural, electronic, and magnetic properties. The physical complexity of this class of compounds, manifested by the largely varying electronic characters (band/Mott-Hubbard/charge-transfer insulators and metals), magnetic orderings, structural distortions (cooperative Jahn-Teller like instabilities), as well as by the strong competition between localization/delocalization effects associated with the gradual filling of the t_2g and e_g orbitals, symbolize a critical and challenging case for theory. Our results indicates that HSE is able to provide a consistent picture of the complex physical scenario encountered across the LaMO3 series and significantly improve the standard DFT description. The only exceptions are the correlated paramagnetic metals LaNiO3 and LaCuO3, which are found to be treated better within DFT. By fitting the ground state properties with respect to alpha we have constructed a set of 'optimum' values of alpha from LaScO3 to LaCuO3: it is found that the 'optimum' mixing parameter decreases with increasing filling of the d manifold (LaScO3: 0.25; LaTiO3 & LaVO3: 0.10-0.15; LaCrO3, LaMnO3, and LaFeO3: 0.15; LaCoO3: 0.05; LaNiO3 & LaCuO3: 0). This trend can be nicely correlated with the modulation of the screening and dielectric properties across the LaMO3 series, thus providing a physical justification to the empirical fitting procedure.Comment: 32 pages, 29 figure

The Zamolodchikov-Faddeev algebra for open strings attached to giant gravitons

We extend the Zamolodchikov-Faddeev algebra for the superstring sigma model on $AdS_{5}\times S^{5}$, which was formulated by Arutyunov, Frolov and Zamaklar, to the case of open strings attached to maximal giant gravitons, which was recently considered by Hofman and Maldacena. We obtain boundary $S$-matrices which satisfy the standard boundary Yang-Baxter equation.Comment: 22 pages, no figure; added a referenc

Quantum finite-size effects for dyonic magnons in the AdS_4 x CP^3

We compute quantum corrections to finite-size effects for various dyonic giant magnons in the AdS_4 x CP^3 in two different approaches. The off-shell algebraic curve method is used to quantize the classical string configurations in semi-classical way and to compute the corrections to the string energies. These results are compared with the F-term L\"uscher formula based on the S-matrix of the AdS_4 / CFT_3. The fact that the two results match exactly provides another stringent test for the all-loop integrability conjecture and the exact S-matrix based on it.Comment: 21 pages, No figures, corrected typos, added some reference

Factorized Tree-level Scattering in AdS_4 x CP^3

AdS_4/CFT_3 duality relating IIA string theory on AdS_4 x CP^3 to N=6 superconformal Chern-Simons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the tree-level worldsheet scattering for strings on AdS_4 x CP^3. We compute all bosonic four-, five- and six-point amplitudes in the gauge-fixed action and demonstrate the absence of particle production.Comment: 23 pages, v2. references adde

A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory

Super twistor space admits a certain (super) complex structure deformation that preserves the Poincare subgroup of the symmetry group PSL(4|4) and depends on 10 parameters. In a previous paper [hep-th/0502076], it was proposed that in twistor string theory this deformation corresponds to augmenting N=4 super Yang-Mills theory by a mass term for the left-chirality spinors. In this paper we analyze this proposal in more detail. We calculate 4-particle scattering amplitudes of fermions, gluons and scalars and show that they are supported on holomorphic curves in the deformed twistor space.Comment: 52 pages, 15 figure

Non-planar ABJM Theory and Integrability

Using an effective vertex method we explicitly derive the two-loop dilatation generator of ABJM theory in its SU(2)xSU(2) sector, including all non-planar corrections. Subsequently, we apply this generator to a series of finite length operators as well as to two different types of BMN operators. As in N=4 SYM, at the planar level the finite length operators are found to exhibit a degeneracy between certain pairs of operators with opposite parity - a degeneracy which can be attributed to the existence of an extra conserved charge and thus to the integrability of the planar theory. When non-planar corrections are taken into account the degeneracies between parity pairs disappear hinting the absence of higher conserved charges. The analysis of the BMN operators resembles that of N=4 SYM. Additional non-planar terms appear for BMN operators of finite length but once the strict BMN limit is taken these terms disappear.Comment: 1+26 pages, uses axodraw.sty. v2: typos fixed, references added. v3: more typos fixed, minor correction

Contour deformation trick in hybrid NLIE

The hybrid NLIE of AdS_5 x S^5 is applied to a wider class of states. We find that the Konishi state of the orbifold AdS_5 x (S^5/Z_S) satisfies A_1 NLIE with the source terms which are derived from contour deformation trick. For general states, we construct a deformed contour with which the contour deformation trick yields the correct source terms.Comment: 39 pages, 6 figures, v2: discussion on analyticity constraints replaced by consistent deformed contou