Anomalous Dimensions of Non-Chiral Operators from AdS/CFT

Non-chiral operators with positive anomalous dimensions can have interesting applications to supersymmetric model building. Motivated by this, we develop a new method for obtaining the anomalous dimensions of non-chiral double-trace operators in N=1 superconformal field theories (SCFTs) with weakly-coupled AdS duals. Via the Hamiltonian formulation of AdS/CFT, we show how to directly compute the anomalous dimension as a bound state energy in the gravity dual. This simplifies previous approaches based on the four-point function and the OPE. We apply our method to a class of effective AdS5 supergravity models, and we find that the binding energy can have either sign. If such models can be UV completed, they will provide the first calculable examples of SCFTs with positive anomalous dimensions.Comment: 38 pages, 2 figures, refs adde

Scattering in Anti-de Sitter Space and Operator Product Expansion

We develop a formalism to evaluate generic scalar exchange diagrams in AdS_{d+1} relevant for the calculation of four-point functions in AdS/CFT correspondence. The result may be written as an infinite power series of functions of cross-ratios. Logarithmic singularities appear in all orders whenever the dimensions of involved operators satisfy certain relations. We show that the AdS_{d+1} amplitude can be written in a form recognisable as the conformal partial wave expansion of a four-point function in CFT_{d} and identify the spectrum of intermediate operators. We find that, in addition to the contribution of the scalar operator associated with the exchanged field in the AdS diagram, there are also contributions of some other operators which may possibly be identified with two-particle bound states in AdS. The CFT interpretation also provides a useful way to ``regularize'' the logarithms appearing in AdS amplitude.Comment: 39 pages, using harvmac and epsf, eight figures; discussion in coinciding pole cases expanded, references added, misprints correcte

A conical deficit in the AdS4/CFT3 correspondence

Inspired by the AdS/CFT correspondence we propose a new duality that allow the study of strongly coupled field theories living in a 2+1 conical space-time. Solving the 4-d Einstein equations in the presence of an infinite static string and negative cosmological constant we obtain a conical AdS4 space-time whose boundary is identified with the 2+1 cone found by Deser, Jackiw and 't Hooft. Using the AdS4/CFT3 correspondence we calculate retarded Green's functions of scalar operators living in the cone.Comment: v3, 14 pages. We reinterpret our results for the Green's functions in the con

From Free Fields to AdS -- II

We continue with the program of hep-th/0308184 to implement open-closed string duality on free gauge field theory (in the large $N$ limit). In this paper we consider correlators such as \la \prod_{i=1}^n \Tr\Phi^{J_i}(x_i)\ra. The Schwinger parametrisation of this $n$-point function exhibits a partial gluing up into a set of basic skeleton graphs. We argue that the moduli space of the planar skeleton graphs is exactly the same as the moduli space of genus zero Riemann surfaces with $n$ holes. In other words, we can explicitly rewrite the $n$-point (planar) free field correlator as an integral over the moduli space of a sphere with $n$ holes. A preliminary study of the integrand also indicates compatibility with a string theory on $AdS$. The details of our argument are quite insensitive to the specific form of the operators and generalise to diagrams of higher genus as well. We take this as evidence of the field theory's ability to reorganise itself into a string theory.Comment: 26 pages, 2 figures; v2. some additional comments, references adde

Group-Theoretical Classification of BPS States in D=4 Conformal Supersymmetry: the Case of (1/N)-BPS

In an earlier paper we gave the complete group-theoretical classification of BPS states of the N-extended D=4 conformal superalgebras su(2,2/N), but not all interesting cases were given in detail. In the present paper we spell out the interesting case of (1/N)-BPS and possibly protected states.Comment: LATEX2e, 8 pages, Plenary talk at the International Workshop 'Supersymmetries and Quantum Symmetries', Dubna, 18-23.7.2011, to appear in the Proceedings, editors Evgeny Ivanov et a

Intersecting D3-branes and Holography

We study a defect conformal field theory describing D3-branes intersecting over two space-time dimensions. This theory admits an exact Lagrangian description which includes both two- and four-dimensional degrees of freedom, has (4,4) supersymmetry and is invariant under global conformal transformations. Both two- and four-dimensional contributions to the action are conveniently obtained in a two-dimensional (2,2) superspace. In a suitable limit, the theory has a dual description in terms of a probe D3-brane wrapping an AdS_3 x S^1 slice of AdS_5 x S^5. We consider the AdS/CFT dictionary for this set-up. In particular we find classical probe fluctuations corresponding to the holomorphic curve wy=c\alpha^{\prime}. These fluctuations are dual to defect fields containing massless two-dimensional scalars which parameterize the classical Higgs branch, but do not correspond to states in the Hilbert space of the CFT. We also identify probe fluctuations which are dual to BPS superconformal primary operators and to their descendants. A non-renormalization theorem is conjectured for the correlators of these operators, and verified to order g^2.Comment: 46 pages, 5 figures, Latex, minor corrections to section 4.2, version published in Phys. Rev.

Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry

We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity threshold. These results are also applicable to irreps of the complex Lie superalgebras sl(4/N). Our derivations use results from the representation theory of su(2,2/N) developed already in the 80s.Comment: 81 pages, input files: harvmac, amssym.def, amssym.tex; corrected presentation on odd reflection