Note on the boundary terms in AdS/CFT correspondence for Rarita-Schwinger field

In this letter the boundary problem for massless and massive Rarita-Schwinger field in the AdS/CFT correspondence is considered. The considerations are along the lines of a paper by Henneaux (hep-th/9902137) and are based on the requirement the solutions to be a stationary point for the action functional. It is shown that this requirement, along with a definite asymptotic behavior of the solutions, fixes the boundary term that must be added to the initial Rarita-Schwinger action. It is also shown that the boundary term reproduce the known two point correlation functions of certain local operators in CFT living on the boundary.Comment: 12 pages, one more refernce added, some typos correcte

The massless gravitino and the AdS/CFT correspondence

We solve the Dirichlet boundary value problem for the massless gravitino on $AdS_{d+1}$ space and compute the two-point function of the dual CFT supersymmetry currents using the $AdS$/CFT correspondence principle. We find analogously to the spinor case that the boundary data for the massless $(d+1)$ dimensional bulk gravitino field consists of only a $(d-1)$ dimensional gravitino.Comment: 10 pages, RevTe

Conformal Field Theory Correlators from Classical Field Theory on Anti-de Sitter Space II. Vector and Spinor Fields

We use the AdS/CFT correspondence to calculate CFT correlation functions of vector and spinor fields. The connection between the AdS and boundary fields is properly treated via a Dirichlet boundary value problem.Comment: 14 pages, LaTeX2e with amsmath,amsfonts packages; v2:interactions section corrected, reference adde

Three-point Green function of the stress-energy tensor in the AdS/CFT correspondence

We compute the 3-point function of the stress-energy tensor in the d-dimensional CFT from the AdS_{d+1} gravity. For d=4 the coefficients of the three linearly independent conformally covariant forms entering the 3-point function are exactly the same as given by the free field computations in the ${\cal N}=4$ SYM just as expected from the known renormalization theorems. For d=3 and d=6 our results give the value of the corresponding 3-point function in the theories of strongly coupled ${\cal N}=8$ superconformal scalar and (2,0) tensor multiplets respectively.Comment: Latex, 13 pages, eq. (2.10) is correcte

Some Cubic Couplings in Type IIB Supergravity on AdS5×S5AdS_5\times S^5 and Three-point Functions in SYM_4 at Large N

All cubic couplings in type IIB supergravity on $AdS_5\times S^5$ that involve two scalar fields $s^I$ that are mixtures of the five form field strength on $S^5$ and the trace of the graviton on $S^5$ are derived by using the covariant equations of motion and the quadratic action for type IIB supergravity on $AdS_5\times S^5$. All corresponding three-point functions in SYM$_4$ are calculated in the supergravity approximation. It is pointed out that the scalars $s^I$ correspond not to the chiral primary operators in the ${\cal N}=4$ SYM but rather to a proper extension of the operators.Comment: Latex, 24p, misprints are correcte

The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit

The operator product expansion for ``small'' Wilson loops in {\cal N}=4, d=4 SYM is studied. The OPE coefficients are calculated in the large N and g_{YM}^2 N limit by exploiting the AdS/CFT correspondence. We also consider Wilson surfaces in the (0,2), d=6 superconformal theory. In this case, we find that the UV divergent terms include a term proportional to the rigid string action.Comment: 22 pages LaTeX2e, using utarticle.cls (included) and AMS-LaTeX macro

AdS/CFT correspondence in the Euclidean context

We study two possible prescriptions for AdS/CFT correspondence by means of functional integrals. The considerations are non-perturbative and reveal certain divergencies which turn out to be harmless, in the sense that reflection-positivity and conformal invariance are not destroyed.Comment: 20 pages, references and two remarks adde

AdS3_3 vacua and RG flows in three dimensional gauged supergravities

We study $AdS_3$ supersymmetric vacua in N=4 and N=8, three dimensional gauged supergravities, with scalar manifolds $(\frac{SO(4,4)}{SO(4)\times SO(4)})^2$ and $\frac{SO(8,8)}{SO(8)\times SO(8)}$, non-semisimple Chern-Simons gaugings $SO(4)\ltimes {\bf R}^6$ and $(SO(4)\ltimes {\bf R}^6)^2$, respectively. These are in turn equivalent to SO(4) and $SO(4)\times SO(4)$ Yang-Mills theories coupled to supergravity. For the N=4 case, we study renormalization group flows between UV and IR $AdS_3$ vacua with the same amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an analytic solution whereas in another, with (2,0) supersymmetry, we give a numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e. they are driven by the expectation value of a relevant operator in the dual $SCFT_2$. These provide examples of v.e.v. flows between two $AdS_3$ vacua within a gauged supergravity framework.Comment: 35 pages in JHEP form, 3 figures, typos corrected, references 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

Running Scaling Dimensions in Holographic Renormalization Group Flows

Holographic renormalization group flows can be interpreted in terms of effective field theory. Based on such an interpretation, a formula for the running scaling dimensions of gauge-invariant operators along such flows is proposed. The formula is checked for some simple examples from the AdS/CFT correspondence, but can be applied also in non-AdS/non-CFT cases.Comment: 14 pages, 2 figure