David Nolland

Order 1/N2 test of the Maldacena conjecture : cancellation of the one-loop Weyl anomaly.

Abstract We test the Maldacena conjecture for type IIB string theory / N =4 Yang–Mills by calculating the one-loop corrections in the bulk theory to the Weyl anomaly of the boundary CFT when the latter is coupled to a Ricci flat metric. The contributions cancel within each supermultiplet, in agreement with the conjecture.

Order 1/N2 test of the Maldacena conjecture II: the full bulk one-loop contribution to the boundary Weyl anomaly

Abstract We compute the complete bulk one-loop contribution to the Weyl anomaly of the boundary theory for IIB supergravity compactified on AdS5×S5. The result, that δ A =(E+I)/π 2 , reproduces the subleading term in the exact expression A =−(N 2 −1)(E+I)/π 2 for the Weyl anomaly of N =4 super-Yang–Mills theory, confirming the Maldacena conjecture. The anomaly receives contributions from all multiplets casting doubt on the possibility of describing the boundary theory beyond leading order in N by a consistent truncation to the ‘massless’ multiplet of IIB supergravity.

One-loop conformal anomalies from AdS/CFT in the Schrödinger representation.

We compute the conformal anomalies of boundary CFTs for scalar and fermionic fields propagating in AdS spacetime at one-loop. The coefficients are quantized, with values related to the mass-spectra for Kaluza-Klein compactifications of Supergravity on AdS5 × S5 and AdS7 × S4. Our approach interprets the partition function of fields on AdS spacetime in terms of wave-functionals that satisfy the functional Schrodinger equation.

The Boundary Weyl Anomaly in the N=4 SYM/Type IIB Supergravity Correspondence

We give a complete account of the Schrodinger representation approach to the calculation of the Weyl anomaly of = 4 SYM from the AdS/CFT correspondence. On the AdS side, the 1/N2 correction to the leading order result receives contributions from all the fields of type-IIB Supergravity, the contribution of each field being given by a universal formula. The correct matching with the CFT result is thus a highly non-trivial test of the correspondence.

AdS/CFT boundary conditions, multi-trace perturbations, and the c-theorem

Abstract We discuss possible choices for boundary conditions in the AdS/CFT correspondence, and calculate the renormalisation group flow induced by a double-trace perturbation. In running from the UV to the IR there is a unit shift in the central charge. The discrepancy between our result and results obtained by other authors is accounted for by the discovery that there is a non-trivial flow for perturbations induced by bulk fields with masses saturating the Breitenlohner–Freedman bound.

Order 1/N3 corrections to the conformal anomaly of the (2,0) theory in six dimensions.

Using Supergravity on AdS7×S4 we calculate the bulk one-loop contribution to the conformal anomaly of the (2,0) theory describing N coincident M5 branes. When this is added to the tree-level result, and an additional subleading order contribution calculated by Tseytlin, it gives an expression for the anomaly that interpolates correctly between the large N theory and the free (2,0) tensor theory corresponding to N=1. Thus we can argue that we have identified the exact N-dependence of the anomaly, which may have a simple protected form valid away from the large N limit.

Test of gauged N=8 SUGRA/N=1 SYM duality at sub-leading order

Abstract An infra-red fixed point of N =1 super-Yang–Mills theory is believed to be dual to a solution of five-dimensional gauged N =8 supergravity. We test this conjecture at next to leading order in the large N expansion by computing bulk one-loop corrections to the anomaly coefficient a − c . The one-loop corrections are non-zero for all values of the bulk mass, and not just special ones as claimed in previous work.

Gravitinos in non-Ricci-flat backgrounds

Abstract We discuss the gauge invariance and “mass” of the Rarita-Schwinger field in a background spacetime which is assumed to be Einstein but not necessarily Ricci-flat.

THE SCHRÖDINGER REPRESENTATION FOR FERMIONS AND A LOCAL EXPANSION OF THE SCHWINGER MODEL

We discuss the functional representation of fermions, and obtain exact expressions for wave-functionals of the Schwinger model. Known features of the model such as bosonization and the vacuum angle arise naturally. Contrary to expectations, the vacuum wave-functional does not simplify at large distances, but it may be reconstructed as a large time limit of the Schrodinger functional, which has an expansion in local terms. The functional Schrodinger equation reduces to a set of algebraic equations for the coefficients of these terms. These ideas generalize to a numerical approach to QCD in higher dimensions.

Cancellation of divergences in N=4 SYM/type IIB supergravity correspondence

Abstract Using Schrodinger functional methods, we show that in the N =4 SYM/type IIB supergravity correspondence the renormalisation of the boundary Newton and gravitational constants arising from bulk fields cancels when we sum over all the Kaluza–Klein modes of supergravity. This accords with the expected finiteness of N =4 SYM, and it is expected that other renormalisations cancel in a similar way.