Edi Gava

On subleading contributions to the AdS / CFT trace anomaly

In the context of the AdS/CFT correspondence, we perform a direct computation in AdS5 supergravity of the trace anomaly of a d = 4, = 2 SCFT. We find agreement with the field theory result up to next to leading order in the 1/N expansion. In particular, the order N gravitational contribution to the anomaly is obtained from a Riemann tensor squared term in the 7-brane effective action deduced from heterotic - type I duality. We also discuss, in the AdS/CFT context, the order N corrections to the trace anomaly in d = 4, = 4 SCFTs involving SO or Sp gauge groups.

Structure constants of planar Script N = 4 Yang Mills at one loop

We study structure constants of gauge invariant operators in planar = 4 Yang-Mills at one loop with the motivation of determining features of the string dual of weak coupling Yang-Mills. We derive a simple renormalization group invariant formula characterizing the corrections to structure constants of any primary operator in the planar limit. Applying this to the scalar SO(6) sector we find that the one loop corrections to structure constants of gauge invariant operators is determined by the one loop anomalous dimension hamiltonian in this sector. We then evaluate the one loop corrections to structure constants for scalars with arbitrary number of derivatives in a given holomorphic direction. We find that the corrections can be characterized by suitable derivatives on the four point tree function of a massless scalar with quartic coupling. We show that individual diagrams violating conformal invariance can be combined together to restore it using a linear inhomogeneous partial differential equation satisfied by this function.

Instantons in N=2 Sp(N) superconformal gauge theories and the AdS / CFT correspondence

Abstract We study, using ADHM construction, instanton effects in an N =2 superconformal Sp(N) gauge theory, arising as effective field theory on a system of N D3-branes near an orientifold 7-plane and eight D7-branes in type I′ string theory. We work out the measure for the collective coordinates of multi-instantons in the gauge theory and compare with the measure for the collective coordinates of (−1)-branes in the presence of 3- and 7-branes in type I′ theory. We analyse the large-N limit of the measure and find that it admits two classes of saddle points: In the first class the space of collective coordinates has the geometry of AdS5×S3 which on the string theory side has the interpretation of the D-instantons being stuck on the 7-branes and therefore the resulting moduli space being AdS5×S3, In the second class the geometry is AdS5×S5/Z2 and on the string theory side it means that the D-instantons are free to move in the ten-dimensional bulk. We discuss in detail a correlator of four O(8) flavour currents on the Yang–Mills side, which receives contributions from the first type of saddle points only, and show that it matches with the correlator obtained from F4 coupling on the string theory side, which receives contribution from D-instantons, in perfect accord with the AdS/CFT correspondence. In particular we observe that the sectors with an odd number of instantons give contributions to an O(8)-odd invariant coupling, thereby breaking O(8) down to SO(8) in type I′ string theory. We finally discuss correlators related to R4, which receive contributions from both saddle points.

D-strings in unconventional type I vacuum configurations

Abstract We determine the spectrum of D-string bound states in various classes of generalized type I vacuum configurations with sixteen and eight supercharges. The precise matching of the BPS spectra confirms the duality between unconventional type IIB orientifolds with quantized NS-NS antisymmetric tensor and heterotic CHL models in D = 8. A similar analysis puts the duality between type II (4,0) models and type I strings without open strings on a firmer ground. The analysis can be extended to type II (2,0) asymmetric orbifolds and their type I duals that correspond to unconventional K3 compactifications. Finally we discuss BPS-saturated threshold corrections to the corresponding low-energy effective Lagrangians. In particular we show how the exact moduli dependence of some F4 terms in the eight-dimensional type II (4,0) orbifold is reproduced by the infinite sum of D-instanton contributions in the dual type I theory.

Gravitational F-terms through anomaly equations and deformed chiral rings

We study effective gravitational F-terms, obtained by integrating an U(N) adjoint chiral superfield Φ coupled to the = 1 gauge chiral superfield Wα and supergravity, to arbitrary orders in the gravitational background. The latter includes in addition to the = 1 Weyl superfield Gαβγ, the self-dual graviphoton field strength Fαβ of the parent, broken = 2 theory. We first study the chiral ring relations resulting from the above non-standard gravitational background and find agreement, for gauge invariant operators, with those obtained from the dual closed string side via Bianchi identities for = 2 supergravity coupled to vector multiplets. We then derive generalized anomaly equations for connected correlators on the gauge theory side, which allow us to solve for the basic one-point function TrW2/(z−Φ) to all orders in F2. By generalizing the matrix model loop equation to the generating functional of connected correlators of resolvents, we prove that the gauge theory result coincides with the genus expansion of the associated matrix model, after identifying the expansion parameters on the two sides.

AdS3 vacua and RG flows in three dimensional gauged supergravities

We study AdS3 supersymmetric vacua in N = 4 and N = 8, three dimensional gauged supergravities, with scalar manifolds

Large AdS/CFT correspondence and D1/D5 systems in theories with 16 supercharges

{\left( {\frac{{{\text{SO}}\left( {4,4} \right)}}{{{\text{SO}}(4) \times {\text{SO}}(4)}}} \right)^2}

Partial Script N = 2?Script N = 1 supersymmetry breaking and gravity deformed chiral rings

and

3D gauged supergravity from SU(2) reduction of

\frac{{{\text{SO}}\left( {8,8} \right)}}{{{\text{SO}}(8) \times {\text{SO}}(8)}}

N=1

, non-semisimple Chern-Simons gaugings SO(4) ⋉ R6 and (SO(4) ⋉ R6)2, respectively. These are in turn equivalent to SO(4) and SO(4) × SO(4) Yang-Mills theories coupled to supergravity. For the N = 4 case, we study renormalization group flows between UV and IR AdS3 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 SCFT2. These provide examples of v.e.v. flows between two AdS3 vacua within a gauged supergravity framework.