Supergravity Picture Research Articles

Betti multiplets, flows across dimensions and c-extremization

We consider 4d mathcal{N} = 1 SCFTs, topologically twisted on compact constant curvature Riemann surfaces, giving rise to 2d mathcal{N} = (0, 2) SCFTs. The exact R-current of these 2d SCFT extremizes the central charge c2d, similarly to the 4d picture, where the exact R-current maximizes the central charge a4d. There are global currents that do not mix with the R-current in 4d but their mixing becomes non trivial in 2d. In this paper we study the holographic dual of this process by analyzing a 5d mathcal{N} = 2 truncation of T1,1 with one Betti vector multiplet, dual to the baryonic current on the CFT side. The holographic realization of the flow across dimensions connects AdS5 to AdS3 vacua in the supergravity picture. We verify the existence of the flow to AdS3 solutions and we retrieve the field theory results for the mixing of the Betti vector with the graviphoton. Moreover, we extract the central charge from the Brown-Henneaux formula, matching with the results obtained in field theory. We develop a general formalism to obtain the central charge of a 2d SCFT from 5d mathcal{N} = 2 gauged supergravity with a generic number of vector multiplets, showing that its extremization corresponds to an attractor mechanism for the scalars in the supergravity picture.

Kutasov-like duality from D5-branes wrapping hyperbolic cycles

We study the addition of N f flavor D5-branes to supergravity solutions describing D5-branes wrapping two-cycles of genus g > 1 inside a six-dimensional space equipped with an SU ( 3 ) -structure. The non-zero genus g on the gravity side is dual to the existence of massless adjoint chiral superfields. Three types of internal manifolds are considered, each involving one of the following fibered products: H 2 × SL ˜ 2 , S 2 × SL ˜ 2 or H 2 × S 3 , where SL ˜ 2 stands for the universal cover of SL ( 2 , R ) . For the first one, we investigate the dual field theories. We show that some of the solutions with N f ≠ 0 are dual to four-dimensional N = 1 field theories exhibiting a Kutasov-like duality taking N c → k N f − N c and keeping N f fixed. Computed from the supergravity picture, k is in general a rational number, which can be made integer to fit the expectation from the field theory side. We finally study some other properties of those field theories.

Torsion and supersymmetry breaking

We identify the auxiliary fields in the hypermultiplets of type IIB string theory compactified on a Calabi-Yau manifold, using a combination of worldsheet and supergravity techniques. The SUSY-breaking squark and gaugino masses in type IIB models depend on these auxiliary fields, which parametrize deformations away from a pure Calabi-Yau compactification to one with NS-NS 3-form flux and SU(3) x SU(3) structure. Worldsheet arguments show that such compactifications are generically globally nongeometric. Our results, combined with earlier results for type IIA compactifications, imply that these deformations are the mirrors of NS-NS 3-form flux, in accord with work from the supergravity point of view. Using the worldsheet current algebra, we explain why mirror symmetry may continue to hold in the presence of fluxes breaking the symmetries (e.g., (2,2) SUSY) on which mirror symmetry is typically taken to depend. Finally, we give evidence that nonperturbative worldsheet effects (such as worldsheet instantons) provide important corrections to the supergravity picture in the presence of auxiliary fields for Kahler moduli.

A note on interactions of (non-commutative) instantons via AdS/CFT

We consider the interaction between instantons and anti-instantons in four-dimensional N=4 super-Yang–Mills theory at large N and large 't Hooft coupling, as described by D-instantons via AdS/CFT duality. We give an estimate of the strength of the interaction in various regimes. We also discuss the case of non-commutative super-Yang–Mills theory where the interaction between instantons and anti-instantons can be used as a way to probe the locality properties of the theory in the supergravity picture, without explicit reference to the definition of local operators.

D3-brane holography

It has recently been conjectured that the AdS_5/SYM_4 correspondence can be generalized away from the conformal limit, to a duality between supergravity on the full asymptotically flat three-brane background and a theory characterized as N=4 SYM deformed in the IR by a specific dimension-eight operator. Assuming that this relation is valid, we derive a prescription for computing n-point correlation functions in the holographic theory, which reduces to the standard AdS/CFT recipe at low energies. One- and two-point functions are discussed in detail. The prescription follows from very simple considerations and appears to be applicable to any asymptotically flat background. We also compute the quark-antiquark potential and comment on the description of the baryon in the supergravity picture. We conclude with some comments on the possible relation between our work and recent results in non-commutative field theories.

Domain walls of D=5 supergravity and fixed points of N=1 super-Yang–Mills

Employing the AdS/CFT correspondence, we give an explicit supergravity picture for the renormalization group flow of couplings 4-d super-Yang–Mills with four supercharges. The solution represents a domain wall of 5-d, N=2 supergravity, that interpolates between two (different) AdS 5 vacua and is obtained by gauging a U(1) subgroup of the SU(2) R-symmetry. On the supergravity side the domain wall couples only to scalar fields from vector multiplets, but not to scalars from hypermultiplets. We discuss the c-theorem, the β-functions and consider two examples: one is the sugra solution related to Z k orbifolds (corresponding to N=2 SYM) and the other is an orientifold construction for an elliptically fibered CY with F 1 basis (corresponding to N=1 SYM).

Aspects of instanton dynamics in AdS/CFT duality

We consider aspects of instanton dynamics in the large- N limit using the AdS/CFT duality for D0/D4 bound states. In the supergravity picture of wrapped D0-brane world-lines on D4-branes, we find the single-instanton measure and discuss its dependence on compactification finite-size effects, as well as its matching to perturbative results. In the non-supersymmetric case, the same dynamical effects that produce the theta-angle dependence perturbatively in 1/ N, render the instantons unstable, although approximate instantons of very small size still exist. The smeared D0/D4 black-brane supergravity solution can be interpreted as dual to a field theory configuration of an instanton condensate in the vacuum. In this case, we derive a holographic relation between the bare theta angle and the topological charge density of the instanton condensate.