Abstract

We discuss AdS2 × S3 × CY2 × Iρ solutions to massive Type IIA supergravity with 4 Poincaré supersymmetries. We propose explicit dual quiver quantum mechanics built out of D0 and D4 colour branes coupled to D4’ and D8 flavour branes. We propose that these quivers describe the interactions of instantons and Wilson lines in 5d gauge theories with 8 Poincaré supersymmetries. Using the RR Maxwell fluxes of the solutions, conveniently put off-shell, we construct a functional from which the holographic central charge can be derived through a geometrical extremisation principle.

Highlights

  • As the dimensionality of the internal space increases, the richer the structure of all possible geometries and topologies thereof becomes

  • We propose explicit dual quiver quantum mechanics built out of D0 and D4 colour branes coupled to D4’ and D8 flavour branes

  • At the level of the dual CFTs the Superconformal Quantum Mechanics (SCQM) dual to the AdS2 solutions arise from the 2d CFTs dual to the AdS3 backgrounds upon dimensional reduction

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Summary

Brane set-up

The brane set-up associated to the previous solutions was identified in [37] (see [24]), for the case of u = constant.3 It consists on a D0-F1-D4-D4’-D8 brane intersection, depicted, preserving four supersymmetries. The second component of F(4) in (2.5) is the Hodge-dual of the F(6) used in (2.14) to compute the electric charge of the D4-branes. The first component gives rise to a magnetic charge associated to a second type of D4’-branes. There are D8 brane sources localised in the ρ direction, behaving as flavour branes They are wrapped on AdS2 × S3 × CY2.

The local solutions
Holographic central charge
The dual superconformal quantum mechanics
Warm up: quantum mechanics of the D0-D4 system
The dual quiver quantum mechanics
Quantum mechanical central charge
Relation with the electric-magnetic charges
An action functional for the central charge
Conclusions
A The seed backgrounds and their dual SCFTs
B D0-D4-D4’-D8 quantum mechanics
C Holographic calculation of SQM observables
D Continuity of the NS sector
E Volumes and stringy volumes
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