On AdS2 × S7, its ℤk orbifold and their dual quantum mechanics

A bstract We consider a previously constructed class of massive Type IIA AdS 2 × S 7 × I solutions with OSp(8|2) symmetry, as well as OSp(6|2)-symmetric ones, by replacing the S 7 with the orbifold S 7 /ℤ k . In both cases we construct global solutions for which the interval I is bounded between physical singularities, by allowing D8-branes transverse to I . We also generate a new class of Type IIB AdS 2 × ℂℙ 3 × S 1 × I solutions by T-duality and establish a chain of dualities that maps the massless limit of these classes to $$ {\textrm{AdS}}_4/{\mathbb{Z}}_{k^{\prime }}\times \textrm{S}/{\mathbb{Z}}_k $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>AdS</mml:mi> <mml:mn>4</mml:mn> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>ℤ</mml:mi> <mml:msup> <mml:mi>k</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:msub> <mml:mo>×</mml:mo> <mml:mi>S</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>ℤ</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:math> , thus identifying the brane configurations yielding these solutions. We propose that the $$ \mathcal{N}=8 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>8</mml:mn> </mml:math> solutions are dual to a theory living on a D0-F1-D8 brane intersection which has a description in terms of disconnected quivers and similarly for the $$ \mathcal{N}=6 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>6</mml:mn> </mml:math> solutions.