JHEP10(2018)190
branes t y r θ
1
θ
2
θ
3
θ
4
θ
5
θ
6
θ
7
D0 × − − − − − − − − −
F1 × × − − − − − − − −
D8 × − × × × × × × × ×
Table 1. The brane picture underlying the N = (8, 0) superconformal quantum mechanics de-
scribed by a D0-F1-D8 system. The above system is
1
4
-BPS. We anticipate that the radial coordinate
realizing the dual AdS
2
geometry turns out to be a combination of y & r.
The paper is organized as follows. We start out by reviewing some facts concerning
D0-F1-D8 intersec ti ons in massive type IIA stri ng theory and r e l ate them to
1
4
-BPS su-
pergravity solutions discussed in [
10]. Subsequently, we show how to make an educated
guess in the general Ansatz which di r e ct l y produces solutions with enhanced supersym-
metry thus realizing AdS
2
geometry. After integrating the obtained differential equations,
we discuss the relation of the obtained solutions to the aforementioned AdS
7
counterparts
through double analytic continuation. Then, we discuss the possible singularity struct ur e s
as well as the range of the warp c oordinate. We conclude with some further sp e cu l ati ons
concerning the possible holographic interpretation of our work.
2 AdS
2
solutions from D0-F1-D8 intersections
D0-D8 bound states were considered in [
11–14] as UV descriptions of N = (8, 0) super-
conformal quantum mechanics. Such bound states require a non-trivial B-field sourced by
a fundamental string. Note that, c ontrary to all other D-branes, strings cannot end on
a D-particle due to charge conservation issues [
15, 16]. However the situation changes in
presence of D8-b ran es in the background, where in fact an F1 stretched between a D0 and
the D8 has to be formed whenever the D0 crosses a D8 [
17]. This physical pro c e ss can be
understood as a dual version of the Hanany-Witten (HW) effect [
18].
D0-F1-D8 brane systems were exhaustively studied in [
10, 19] as a class of
1
4
-BPS
solutions in massi ve type IIA supergravity. The explicit set-up is summarized in table
1.
The complete Ansatz for the 10D fields of massive type II A supergravity can be com-
pletely specified in terms of two arbitrary functions of the (y, r) coordinates, denoted by S
& K. This reads
ds
2
10
= −S
−1
K
−1/2
dt
2
+ S
−1
K
1/2
dy
2
+ K
1
2
(dr
2
+ r
2
dΩ
2
(7)
),
e
Φ
= g
s
K
3/4
S
−1/2
,
F
(0)
= m,
C
(1)
= g
−1
s
K
−1
dt,
B
(2)
= S
−1
dt ∧ dy,
(2.1)
where g
s
> 0 is th e string coupling and dΩ
2
(7)
denotes the metric of a unit-r adi us seven-
sphere.
– 2 –