Comments on AdS2 solutions of D=11 Supergravity(8)

We study the supersymmetric solutions of 11-dimensional supergravity with a factor of $AdS_2$ made of M2-branes. Such solutions can provide gravity duals of superconformal quantum mechanics, or through double Wick rotation, the generic bubbling geometry of

Onecanalsocheckthat,asrequiredbyEq.(4.4),

d =2i

4)∧ .(4.8)

AndEq.(3.20)isindeedsatis ed.

Thenextexampleisthe1/2-BPSbubblinggeometryofM-theorygiantgravitonsobtainedin[7].Thisclassofsolutionsdescribegeneric1/2-BPSoperatorsofM2-braneorM5-braneconformal eldtheories.Fromsuperalgebraarguments,suchcon gurationsshouldpossessSO(3)×SO(6)symmetry,whicharerealizedasaS2×S5factorinthemetric.S2canbetreatedasaWick-rotatedAdS2to tintoourresult.AnothercommentinorderisthatnowthecanonicalKillingvectormadeoutoftheKillingspinorbecomestime-like,sooursolutionscandescribemagnetic,orM5-branes,aswellaselectricorM2-branecon gurations.Thesolutionsaresummarizedasfollows.

ds2

11= 4e2λ(1+y2e 6λ)(dt+Vidxi)24λ

+e

y(1 y yD)

Vi=1

2 3[d( yD)+( yD)2dy]

F=dBt∧(dt+V)+BtdV+dB

Bt= 4y3e 6λ

dB =2 3[(y 2

yD+y( yD)2 yD)dy+y i yDdxi]

=2 3[y2( y1

3)2+ds2

KE4]

4e2λ(1+y2e 6λ)(dt+V)2

e 4λ

+