Presentation on theme: "Type IIB Supergravity, D3 branes and ALE manifolds"— Presentation transcript:
1 Type IIB Supergravity, D3 branes and ALE manifolds Based on recent work by:M. Bertolini, G. Ferretti, (P. F.) M. Trigiante, L. Campos, P. Salomonson hep-thM.Billo, (P.F.), C. Herman, L. Modesto, I. Pesando (to appear)
2 IntroductionThere are interesting solutions of type IIB theory, named fractional D3 branes.The gauge duals are non-conformal N=2 gauge theories in d=4Fractional branes are commonly viewed as 5-branes wrapped on a vanishing cycle of transverse spaceTransverse space is R2 x R4/G.We have found a supersymmetric (BPS) D3-brane solution where transverse space is R2 x ALEIn the orbifold limit we recover fractional branesThe warp factor is determined by a harmonic equation on ALEIn Eguchi Hanson case the harmonic equation reduces to a confluent Heun equationOpen questions on the boundary action and the gauge dual.
3 Type IIB SugraThe D3 brane couples to C whose field strength involves a Chern Simons of lower formsCastellani & Pesando (1991) established geometric formulation
4 The SL(2,R)~SU(1,1) structure The solvable Lie algebra parametrization of the coset naturally introduces the dilaton and the RR 0-form
5 The FDA defining the Theory Note the Chern SimonsAs for all supergravities the algebraic structure is encoded in an FDA. (D’Auria, Fré, (1982), Castellani, P. Van Nieuwenhuizen, K. Pilch (1982)
7 Always running to get ahead ......... while Sergio relaxes in L.A!Ops!.. I was also there but do nottell anybody....
8 The rheonomic parametrizations~susy rules FermionicComponents areexpressedin terms ofspace-timecomponents
9 Our task: the equations to be solved Note that these equations are written in flat indices and appear as cosntraints on the curvature components
10 Fractional Branes= D3 branes on orbifolds C2/G In the dual gauge theory, x4+ix5 makes the complex scalar of the vector multiplet whilex6, x7 , x8 , x9 constitute the scalar part of a hypermultipletSusy ishalvedin the bulkbyrestrictedholonomy
11 ALE manifolds as orbifold resolutions ALE manifolds are related to the ADE classification of Lie algebras. They can be obtained as suitable Hyperkahler quotients of flat HyperKahler manifoldsKronheimer construction of ALE spaces is realized by String Theory
23 Interpolation and singularity Far from the cycle we just seethe charge of a normal D3 in D=10Near the cycle we see aD3 brane in D=8. It is as if we had compactified sugra on an S2
24 The World Volume Action Kappa supersymmetric: the fermions are hidden in the p—forms that are superformsThe interactions of world—volume fields (fluctuations from vacuum values) feel all the bckg fields. Yet this action is source only for C4.. Where is the source of AL ?Red=Auxiliary fieldsBrown=Sugra bckg fieldsBlue=World volume fieldsThis is the open question answering the which will shed light on the real nature of fractional branes
25 The End Such people are always running when someone watches.......... Let us make an appointment for all supergravity peopleto be back here for 50Such people are always running when someone watches