Mass spectrum of chiral ten-dimensional N=2 supergravity on S 5

This paper focuses on supergravity duals of BPS states in N = 4 super YangMills. In order to describe these duals, we begin with a sequence of breathing mode reductions of IIB supergravity: first on S 3 , then S 3 × S 1 , and finally on S 3 × S 1 × CP 1 . We then follow with a complete supersymmetry analysis, yielding 1/8, 1/4 and 1/2 BPS configurations, respectively (where in the last step we take the Hopf fibration of S 3 ). The 1/8 BPS geometries, which have an S 3 isometry and are time-fibered over a six-dimensional base, are determined by solving a non-linear equation for the Kähler metric on the base. Similarly, the 1/4 BPS configurations have an S 3 × S 1 isometry and a four-dimensional base, whose Kähler metric obeys another non-linear, Monge-Ampère type equation. Despite the non-linearity of the problem, we develop a universal bubbling AdS description of these geometries by focusing on the boundary conditions which ensure their regularity. In the 1/8 BPS case, we find that the S 3 cycle shrinks to zero size on a five-dimensional locus inside the six-dimensional base. Enforcing regularity of the full solution requires that the interior of a smooth, generally disconnected five-dimensional surface be removed from the base. The AdS 5 × S 5 ground state corresponds to excising the interior of an S 5 , while the 1/8 BPS excitations correspond to deformations (including topology change) of the S 5 and/or the excision of additional droplets from the base. In the case of 1/4 BPS configurations, by enforcing regularity conditions, we identify three-dimensional surfaces inside the four-dimensional base which separate the regions where the S 3 shrinks to zero size from those where the S 1 shrinks. We discuss a large class of examples to show the emergence of a universal bubbling AdS picture for all 1/2, 1/4 and 1/8 BPS geometries.

Section: Three-charge Smooth Solutionsmentioning

confidence: 99%

Section: Jhep10(2007)003mentioning

confidence: 99%

See 1 more Smart Citation

Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

Chen¹,

Cremonini²,

Lin³

et al. 2007

“…Thus, the O(N ) contributions to the anomalies come purely from the Chern-Simons interactions on the 7-brane at the singularity, which include terms of the form C 4 ∧ tr(R ∧ R) and C 4 ∧ tr(F ∧ F ). The dimensional reduction of these terms gives rise to five-dimensional Chern-Simons interactions, since the five dimensional gauge fields involving the isometries include [29], in addition to the ten dimensional metric, a contribution of the form C 4 ∼ A R ∧ ω where A R is the U (1) R gauge potential on AdS 5 and ω is the volume form of the 3-cycle wrapped by the singularity.…”

Section: O(n ) Contributionsmentioning

confidence: 99%

A holographic computation of the central charges ofd= 4, 𝒩 = 2 SCFTs

Aharony¹,

Tachikawa²

2008

102

162

We use the AdS/CFT correspondence to compute the central charges of the d = 4, N = 2 superconformal field theories arising from N D3-branes at singularities in F-theory. These include the conformal theories with E n global symmetries. We compute the central charges a and c related to the conformal anomaly, and also the central charges k associated to the global symmetry in these theories. All of these are related to the coefficients of ChernSimons terms in the dual string theory on AdS 5 . Our computation is exact for all values of N , enabling several tests of the dualities recently proposed by Argyres and Seiberg for the E 6 and E 7 theories with N = 1.

“…Even a mixing of several scalar modes of this kind is allowed. The mixing case is interesting because it occurs in supergravity theories on AdS d+1 × S d+1 backgrounds [23][24][25][26][27]. For example in type II B supergravity in AdS 5 × S 5 the mass eigenstates of the mixing matrix for scalar modes [26,27] correspond to the bosonic chiral primary and descendant operators in the AdS/CFT dictionary [28].…”

Section: Mode Summation On Adsmentioning

confidence: 99%

On the propagator of a scalar field in AdS × S and in its plane wave limit

Dorn¹,

Salizzoni²,

Sieg³

2005

We discuss the scalar propagator on generic AdS d+1 × S d ′ +1 backgrounds. For the conformally flat situations and masses corresponding to Weyl invariant actions, the propagator is powerlike in the sum of the chordal distances with respect to AdS d+1 and S d ′ +1 . In these cases we analyze its source structure. In all other cases the propagator depends on both chordal distances separately. There an explicit formula is found for certain special mass values. For pure AdS we show how the well known propagators in the Weyl invariant case can be expressed as linear combinations of simple powers of the chordal distance. For AdS 5 × S 5 we relate our propagator to the expression in the plane wave limit and find a geometric interpretation of the variables occurring in the known explicit construction on the plane wave. As a byproduct of comparing different techniques, including the KK mode summation, a theorem for summing certain products of Legendre and Gegenbauer functions is derived.