On short and semi-short representations for four-dimensional superconformal symmetry

Dolan, F.A.; Osborn, H.

doi:10.1016/s0003-4916(03)00074-5

Cited by 352 publications

(775 citation statements)

References 41 publications

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“…A Kähler potential satisfying our requirement is 8) up to an irrelevant constant. Given the definition of y in (7.6), it follows that for y ≪ 1, the six-dimensional base is toric, with a U(1) 3 isometry.…”

Section: Jhep10(2007)003mentioning

confidence: 92%

“…However, unlike for LLM geometries, in these cases the supersymmetry analysis is not particularly constructive. For example, it was found in [20] that 1/8 BPS configurations with an S 3 isometry may be written using a metric of the form ds 2 10 = −e 2α (dt + ω) 2 + e −2α h ij dx i dx j + e 2α dΩ 2 3 , ( 8) where h ij is a Kähler metric of complex dimension three. In the end, the invariant tensor analysis does not provide an actual procedure for obtaining this metric short of solving a non-linear equation on its curvature [20] 6 R = −R ij R ij + 1 2 R 2 .…”

Section: Jhep10(2007)003mentioning

confidence: 99%

“…To proceed in this direction, we first consider the realization of the AdS 5 × S 5 ground state itself. In this case, we take the ten-dimensional metric 1 8) and identify the S 3 in AdS 5 with the S 3 of (5.1). This determines…”

Section: Ads 5 × Smentioning

confidence: 99%

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Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

Chen¹,

Cremonini²,

Lin³

et al. 2007

J. High Energy Phys.

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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.

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Section: Jhep10(2007)003mentioning

confidence: 92%

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

J. High Energy Phys.

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“…This is not possible because four-dimensional N = 2 SCFTs cannot have enhanced global symmetries as exactly marginal couplings are continuously varied, without having also enhanced higher-spin symmetries (see also [22,23]). We can see this by examining the list of allowed multiplets of the four-dimensional N = 2 superconformal algebra [24][25][26][27][28], in which there is no superconformal multiplet including a vector operator with a dimension that continuously goes down to the conserved current dimension ∆ = 3, without containing also additional conserved currents of higher spins. 13 Indeed, there are several loose points in the expectation that such an enhanced SU(K) gauge symmetry should arise.…”

Section: Jhep03(2015)121mentioning

confidence: 99%

“…The previous exact computations of Wilson loop operators [19] indicated hierarchically separated BPS string tensions in the singular limit. 28 Extensions to 't Hooft loops and some correlation functions are straightforward, and the correlation functions of loop operators should be compared with those of the BPS strings in the six-dimensional N = (2, 0) theory on AdS 5 × S 1 . Equating the two computations, we should be able to extract the relation between the position in the 'moduli space' and the couplings of the SU(K) and P (K) theories [67,68].…”

Section: Rigid Holography Made Precisementioning

confidence: 99%

Rigid holography and six-dimensional N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ theories on AdS5 × S $$ \mathbb{S} $$ 1

Aharony

Berkooz

Rey

2015

J. High Energ. Phys.

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Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A K−1 superconformal field theory (SCFT) on AdS 5 ×S 1 , with equal radii for AdS 5 and for S 1 . We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS 5 × S 5 /Z K . On R 4,1 × S 1 , this six-dimensional theory has a 5(K − 1)-dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS 5 × S 1 , the theory has a 2(K − 1)-dimensional 'moduli space' of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the 'moduli space' and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS 5 whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS 5 . Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional N = 2 supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the 'moduli space'. The embedding in string theory implies that the six-dimensional N = (2, 0) theory on AdS 5 × S 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2 JHEP03(2015)121quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories' on AdS 5 × S 1 .

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Higher spins and stringy AdS₅ × S⁵

Bianchi¹

2005

Fortschritte der Physik

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In this lecture I review recent work done in collaboration with N. Beisert, J. F. Morales and H. Samtleben [1-3] 1 . After a notational flash on the AdS/CFT correspondence, I will discuss higher spin (HS) symmetry enhancement at small radius and how this is holographically captured by free N=4 SYM theory. I will then derive the spectrum of perturbative superstring excitations on AdS in this particular limit and successfully compare it with the spectrum of single-trace operators in free N = 4 SYM at large N, obtained by means of Polya(kov)'s counting. Decomposing the spectrum into HS multiplets allows one to precisely identify the 'massless' HS doubleton and the lower spin Goldstone multiplets which participate in the pantagruelic Higgs mechanism, termed "La Grande Bouffe". After recalling some basic features of Vasiliev's formulation of HS gauge theories, I will eventually sketch how to describe mass generation in the AdS bulkà la Sückelberg and its holographic implications such as the emergence of anomalous dimensions in the boundary N = 4 SYM theory.

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On short and semi-short representations for four-dimensional superconformal symmetry

Cited by 352 publications

References 41 publications

Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

Rigid holography and six-dimensional N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ theories on AdS5 × S $$ \mathbb{S} $$ 1

Higher spins and stringy AdS₅ × S⁵

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On short and semi-short representations for four-dimensional superconformal symmetry

Cited by 352 publications

References 41 publications

Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity

Rigid holography and six-dimensional N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ theories on AdS5 × S $$ \mathbb{S} $$ 1

Higher spins and stringy AdS5 × S5

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Higher spins and stringy AdS₅ × S⁵