A new approach to conformal invariant field theories

Fubini, S.

doi:10.1007/bf02785664

Cited by 244 publications

(197 citation statements)

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“…Those same inversions continue to play an important role also in the smaller symmetry group O(4, 1) since they map "modified translations" to themselves. In particular, they coincide with the inversions of the AdS background if the scale introduced in [7] is identified with the AdS radius, i.e. b = L. We should mention the fact that the original group that one starts with is higher-dimensional, O(5, 1).…”

Section: Instantons and Conformal Holographymentioning

confidence: 62%

“…When the dimensionless coupling constant g < 0, the equations of motion have the real instanton solution [7] ϕ 0 ( x) = 360 −g…”

Section: The Proposal For the Dual Boundary Cftmentioning

confidence: 99%

“…We will discuss an exact solution of the equations of motion [7] with special properties. It is the unique non-trivial solution wich preserves a large symmetry group.…”

Section: Instantons and Conformal Holographymentioning

confidence: 99%

“…The idea in [7] was to start with a conformal theory in flat space and break conformal invariance spontaneously. The vacuum should preserve a subgroup of the conformal group, but in particular it should break dilatations.…”

Section: Instantons and Conformal Holographymentioning

confidence: 99%

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Instantons and conformal holography

Haro

Petkou

2006

J. High Energy Phys.

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We study a subsector of the AdS 4 /CFT 3 correspondence where a class of solutions in the bulk and on the boundary can be explicitly compared. The bulk gravitational theory contains a conformally coupled scalar field with a φ 4 potential, and is holographically related to a massless scalar with a φ 6 interaction in three dimensions. We consider the scalar sector of the bulk theory and match bulk and boundary classical solutions of the equations of motion. Of particular interest is the matching of the bulk and the boundary instanton solutions which underlies the relationship between bulk and boundary vacua with broken conformal invariance. Using a form of radial quantization we show that quantum states in the bulk correspond to multiply-occupied single particle quantum states in the boundary theory. This allows us to explicitly identify the boundary composite operator which is dual to the bulk scalar, at the free theory level as well as in the instanton vacuum. We conclude with a discussion of possible implications of our results.

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Section: Instantons and Conformal Holographymentioning

confidence: 62%

“…When the dimensionless coupling constant g < 0, the equations of motion have the real instanton solution [7] ϕ 0 ( x) = 360 −g…”

Section: The Proposal For the Dual Boundary Cftmentioning

confidence: 99%

“…We will discuss an exact solution of the equations of motion [7] with special properties. It is the unique non-trivial solution wich preserves a large symmetry group.…”

Section: Instantons and Conformal Holographymentioning

confidence: 99%

Section: Instantons and Conformal Holographymentioning

confidence: 99%

See 2 more Smart Citations

Instantons and conformal holography

Haro

Petkou

2006

J. High Energy Phys.

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“…Using this map we can profit from the knowledge of instanton solutions of the massless theory, defined on R d . Such instantons are Euclidean versions of field configurations discussed by Fubini in [14] (see also [28] for a review) and take the form…”

Section: The Large-brane Cft and The Fubini Instantonmentioning

confidence: 99%

Holography of AdS vacuum bubbles

Barbón

Rabinovici

2010

J. High Energ. Phys.

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We consider the fate of AdS vacua connected by tunneling events. A precise holographic dual of thin-walled Coleman-de Luccia bounces is proposed in terms of Fubini instantons in an unstable CFT. This proposal is backed by several qualitative and quantitative checks, including the precise calculation of the instanton action appearing in evaluating the decay rate. Big crunches manifest themselves as time dependent processes which reach the boundary of field space in a finite time. The infinite energy difference involved is identified on the boundary and highlights the ill-defined nature of the bulk setup. We propose a qualitative scenario in which the crunch is resolved by stabilizing the CFT, so that all attempts at crunching always end up shielded from the boundary by the formation of black hole horizons. In all these well defined bulk processes the configurations have the same asymptotics and are finite energy excitations.

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