Towards the classification of conformal field theories in arbitrary even dimension

Anselmi, Damiano

doi:10.1016/s0370-2693(00)00135-0

Cited by 18 publications

(54 citation statements)

References 19 publications

(56 reference statements)

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“…The Diophantine equation, written in term of only (α, β, γ, δ) and the quiver matrix, is a generalization of the 3-block one (3.9): 6) which has to be supplemented by the rank-2 constraint (5.3):…”

Section: Results For the Four Blocks Casementioning

confidence: 99%

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New results on superconformal quivers

Benvenuti¹,

Hanany²

2006

J. High Energy Phys.

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All superconformal quivers are shown to satisfy the relation c = a and are thus good candidates for being the field theory living on D3 branes probing CY singularities. We systematically study 3 block and 4 block chiral quivers which admit a superconformal fixed point of the RG equation. Most of these theories are known to arise as living on D3 branes at a singular CY manifold, namely complex cones over del Pezzo surfaces. In the process we find a procedure of getting a new superconformal quiver from a known one. This procedure is termed "shrinking" and, in the 3 block case, leads to the discovery of two new models. Thus, the number of superconformal 3 block quivers is 16 rather than the previously known 14. We prove that this list exausts all the possibilities. We suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be obtained by shrinking a del Pezzo quiver and verify this statement for all 4 block quivers, where a lot of "shrunk" del Pezzo models exist.

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Section: Results For the Four Blocks Casementioning

confidence: 99%

“…We remark that in general there can be loops in this tree. 6 These loops give the possibility of engineering Duality Cascades of the Klebanov-Strassler type [11,26,33].…”

Section: Duality Treesmentioning

confidence: 99%

New results on superconformal quivers

Benvenuti¹,

Hanany²

2006

J. High Energy Phys.

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“…The knowledge we have at present in this domain is only empirical [11]. We know that the flow invariant of [5] is proportional to ∆c = c UV −c IR and not ∆a = a UV −a IR , in massive free-field theories.…”

Section: Open Questionsmentioning

confidence: 99%

“…We know that the flow invariant of [5] is proportional to ∆c = c UV −c IR and not ∆a = a UV −a IR , in massive free-field theories. A natural implication of this fact is the definition of "c = a" theories [11], which have interesting properties in this context (see below). Yet, several issues remain open.…”

Section: Open Questionsmentioning

confidence: 99%

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A universal flow invariant in quantum field theory

Anselmi¹

2001

Class. Quantum Grav.

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A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories scale invariance is broken by quantum effects and the flow invariant a UV − a IR is measured by the area of the graph of the beta function between the fixed points. There exists a theoretical explanation of this non-trivial fact. On the other hand, when scale invariance is broken at the classical level, it is empirically known that the flow invariant equals c UV − c IR in massive free-field theories, but a theoretical argument explaining why it is so is still missing. A number of related open questions are answered here. A general formula of the flow invariant is found, which holds also when the stress tensor has improvement terms. The conditions under which the flow invariant equals c UV − c IR are identified. Several non-unitary theories are used as a laboratory, but the conclusions are general and an application to the Standard Model is addressed. The analysis of the results suggests some new minimum principles, which might point towards a new understanding of quantum field theory.

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Simple recipe for holographic Weyl anomaly

Bugini

Díaz

2017

J. High Energ. Phys.

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We propose a recipe -arguably the simplest -to compute the holographic type-B Weyl anomaly for general higher-derivative gravity in asymptotically AdS spacetimes. In 5 and 7 dimensions we identify a suitable basis of curvature invariants that allows to read off easily, without any further computation, the Weyl anomaly coefficients of the dual CFT. We tabulate the contributions from quadratic, cubic and quartic purely algebraic curvature invariants and also from terms involving derivatives of the curvature. We provide few examples, where the anomaly coefficients have been obtained by other means, to illustrate the effectiveness of our prescription.

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Towards the classification of conformal field theories in arbitrary even dimension

Cited by 18 publications

References 19 publications

New results on superconformal quivers

New results on superconformal quivers

A universal flow invariant in quantum field theory

Simple recipe for holographic Weyl anomaly

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