A CFT distance conjecture

Perlmutter, Eric; Rastelli, Leonardo; Vafa, Cumrun; Valenzuela, Irene

doi:10.1007/jhep10(2021)070

Cited by 56 publications

(54 citation statements)

References 137 publications

(247 reference statements)

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“…Instead, they treat a fixed CFT irrespective of its deformations. New methods are needed to take advantage of the vast additional data encoded elsewhere in the conformal manifold, and to address questions about the manifold itself, such as whether there are universal properties of CFTs at infinite distance [204]. See [205][206][207] for recent works exploring conformal manifolds from the bootstrap perspective.…”

Section: Conformal Manifolds and Deformationsmentioning

confidence: 99%

Snowmass White Paper: The Analytic Conformal Bootstrap

Hartman¹,

Mazáč²,

Simmons-Duffin³

et al. 2022

Preprint

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The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles. In the last decade, bolstered by the development of new Lorentzian methods, it has been used to solve conformal field theories at large spin; to place bounds on energy distributions, event shapes, operator product coefficients, and other observables; and to understand aspects of quantum gravity in anti-de Sitter space. We review these advances and highlight several promising areas for future exploration. Targets include developing new methods to close the gap between numerical and analytic bounds, extending the bootstrap beyond conformal fixed points, applications to quantum gravity and cosmology, and building on ties to condensed matter theory and mathematics.

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Section: Conformal Manifolds and Deformationsmentioning

confidence: 99%

Snowmass White Paper: The Analytic Conformal Bootstrap

Hartman¹,

Mazáč²,

Simmons-Duffin³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Another interesting direction for future research involves the classification of weak coupling limits, as initiated in e.g. [44,110,112,89,115,113,114]. The Emergent String Conjecture of [112], in particular, suggests that any infinite distance/weak coupling limit must be either a decompactification limit or an emergent string limit, in which a fundamental string becomes tensionless.…”

Section: Discussionmentioning

confidence: 99%

“…Conversely, in compactifications of M-theory to 5d, it has been shown that every point of vanishing gauge coupling is at infinite distance in moduli space [111]. An analogous statement holds in the context of AdS/CFT: in any SCFT in d > 2 dimensions, every point on the conformal manifold at which some sector of the theory becomes free is at infinite distance in the Zamolodchikov metric [115]. This translates to the statement that the vanishing of a gauge coupling must occur at infinite distance in the moduli space of the bulk AdS dual theory.…”

Section: Relation To the Swampland Distance Conjecturementioning

confidence: 91%

The Weak Gravity Conjecture: A Review

Harlow¹,

Heidenreich²,

Reece³

et al. 2022

Preprint

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The Weak Gravity Conjecture holds that in a theory of quantum gravity, any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different areas of physics and mathematics. Several variations on the basic conjecture have been proposed, including statements that are much stronger but are nonetheless satisfied by all known consistent quantum gravity theories. We review these related conjectures and the evidence for their validity in the string theory landscape. We also review a variety of arguments for these conjectures, which tend to fall into two categories: qualitative arguments which claim the conjecture is plausible based on general principles, and quantitative arguments for various special cases or analogues of the conjecture. We also outline the implications of these conjectures for particle physics, cosmology, general relativity, and mathematics. Finally, we highlight important directions for future research.

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“…Let us conclude by noting that for cases in which one of the Coulomb branch scaling dimensions is ∆ u i = 2, the theory has an exactly marginal operator parameterizing a conformal manifold. In [85,86] it was conjectured that any N = 2 n-dimensional conformal manifold arises by gauging n simple factors in the global symmetry of isolated N = 2 SCFTs. This means that if ∆ u i = 2 the corresponding theory is either Lagrangian, or an SU(2) conformal gauging of a lower rank theory.…”

Section: B Allowed Rank-two Coulomb Branch Dimensionsmentioning

confidence: 99%

Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs

Kaidi,

Martone,

Rastelli

et al. 2022

Preprint

Self Cite

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There is a well-known map from 4d N = 2 superconformal field theories (SCFTs) to 2d vertex operator algebras (VOAs). The 4d Schur index corresponds to the VOA vacuum character, and must be a solution with integral coefficients of a modular differential equation. This suggests a classification program for 4d N = 2 SCFTs that starts with modular differential equations and proceeds by imposing all known constraints that follow from the 4d → 2d map. This program becomes fully algorithmic once one specifies the order of the modular differential equation and the rank (complex dimension of the Coulomb branch) of the N = 2 theory. As a proof of concept, we apply the algorithm to the study of rank-two N = 2 SCFTs whose Schur indices satisfy a fourth-order untwisted modular differential equation. Scanning over a large number of putative cases, only 15 satisfy all of the constraints imposed by our algorithm, six of which correspond to known 4d SCFTs. More sophisticated constraints can be used to argue against the existence of the remaining nine cases. Altogether, this indicates that our knowledge of such rank-two SCFTs is surprisingly complete.

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A CFT distance conjecture

Cited by 56 publications

References 137 publications

Snowmass White Paper: The Analytic Conformal Bootstrap

Snowmass White Paper: The Analytic Conformal Bootstrap

The Weak Gravity Conjecture: A Review

Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs

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