Spontaneously broken boosts in CFTs

Komargodski, Zohar; Pal, Sridip; Raviv-Moshe, Avia

doi:10.1007/jhep09(2021)064

Cited by 27 publications

(30 citation statements)

References 55 publications

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“…No solutions exist for εs > 1/π (see the orange curve of figure 7). 27 We will indeed see that for finite ε and large s the infrared limit of the defect is not described by a DCFT, rather, the flow never terminates and tends towards s D → −∞.…”

Section: 33mentioning

confidence: 68%

Spin Impurities, Wilson Lines and Semiclassics

Cuomo,

Komargodski,

Mezei

et al. 2022

Preprint

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We consider line defects with large quantum numbers in conformal field theories. First, we consider spin impurities, both for a free scalar triplet and in the Wilson-Fisher O(3) model. For the free scalar triplet, we find a rich phase diagram that includes a perturbative fixed point, a new nonperturbative fixed point, and runaway regimes. To obtain these results, we develop a new semiclassical approach. For the Wilson-Fisher model, we propose an alternative description, which becomes weakly coupled in the large spin limit. This allows us to chart the phase diagram and obtain numerous rigorous predictions for large spin impurities in 2 + 1 dimensional magnets. Finally, we also study 1/2-BPS Wilson lines in large representations of the gauge group in rank-1 N = 2 superconformal field theories. We contrast the results with the qualitative behavior of large spin impurities in magnets.

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Section: 33mentioning

confidence: 68%

Spin Impurities, Wilson Lines and Semiclassics

Cuomo,

Komargodski,

Mezei

et al. 2022

Preprint

Self Cite

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“…It is interesting that in this case the function ∆(q) is not analytic even in the large q limit beyond the leading order [33], but this does not affect our analysis.…”

Section: Application To General Cftsmentioning

confidence: 99%

“…In the second and third cases, we can compute the spectrum exactly and the conjecture is satisfied (for q 0 that is equal to the charge of the free scalar/fermion, or to the lowest charge carried by a BPS operator O that is non-zero on the moduli space). In the fermion case, if we take q 0 equal to the number of components of the fermion field, the spectrum is not even marginally convex [33]. This means that 7 For d = 2 there is no space of vacua like in higher dimensions, but we can still discuss BPS operators O convexity (for that value of q 0 ) is maintained under any small-parameter perturbation of the free fermion theory.…”

Section: Application To General Cftsmentioning

confidence: 99%

On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

Aharony,

Palti

2021

Preprint

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The Weak Gravity Conjecture is typically stated as a bound on the mass-to-charge ratio of a particle in the theory. Alternatively, it has been proposed that its natural formulation is in terms of the existence of a particle which is self-repulsive under all long-range forces. We propose a closely related, but distinct, formulation, which is that it should correspond to a particle with non-negative self-binding energy. This formulation is particularly interesting in anti-de Sitter space, because it has a simple conformal field theory (CFT) dual formulation: let ∆(q) be the dimension of the lowest-dimension operator with charge q under some global U (1) symmetry, then ∆(q) must be a convex function of q. This formulation avoids any reference to holographic dual forces or even to locality in spacetime, and so we make a wild leap, and conjecture that such convexity of the spectrum of charges holds for any (unitary) conformal field theory, not just those that have weakly coupled and weakly curved duals. This Charge Convexity Conjecture, and its natural generalization to larger global symmetry groups, can be tested in various examples where anomalous dimensions can be computed, by perturbation theory, 1/N expansions and semi-classical methods. In all examples that we tested we find that the conjecture holds. We do not yet understand from the CFT point of view why this is true.

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“…Large charge operators in CFTs are not always described by a superfluid EFT. Alternative phases are for instance found in free theories, N ≥ 2 SCFTs [12,56,57] and free fermions [58].…”

Section: Other Large Charge Phases In Bcftsmentioning

confidence: 99%

“…In the absence of a boundary, the free Dirac field enjoys a U(1) × U(1) symmetry under which the phases of ψ α and ζ † α shift independently. Bulk operators with charge Q 1 under the diagonal U(1) acting as ψ D → e iα ψ D were constructed explicitly in [58]. These correspond to Fermi spheres with all spinor harmonic levels filled up to spin j = j max − 1 and a number δQ of modes filled in the j = j max level.…”

Section: Free Fermion In Four Dimensionsmentioning

confidence: 99%

Boundary conformal field theory at large charge

Cuomo

Raviv-Moshe

2021

J. High Energ. Phys.

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We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between the scaling dimension of the lowest dimensional CFT and BCFT charged operators to leading order in the charge. We also construct the superfluid effective field theory for theories with boundaries and use it to systematically calculate the BCFT spectrum in a systematic expansion. We verify explicitly many of the predictions from the EFT analysis in concrete examples including the classical conformal scalar field with a |ϕ|6 interaction in three dimensions and the O(2) Wilson-Fisher model near four dimensions in the presence of boundaries. In the appendices we additionally discuss a systematic background field approach towards Ward identities in general boundary and defect conformal field theories, and clarify its relation with Noether’s theorem in perturbative theories.

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Spontaneously broken boosts in CFTs

Cited by 27 publications

References 55 publications

Spin Impurities, Wilson Lines and Semiclassics

Spin Impurities, Wilson Lines and Semiclassics

On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

Boundary conformal field theory at large charge

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