# Sparseness bounds on local operators in holographic CFTd

@article{Mefford2018SparsenessBO, title={Sparseness bounds on local operators in holographic CFTd}, author={Eric Mefford and Edgar Shaghoulian and Milind Shyani}, journal={Journal of High Energy Physics}, year={2018}, volume={2018}, pages={1-28} }

A bstractWe use the thermodynamics of anti-de Sitter gravity to derive sparseness bounds on the spectrum of local operators in holographic conformal field theories. The simplest such bound is ρΔ≲exp2πΔd−1$$ \rho \left(\varDelta \right)\lesssim \exp \left(\frac{2\pi \Delta}{d-1}\right) $$ for CFTd. Unlike the case of d = 2, this bound is strong enough to rule out weakly coupled holographic theories. We generalize the bound to include spins Ji and U(1) charge Q, obtaining bounds on ρ(Δ, Ji, Q) in…

## 7 Citations

### Einstein gravity from ANEC correlators

- PhysicsJournal of High Energy Physics
- 2019

Abstract
We study correlation functions with multiple averaged null energy (ANEC) operators in conformal field theories. For large N CFTs with a large gap to higher spin operators, we show that…

### The holographic landscape of symmetric product orbifolds

- Physics, MathematicsJournal of High Energy Physics
- 2020

We investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge. We find that this landscape decomposes into two regions. In one region, the…

### UvA-DARE (Digital Academic Repository) The holographic landscape of symmetric product orbifolds

- Physics
- 2020

: We investigate the growth of coe(cid:14)cients in the elliptic genus of symmetric product orbifolds at large central charge. We (cid:12)nd that this landscape decomposes into two regions. In one…

### UvA-DARE (Digital Academic Repository) Einstein gravity from ANEC correlators

- Physics
- 2019

: We study correlation functions with multiple averaged null energy (ANEC) operators in conformal (cid:12)eld theories. For large N CFTs with a large gap to higher spin operators, we show that the…

### Sublunar-mass primordial black holes from closed axion domain walls

- PhysicsPhysics of the Dark Universe
- 2020

### Several Problems in Particle Physics and Cosmology Solved in One SMASH

- PhysicsFront. Astron. Space Sci.
- 2019

The Standard Model (SM) of particle physics is a big success. However, it lacks explanations for cosmic inflation, the matter-anti-matter asymmetry of the Universe, dark matter, neutrino…

### Probing axion mediated fermion–fermion interaction by means of entanglement

- PhysicsPhysics Letters B
- 2020

## References

SHOWING 1-10 OF 50 REFERENCES

### Detachable circles and temperature-inversion dualities for CFTd

- Mathematics
- 2017

A bstractWe use a Weyl transformation between S1 × Sd−1 and S1×ℋd−1/ℤ$$ {S}^1\times {\mathrm{\mathscr{H}}}^{d-1}/\mathbb{Z} $$ to relate a conformal field theory at arbitrary temperature on Sd−1 to…

### Universal spectrum of 2d conformal field theory in the large c limit

- Physics
- 2014

A bstractTwo-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. We show that a much…

### Semiclassics, Goldstone bosons and CFT data

- Physics
- 2016

A bstractHellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers…

### Universality of sparse d > 2 conformal field theory at large N

- Geology
- 2017

A bstractWe derive necessary and sufficient conditions for large N conformal field theories to have a universal free energy and an extended range of validity of the higher-dimensional Cardy formula.…

### Holography from Conformal Field Theory

- Physics
- 2009

The locality of bulk physics at distances below the AdS length scale is one of the remarkable aspects of AdS/CFT duality, and one of the least tested. It requires that the AdS radius be large…

### Modular forms and a generalized Cardy formula in higher dimensions

- Mathematics
- 2016

We derive a formula which applies to conformal field theories on a spatial torus and gives the asymptotic density of states solely in terms of the vacuum energy on a parallel plate geometry. The…

### On the Holographic Principle in a Radiation Dominated Universe

- Physics
- 2000

The holographic principle is studied in the context of a $n+1$ dimensional radiation dominated closed Friedman-Robertson-Walker (FRW) universe. The radiation is represented by a conformal field…

### Black holes from CFT: universality of correlators at large c

- Physics
- 2017

A bstractTwo-dimensional conformal field theories at large central charge and with a sufficiently sparse spectrum of light states have been shown to exhibit universal thermodynamics [1]. This…

### On the CFT operator spectrum at large global charge

- Physics
- 2015

A bstractWe calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the…

### On type IIA Penrose limit and = 6 Chern-Simons theories

- Physics, Mathematics
- 2008

Recently, Aharony, Bergman, Jafferis and Maldacena proposed that the = 6 Chern-Simons gauge theories are holographically dual to the M-theory backgrounds with multiple M2-branes on orbifolds C4/Zk.…