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N. Afkhami-Jeddi, T. Hartman, and A. Tajdini, Fast Conformal Bootstrap and Constraints on 3d Gravity
Original
1903
Earlier work this paper cites.
B. Mukhametzhanov and A. Zhiboedov, Modular invariance, tauberian theorems and microcanonical entropy
Original
1904
Earlier work this paper cites.
T. Hartman, D. Mazáč, and L. Rastelli, Sphere Packing and Quantum Gravity
Original
1905
Earlier work this paper cites.
N. Benjamin, H. Ooguri, S.-H. Shao, and Y. Wang, Light-cone modular bootstrap and pure gravity
Original
1906
Earlier work this paper cites.
W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB
Original
1909
Earlier work this paper cites.
S. Pal and Z. Sun, Tauberian-Cardy formula with spin
Original
1910
Earlier work this paper cites.
J. L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories
1986
Earlier work this paper cites.
R. Dijkgraaf, E. P. Verlinde, and H. L. Verlinde, On Moduli Spaces of Conformal Field Theories with c ≥ 1 c\geq 1
1987
Earlier work this paper cites.
N. A. Obers and B. Pioline, Eisenstein series and string thresholds
2000
Earlier work this paper cites.
L. F. Alday and J.-B. Bae, Rademacher Expansions and the Spectrum of 2d CFT
Original
2001
Earlier work this paper cites.
N. Benjamin, H. Ooguri, S.-H. Shao, and Y. Wang, Twist gap and global symmetry in two dimensions
Original
2003
Earlier work this paper cites.
D. Platt and T. Trudgian, The Riemann hypothesis is true up to 3 ⋅ 10 12 3\cdot 10^{12}
Original
2004
Earlier work this paper cites.

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2022

Scalar Modular Bootstrap and Zeros of the Riemann Zeta Function

Benjamin, Nathan, Chang, Cyuan-Han

Understand

Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with $U(1)^c$ symmetry.

From this crossing equation, we derive bounds on the scalar gap of all such theories.
Rather remarkably, our crossing equation contains information about all nontrivial zeros of the Riemann zeta function.
As a result, we rephrase the Riemann hypothesis purely as a statement about the asymptotic density of scalar operators in certain two-dimensional conformal field theories.

Built on

N. Afkhami-Jeddi, T. Hartman, and A. Tajdini, Fast Conformal Bootstrap and Constraints on 3d Gravity
Original
1903
Earlier work this paper cites.
B. Mukhametzhanov and A. Zhiboedov, Modular invariance, tauberian theorems and microcanonical entropy
Original
1904
Earlier work this paper cites.
T. Hartman, D. Mazáč, and L. Rastelli, Sphere Packing and Quantum Gravity
Original
1905
Earlier work this paper cites.
N. Benjamin, H. Ooguri, S.-H. Shao, and Y. Wang, Light-cone modular bootstrap and pure gravity
Original
1906
Earlier work this paper cites.
W. Landry and D. Simmons-Duffin, Scaling the semidefinite program solver SDPB
Original
1909
Earlier work this paper cites.
S. Pal and Z. Sun, Tauberian-Cardy formula with spin
Original
1910
Earlier work this paper cites.
J. L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories
1986
Earlier work this paper cites.
R. Dijkgraaf, E. P. Verlinde, and H. L. Verlinde, On Moduli Spaces of Conformal Field Theories with c ≥ 1 c\geq 1
1987
Earlier work this paper cites.
N. A. Obers and B. Pioline, Eisenstein series and string thresholds
2000
Earlier work this paper cites.
L. F. Alday and J.-B. Bae, Rademacher Expansions and the Spectrum of 2d CFT
Original
2001
Earlier work this paper cites.
N. Benjamin, H. Ooguri, S.-H. Shao, and Y. Wang, Twist gap and global symmetry in two dimensions
Original
2003
Earlier work this paper cites.
D. Platt and T. Trudgian, The Riemann hypothesis is true up to 3 ⋅ 10 12 3\cdot 10^{12}
Original
2004
Earlier work this paper cites.

Similar

A. Bondarenko, D. Radchenko, and K. Seip, Fourier interpolation with zeros of zeta and L L -functions
Original
2005
Cited alongside, same era.
N. Afkhami-Jeddi, H. Cohn, T. Hartman, D. de Laat, and A. Tajdini, High-dimensional sphere packing and the modular bootstrap
Original
2006
Cited alongside, same era.
N. Afkhami-Jeddi, H. Cohn, T. Hartman, and A. Tajdini, Free partition functions and an averaged holographic duality
Original
2006
Cited alongside, same era.
A. Maloney and E. Witten, Averaging over Narain moduli space
Original
2006
Cited alongside, same era.
A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions
Original

Then

Z. Komargodski and A. Zhiboedov, Convexity and Liberation at Large Spin
Original
2013
Later among the works it cites.
D. Simmons-Duffin, A Semidefinite Program Solver for the Conformal Bootstrap
Original
2015
Later among the works it cites.
C. A. Keller and A. Maloney, Poincare Series, 3D Gravity and CFT Spectroscopy
Original
2015
Later among the works it cites.
M. B. Green, S. D. Miller, and P. Vanhove, S L ( 2 , ℤ ) SL(2,\mathbb{Z}) -invariance and D-instanton contributions to the D 6 R 4 D^{6}R^{4} interaction
Original
2015
Later among the works it cites.
N. Benjamin, E. Dyer, A. L. Fitzpatrick, and S. Kachru, Universal Bounds on Charged States in 2d CFT and 3d Gravity

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

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2016