Built on

S. J. Lee, W. Lerche and T. Weigand, “Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions,” JHEP 1908
Original
1901
Earlier work this paper cites.
E. Palti, “The Swampland: Introduction and Review,” Fortsch. Phys. 67
Original
1903
Earlier work this paper cites.
A. Joshi and A. Klemm, “Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds,” JHEP 1908
Original
1903
Earlier work this paper cites.
F. Marchesano and M. Wiesner, “Instantons and infinite distances,” JHEP 1908
Original
1904
Earlier work this paper cites.
A. Font, A. Herraez and L. E. Ibanez, “The Swampland Distance Conjecture and Towers of Tensionless Branes,” JHEP 1908
Original
1904
Earlier work this paper cites.
S. J. Lee, W. Lerche and T. Weigand, “Emergent Strings, Duality and Weak Coupling Limits for Two-Form Fields,” arXiv:1904.06344 [hep-th]
Original
1904
Earlier work this paper cites.
D. Erkinger and J. Knapp, “Refined swampland distance conjecture and exotic hybrid Calabi-Yaus,” JHEP 1907
Original
1905
Earlier work this paper cites.
D. Lüst, E. Palti and C. Vafa, “AdS and the Swampland,” arXiv:1906.05225 [hep-th]
Original
1906
Earlier work this paper cites.
D. Lüst and E. Palti, “A Note on String Excitations and the Higuchi Bound,” arXiv:1907.04161 [hep-th]
Original
1907
Earlier work this paper cites.
C. Gomez, “Gravity as universal UV completion: Towards a unified view of Swampland conjectures,” arXiv:1907.13386 [hep-th]
Original
1907
Earlier work this paper cites.
Q. Bonnefoy, L. Ciambelli, D. Lüst and S. Lüst, “Infinite Black Hole Entropies at Infinite Distances and Tower of States,” [arXiv:1912.07453 [hep-th]]
Original
1912
Earlier work this paper cites.
B. S. DeWitt, Phys. Rev. 160, 1113 (1967)
1967
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Creation,” Phys. Rev. D 15
1977
Earlier work this paper cites.
A. A. Starobinsky, “Spectrum of relict gravitational radiation and the early state of the universe,” JETP Lett. 30
1979
Earlier work this paper cites.
R.S.Hamilton, “Three manifolds with positive Ricci curvature,” Jour. Diff. Geom. 17 (1982), 255-306
1982
Earlier work this paper cites.
A. Strominger, “Superstrings with Torsion,” Nucl. Phys. B 274
1986
Earlier work this paper cites.
C. M. Hull, “Compactifications of the Heterotic Superstring,” Phys. Lett. B 178
1986
Earlier work this paper cites.
A. Higuchi, “Forbidden Mass Range for Spin-2 Field Theory in De Sitter Space-time,” Nucl. Phys. B 282
1987
Earlier work this paper cites.
E. Witten, “On string theory and black holes,” Phys. Rev. D 44
1991
Earlier work this paper cites.
I. Antoniadis, E. Gava, K. S. Narain and T. R. Taylor, “Topological amplitudes in string theory,” Nucl. Phys. B 413
1994
Earlier work this paper cites.
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, “Holomorphic anomalies in topological field theories,” Nucl. Phys. B 405
1996
Earlier work this paper cites.

Similar

G. Lopes Cardoso, G. Curio, D. Lüst, T. Mohaupt and S. J. Rey, “BPS spectra and nonperturbative gravitational couplings in N=2, N=4 supersymmetric string theories,” Nucl. Phys. B 464
1996
Cited alongside, same era.
T. Banks, “Cosmological breaking of supersymmetry?,” Int. J. Mod. Phys. A 16
2001
Cited alongside, same era.
G. Lopes Cardoso, G. Curio, G. Dall’Agata, D. Lüst, P. Manousselis and G. Zoupanos, “NonKahler string backgrounds and their five torsion classes,” Nucl. Phys. B 652
2003
Cited alongside, same era.
B. Chow and D Knopf, “The Ricci Flow: An Introduction,” AMS, 2004
2004
Cited alongside, same era.
D. Lüst and D. Tsimpis, “Supersymmetric AdS(4) compactifications of IIA supergravity,” JHEP 0502
2005
Cited alongside, same era.

Then

G. Dvali, C. Gomez and S. Zell, “Quantum Break-Time of de Sitter,” JCAP 1706
Original
2017
Later among the works it cites.
S. W. Hawking, M. J. Perry and A. Strominger, “Superrotation Charge and Supertranslation Hair on Black Holes,” JHEP 1705
Original
2017
Later among the works it cites.
B. Heidenreich, M. Reece and T. Rudelius, “The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff,” Eur. Phys. J. C 78
Original
2018
Later among the works it cites.
S. Andriolo, D. Junghans, T. Noumi and G. Shiu, “A Tower Weak Gravity Conjecture from Infrared Consistency,” Fortsch. Phys. 66
Original
2018
Later among the works it cites.
T. W. Grimm, E. Palti and I. Valenzuela, “Infinite Distances in Field Space and Massless Towers of States,” JHEP 1808

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2019

Swampland, Gradient Flow and Infinite Distance

Kehagias, Alex, Lust, Dieter, Lüst, Severin

Understand

In the first part of this paper we will work out a close and so far not yet noticed correspondence between the swampland approach in quantum gravity and geometric flow equations in general relativity, most notably the Ricci flow.

We conjecture that following the gradient flow towards a fixed point, which is at infinite distance in the space of background metrics, is accompanied by an infinite tower of states in quantum gravity.
In case of the Ricci flow, this conjecture is in accordance with the generalized distance and AdS distance conjectures, which were recently discussed in the literature, but it should also hold for more general background spaces.
We argue that the entropy functionals of gradient flows provide a useful definition of the generalized distance in the space of background fields.

Built on

S. J. Lee, W. Lerche and T. Weigand, “Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions,” JHEP 1908
Original
1901
Earlier work this paper cites.
E. Palti, “The Swampland: Introduction and Review,” Fortsch. Phys. 67
Original
1903
Earlier work this paper cites.
A. Joshi and A. Klemm, “Swampland Distance Conjecture for One-Parameter Calabi-Yau Threefolds,” JHEP 1908
Original
1903
Earlier work this paper cites.
F. Marchesano and M. Wiesner, “Instantons and infinite distances,” JHEP 1908
Original
1904
Earlier work this paper cites.
A. Font, A. Herraez and L. E. Ibanez, “The Swampland Distance Conjecture and Towers of Tensionless Branes,” JHEP 1908
Original
1904
Earlier work this paper cites.
S. J. Lee, W. Lerche and T. Weigand, “Emergent Strings, Duality and Weak Coupling Limits for Two-Form Fields,” arXiv:1904.06344 [hep-th]
Original
1904
Earlier work this paper cites.
D. Erkinger and J. Knapp, “Refined swampland distance conjecture and exotic hybrid Calabi-Yaus,” JHEP 1907
Original
1905
Earlier work this paper cites.
D. Lüst, E. Palti and C. Vafa, “AdS and the Swampland,” arXiv:1906.05225 [hep-th]
Original
1906
Earlier work this paper cites.
D. Lüst and E. Palti, “A Note on String Excitations and the Higuchi Bound,” arXiv:1907.04161 [hep-th]
Original
1907
Earlier work this paper cites.
C. Gomez, “Gravity as universal UV completion: Towards a unified view of Swampland conjectures,” arXiv:1907.13386 [hep-th]
Original
1907
Earlier work this paper cites.
Q. Bonnefoy, L. Ciambelli, D. Lüst and S. Lüst, “Infinite Black Hole Entropies at Infinite Distances and Tower of States,” [arXiv:1912.07453 [hep-th]]
Original
1912
Earlier work this paper cites.
B. S. DeWitt, Phys. Rev. 160, 1113 (1967)
1967
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Creation,” Phys. Rev. D 15
1977
Earlier work this paper cites.
A. A. Starobinsky, “Spectrum of relict gravitational radiation and the early state of the universe,” JETP Lett. 30
1979
Earlier work this paper cites.
R.S.Hamilton, “Three manifolds with positive Ricci curvature,” Jour. Diff. Geom. 17 (1982), 255-306
1982
Earlier work this paper cites.
A. Strominger, “Superstrings with Torsion,” Nucl. Phys. B 274
1986
Earlier work this paper cites.
C. M. Hull, “Compactifications of the Heterotic Superstring,” Phys. Lett. B 178
1986
Earlier work this paper cites.
A. Higuchi, “Forbidden Mass Range for Spin-2 Field Theory in De Sitter Space-time,” Nucl. Phys. B 282
1987
Earlier work this paper cites.
E. Witten, “On string theory and black holes,” Phys. Rev. D 44
1991
Earlier work this paper cites.
I. Antoniadis, E. Gava, K. S. Narain and T. R. Taylor, “Topological amplitudes in string theory,” Nucl. Phys. B 413
1994
Earlier work this paper cites.
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, “Holomorphic anomalies in topological field theories,” Nucl. Phys. B 405
1996
Earlier work this paper cites.

Similar

G. Lopes Cardoso, G. Curio, D. Lüst, T. Mohaupt and S. J. Rey, “BPS spectra and nonperturbative gravitational couplings in N=2, N=4 supersymmetric string theories,” Nucl. Phys. B 464
1996
Cited alongside, same era.
T. Banks, “Cosmological breaking of supersymmetry?,” Int. J. Mod. Phys. A 16
2001
Cited alongside, same era.
G. Lopes Cardoso, G. Curio, G. Dall’Agata, D. Lüst, P. Manousselis and G. Zoupanos, “NonKahler string backgrounds and their five torsion classes,” Nucl. Phys. B 652
2003
Cited alongside, same era.
B. Chow and D Knopf, “The Ricci Flow: An Introduction,” AMS, 2004
2004
Cited alongside, same era.
D. Lüst and D. Tsimpis, “Supersymmetric AdS(4) compactifications of IIA supergravity,” JHEP 0502
2005
Cited alongside, same era.