Papers
Topics
Authors
Recent
Search
2000 character limit reached

Emergence of $R^4$-terms in M-theory

Published 1 Apr 2024 in hep-th | (2404.01371v3)

Abstract: It has been recently suggested that the strong Emergence Proposal is realized in M-theory limits by integrating out all light towers of states with a typical mass scale not larger than the species scale, i.e. the eleventh dimensional Planck mass. Within the BPS sector, these are transverse $M2$- and $M5$-branes, that can be wrapped and particle-like, carrying Kaluza-Klein momentum along the compact directions. We provide additional evidence for this picture by revisiting and investigating further the computation of $R4$-interactions in M-theory `a la Green-Gutperle-Vanhove. A central aspect is a novel UV-regularization of Schwinger-like integrals, whose actual meaning and power we clarify by first applying it to string perturbation theory. We consider then toroidal compactifications of M-theory and provide evidence that integrating out all light towers of states via Schwinger-like integrals thus regularized yields the complete result for $R4$-interactions. In particular, this includes terms that are tree-level, one-loop and space-time instanton corrections from the weakly coupled point of view. Finally, we comment on the conceptual difference of our approach to earlier closely related work by Kiritsis-Pioline and Obers-Pioline, leading to a correspondence between two types of constrained Eisenstein series.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (51)
  1. E. Palti, “The Swampland: Introduction and Review,” Fortsch. Phys. 67 (2019), no. 6, 1900037, 1903.06239.
  2. N. B. Agmon, A. Bedroya, M. J. Kang, and C. Vafa, “Lectures on the string landscape and the Swampland,” 2212.06187.
  3. H. Ooguri and C. Vafa, “On the Geometry of the String Landscape and the Swampland,” Nucl. Phys. B 766 (2007) 21–33, hep-th/0605264.
  4. N. Arkani-Hamed, L. Motl, A. Nicolis, and C. Vafa, “The String landscape, black holes and gravity as the weakest force,” JHEP 06 (2007) 060, hep-th/0601001.
  5. B. Heidenreich, M. Reece, and T. Rudelius, “The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff,” Eur. Phys. J. C 78 (2018), no. 4, 337, 1712.01868.
  6. T. W. Grimm, E. Palti, and I. Valenzuela, “Infinite Distances in Field Space and Massless Towers of States,” JHEP 08 (2018) 143, 1802.08264.
  7. B. Heidenreich, M. Reece, and T. Rudelius, “Emergence of Weak Coupling at Large Distance in Quantum Gravity,” Phys. Rev. Lett. 121 (2018), no. 5, 051601, 1802.08698.
  8. P. Corvilain, T. W. Grimm, and I. Valenzuela, “The Swampland Distance Conjecture for Kähler moduli,” JHEP 08 (2019) 075, 1812.07548.
  9. F. Marchesano and L. Melotti, “EFT strings and emergence,” JHEP 02 (2023) 112, 2211.01409.
  10. A. Castellano, A. Herráez, and L. E. Ibáñez, “The emergence proposal in quantum gravity and the species scale,” JHEP 06 (2023) 047, 2212.03908.
  11. R. Blumenhagen, A. Gligovic, and A. Paraskevopoulou, “The emergence proposal and the emergent string,” JHEP 10 (2023) 145, 2305.10490.
  12. R. Blumenhagen, N. Cribiori, A. Gligovic, and A. Paraskevopoulou, “Demystifying the Emergence Proposal,” 2309.11551.
  13. G. Dvali, “Black Holes and Large N Species Solution to the Hierarchy Problem,” Fortsch. Phys. 58 (2010) 528–536, 0706.2050.
  14. G. Dvali and M. Redi, “Black Hole Bound on the Number of Species and Quantum Gravity at LHC,” Phys. Rev. D 77 (2008) 045027, 0710.4344.
  15. G. Veneziano, “Large N bounds on, and compositeness limit of, gauge and gravitational interactions,” JHEP 06 (2002) 051, hep-th/0110129.
  16. D. van de Heisteeg, C. Vafa, M. Wiesner, and D. H. Wu, “Moduli-dependent Species Scale,” 2212.06841.
  17. N. Cribiori, D. Lüst, and G. Staudt, “Black hole entropy and moduli-dependent species scale,” Phys. Lett. B 844 (2023) 138113, 2212.10286.
  18. D. van de Heisteeg, C. Vafa, and M. Wiesner, “Bounds on Species Scale and the Distance Conjecture,” 2303.13580.
  19. D. van de Heisteeg, C. Vafa, M. Wiesner, and D. H. Wu, “Bounds on Field Range for Slowly Varying Positive Potentials,” 2305.07701.
  20. N. Cribiori, D. Lüst, and C. Montella, “Species entropy and thermodynamics,” JHEP 10 (2023) 059, 2305.10489.
  21. N. Cribiori and D. Lüst, “A Note on Modular Invariant Species Scale and Potentials,” Fortsch. Phys. 71 (2023), no. 10-11, 2300150, 2306.08673.
  22. D. van de Heisteeg, C. Vafa, M. Wiesner, and D. H. Wu, “Species Scale in Diverse Dimensions,” 2310.07213.
  23. A. Castellano, A. Herráez, and L. E. Ibáñez, “On the Species Scale, Modular Invariance and the Gravitational EFT expansion,” 2310.07708.
  24. C. Long, M. Montero, C. Vafa, and I. Valenzuela, “The desert and the swampland,” JHEP 03 (2023) 109, 2112.11467.
  25. R. Blumenhagen, N. Cribiori, A. Gligovic, and A. Paraskevopoulou, “The Emergent M-theory Limit,” 2309.11554.
  26. T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, “M theory as a matrix model: A Conjecture,” Phys. Rev. D 55 (1997) 5112–5128, hep-th/9610043.
  27. A. Bilal, “M(atrix) theory : A Pedagogical introduction,” Fortsch. Phys. 47 (1999) 5–28, hep-th/9710136.
  28. D. Bigatti and L. Susskind, “Review of matrix theory,” NATO Sci. Ser. C 520 (1999) 277–318, hep-th/9712072.
  29. W. Taylor, “M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory,” Rev. Mod. Phys. 73 (2001) 419–462, hep-th/0101126.
  30. R. Gopakumar and C. Vafa, “M theory and topological strings. 1.,” hep-th/9809187.
  31. R. Gopakumar and C. Vafa, “M theory and topological strings. 2.,” hep-th/9812127.
  32. R. Gopakumar and C. Vafa, “On the gauge theory / geometry correspondence,” Adv. Theor. Math. Phys. 3 (1999) 1415–1443, hep-th/9811131.
  33. J. Hattab and E. Palti, “On the particle picture of Emergence,” JHEP 03 (2024) 065, 2312.15440.
  34. M. R. Douglas, D. N. Kabat, P. Pouliot, and S. H. Shenker, “D-branes and short distances in string theory,” Nucl. Phys. B 485 (1997) 85–127, hep-th/9608024.
  35. J. Calderón-Infante, M. Delgado, and A. M. Uranga, “Emergence of species scale black hole horizons,” JHEP 01 (2024) 003, 2310.04488.
  36. M. B. Green, M. Gutperle, and P. Vanhove, “One loop in eleven-dimensions,” Phys. Lett. B 409 (1997) 177–184, hep-th/9706175.
  37. M. B. Green and P. Vanhove, “D instantons, strings and M theory,” Phys. Lett. B 408 (1997) 122–134, hep-th/9704145.
  38. E. Kiritsis and B. Pioline, “On R**4 threshold corrections in IIb string theory and (p, q) string instantons,” Nucl. Phys. B 508 (1997) 509–534, hep-th/9707018.
  39. B. Pioline and E. Kiritsis, “U duality and D-brane combinatorics,” Phys. Lett. B 418 (1998) 61–69, hep-th/9710078.
  40. N. A. Obers and B. Pioline, “U duality and M theory,” Phys. Rept. 318 (1999) 113–225, hep-th/9809039.
  41. N. A. Obers and B. Pioline, “Eisenstein series and string thresholds,” Commun. Math. Phys. 209 (2000) 275–324, hep-th/9903113.
  42. D. S. Berman and C. D. A. Blair, “The Geometry, Branes and Applications of Exceptional Field Theory,” Int. J. Mod. Phys. A 35 (2020), no. 30, 2030014, 2006.09777.
  43. C. Angelantonj, I. Florakis, and B. Pioline, “A new look at one-loop integrals in string theory,” Commun. Num. Theor. Phys. 6 (2012) 159–201, 1110.5318.
  44. C. Bachas and E. Kiritsis, “F(4) terms in N=4 string vacua,” Nucl. Phys. B Proc. Suppl. 55 (1997) 194–199, hep-th/9611205.
  45. C. Bachas, C. Fabre, E. Kiritsis, N. A. Obers, and P. Vanhove, “Heterotic / type I duality and D-brane instantons,” Nucl. Phys. B 509 (1998) 33–52, hep-th/9707126.
  46. B. de Wit and D. Lüst, “BPS amplitudes, helicity supertraces and membranes in M theory,” Phys. Lett. B 477 (2000) 299–308, hep-th/9912225.
  47. M. B. Green, J. G. Russo, and P. Vanhove, “String theory dualities and supergravity divergences,” JHEP 06 (2010) 075, 1002.3805.
  48. S.-J. Lee, W. Lerche, and T. Weigand, “Emergent strings from infinite distance limits,” JHEP 02 (2022) 190, 1910.01135.
  49. A. Terras, “Harmonic Analysis on Symmetric Spaces and Applications I,” Springer Verlag 29 (1985), no. 2, 330–332.
  50. B. Pioline, “R**4 couplings and automorphic unipotent representations,” JHEP 03 (2010) 116, 1001.3647.
  51. L. J. Mordell, Diophantine Equations. Academic Press, London & New York, 1969.
Citations (4)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 3 tweets with 2 likes about this paper.

Sign Up for Free