Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash 103 tok/s
Gemini 2.5 Pro 54 tok/s Pro
GPT-5 Medium 27 tok/s
GPT-5 High 37 tok/s Pro
GPT-4o 92 tok/s
GPT OSS 120B 467 tok/s Pro
Kimi K2 241 tok/s Pro
2000 character limit reached

Large-$N$ integrated correlators in $\mathcal{N}=4$ SYM: when resurgence meets modularity (2405.10204v1)

Published 16 May 2024 in hep-th

Abstract: Exact expressions for certain integrated correlators of four half-BPS operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory with gauge group $SU(N)$ have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-$N$ expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large $N$, interpreted as contributions from coincident $(p,q)$-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-$N$ expansion of these integrated correlators, from which we extract the exact non-perturbative large-$N$ sectors via resurgence analysis. Furthermore, we show that in the 't Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on $\rm{SL}(2,\mathbb{Z})$ spectral theory.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (47)
  1. C. Montonen and D. Olive, “Magnetic monopoles as gauge particles?,” Physics Letters B 72 (1977) no. 1, 117–120.
  2. J. M. Maldacena, “The Large N𝑁Nitalic_N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys. 38 (1999) 1113–1133, arXiv:hep-th/9711200 [hep-th]. [Adv. Theor. Math. Phys.2,231(1998)].
  3. D. J. Binder, S. M. Chester, S. S. Pufu, and Y. Wang, “𝒩𝒩\mathcal{N}caligraphic_N = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization,” JHEP 12 (2019) 119, arXiv:1902.06263 [hep-th].
  4. S. M. Chester and S. S. Pufu, “Far beyond the planar limit in strongly-coupled 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM,” JHEP 01 (2021) 103, arXiv:2003.08412 [hep-th].
  5. V. Pestun, “Localization of gauge theory on a four-sphere and supersymmetric Wilson loops,” Commun. Math. Phys. 313 (2012) 71–129, arXiv:0712.2824 [hep-th].
  6. S. M. Chester, M. B. Green, S. S. Pufu, Y. Wang, and C. Wen, “Modular invariance in superstring theory from 𝒩𝒩\mathcal{N}caligraphic_N = 4 super-Yang-Mills,” JHEP 11 (2020) 016, arXiv:1912.13365 [hep-th].
  7. S. M. Chester, M. B. Green, S. S. Pufu, Y. Wang, and C. Wen, “New modular invariants in 𝒩𝒩\mathcal{N}caligraphic_N = 4 Super-Yang-Mills theory,” JHEP 04 (2021) 212, arXiv:2008.02713 [hep-th].
  8. L. F. Alday, S. M. Chester, and T. Hansen, “Modular invariant holographic correlators for 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM with general gauge group,” JHEP 12 (2021) 159, arXiv:2110.13106 [hep-th].
  9. D. Dorigoni, M. B. Green, and C. Wen, “Novel Representation of an Integrated Correlator in 𝒩𝒩\mathcal{N}caligraphic_N = 4 Supersymmetric Yang-Mills Theory,” Phys. Rev. Lett. 126 (2021) no. 16, 161601, arXiv:2102.08305 [hep-th].
  10. D. Dorigoni, M. B. Green, and C. Wen, “Exact properties of an integrated correlator in 𝒩𝒩\mathcal{N}caligraphic_N = 4 SU(N) SYM,” JHEP 05 (2021) 089, arXiv:2102.09537 [hep-th].
  11. D. Dorigoni, M. B. Green, and C. Wen, “Exact results for duality-covariant integrated correlators in 𝒩=4𝒩4\mathcal{N}=4caligraphic_N = 4 SYM with general classical gauge groups,” SciPost Phys. 13 (2022) no. 4, 092, arXiv:2202.05784 [hep-th].
  12. D. Dorigoni and P. Vallarino, “Exceptionally simple integrated correlators in 𝒩𝒩\mathcal{N}caligraphic_N = 4 supersymmetric Yang-Mills theory,” JHEP 09 (2023) 203, arXiv:2308.15252 [hep-th].
  13. D. Dorigoni, M. B. Green, and C. Wen, “The SAGEX review on scattering amplitudes Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their  supersymmetric Yang–Mills duals,” J. Phys. A 55 (2022) no. 44, 443011, arXiv:2203.13021 [hep-th].
  14. M. B. Green and C. Wen, “Maximal U(1)Y-violating n-point correlators in 𝒩𝒩\mathcal{N}caligraphic_N = 4 super-Yang-Mills theory,” JHEP 02 (2021) 042, arXiv:2009.01211 [hep-th].
  15. D. Dorigoni, M. B. Green, and C. Wen, “Exact expressions for n𝑛nitalic_n-point maximal U⁢(1)Y𝑈subscript1𝑌U(1)_{Y}italic_U ( 1 ) start_POSTSUBSCRIPT italic_Y end_POSTSUBSCRIPT-violating integrated correlators in S⁢U⁢(N)𝑆𝑈𝑁SU(N)italic_S italic_U ( italic_N ) 𝒩=4𝒩4\mathcal{N}=4caligraphic_N = 4 SYM,” JHEP 11 (2021) 132, arXiv:2109.08086 [hep-th].
  16. H. Paul, E. Perlmutter, and H. Raj, “Integrated correlators in 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM via SL(2, ℤℤ\mathbb{Z}blackboard_Z) spectral theory,” JHEP 01 (2023) 149, arXiv:2209.06639 [hep-th].
  17. A. Brown, C. Wen, and H. Xie, “Laplace-difference equation for integrated correlators of operators with general charges in 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM,” JHEP 06 (2023) 066, arXiv:2303.13195 [hep-th].
  18. H. Paul, E. Perlmutter, and H. Raj, “Exact large charge in 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM and semiclassical string theory,” JHEP 08 (2023) 078, arXiv:2303.13207 [hep-th].
  19. A. Brown, C. Wen, and H. Xie, “Generating functions and large-charge expansion of integrated correlators in 𝒩=4𝒩4\mathcal{N}=4caligraphic_N = 4 supersymmetric Yang-Mills theory,” JHEP 07 (2023) 129, arXiv:2303.17570 [hep-th].
  20. A. Brown, F. Galvagno, and C. Wen, “Exact results for giant graviton four-point correlators,” arXiv:2403.17263 [hep-th].
  21. S. S. Pufu, V. A. Rodriguez, and Y. Wang, “Scattering From (p,q)𝑝𝑞(p,q)( italic_p , italic_q )-Strings in AdS5×S5subscriptAdS5superscriptS5\text{AdS}_{5}\times\text{S}^{5}AdS start_POSTSUBSCRIPT 5 end_POSTSUBSCRIPT × S start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT,” arXiv:2305.08297 [hep-th].
  22. M. Billo’, F. Galvagno, M. Frau, and A. Lerda, “Integrated correlators with a Wilson line in 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM,” JHEP 12 (2023) 047, arXiv:2308.16575 [hep-th].
  23. M. Billo, M. Frau, A. Lerda, and A. Pini, “A matrix-model approach to integrated correlators in a 𝒩𝒩\mathcal{N}caligraphic_N = 2 SYM theory,” JHEP 01 (2024) 154, arXiv:2311.17178 [hep-th].
  24. C. Behan, S. M. Chester, and P. Ferrero, “Gluon scattering in AdS at finite string coupling from localization,” arXiv:2305.01016 [hep-th].
  25. A. Pini and P. Vallarino, “Integrated correlators at strong coupling in an orbifold of 𝒩=4𝒩4\mathcal{N}=4caligraphic_N = 4 SYM,” arXiv:2404.03466 [hep-th].
  26. S. M. Chester, R. Dempsey, and S. S. Pufu, “Bootstrapping 𝒩𝒩\mathcal{N}caligraphic_N = 4 super-Yang-Mills on the conformal manifold,” JHEP 01 (2023) 038, arXiv:2111.07989 [hep-th].
  27. C. Behan, S. M. Chester, and P. Ferrero, “Towards Bootstrapping F-theory,” arXiv:2403.17049 [hep-th].
  28. L. F. Alday, S. M. Chester, D. Dorigoni, M. B. Green, and C. Wen, “Relations between integrated correlators in 𝒩𝒩\mathcal{N}caligraphic_N = 4 supersymmetric Yang-Mills theory,” JHEP 05 (2024) 044, arXiv:2310.12322 [hep-th].
  29. Y. Hatsuda and K. Okuyama, “Large N expansion of an integrated correlator in 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM,” JHEP 11 (2022) 086, arXiv:2208.01891 [hep-th].
  30. S. Collier and E. Perlmutter, “Harnessing S-duality in 𝒩𝒩\mathcal{N}caligraphic_N = 4 SYM & supergravity as SL(2, ℤℤ\mathbb{Z}blackboard_Z)-averaged strings,” JHEP 08 (2022) 195, arXiv:2201.05093 [hep-th].
  31. D. Dorigoni, M. B. Green, C. Wen, and H. Xie, “Modular-invariant large-N completion of an integrated correlator in 𝒩𝒩\mathcal{N}caligraphic_N = 4 supersymmetric Yang-Mills theory,” JHEP 04 (2023) 114, arXiv:2210.14038 [hep-th].
  32. P. Goddard, J. Nuyts, and D. I. Olive, “Gauge Theories and Magnetic Charge,” Nucl. Phys. B 125 (1977) 1–28.
  33. D. Dorigoni, “An Introduction to Resurgence, Trans-Series and Alien Calculus,” Annals Phys. 409 (2019) 167914, arXiv:1411.3585 [hep-th].
  34. E. Delabaere and F. Pham, “Resurgent methods in semi-classical asymptotics,” Ann. Inst. H. Poincaré Phys. Théor. 71 (1999) 1.
  35. D. Dorigoni and A. Kleinschmidt, “Modular graph functions and asymptotic expansions of Poincaré series,” Commun. Num. Theor. Phys. 13 (2019) no. 3, 569–617, arXiv:1903.09250 [hep-th].
  36. D. Dorigoni, A. Kleinschmidt, and O. Schlotterer, “Poincaré series for modular graph forms at depth two. Part I. Seeds and Laplace systems,” JHEP 01 (2022) 133, arXiv:2109.05017 [hep-th].
  37. D. Dorigoni, A. Kleinschmidt, and R. Treilis, “To the cusp and back: resurgent analysis for modular graph functions,” JHEP 11 (2022) 048, arXiv:2208.14087 [hep-th].
  38. K. Klinger-Logan, “Differential equations in automorphic forms,” Commun. Num. Theor. Phys. 12 (2018) 767–827.
  39. D. Dorigoni, A. Kleinschmidt, and O. Schlotterer, “Poincaré series for modular graph forms at depth two. Part II. Iterated integrals of cusp forms,” JHEP 01 (2022) 134, arXiv:2109.05018 [hep-th].
  40. D. Dorigoni and R. Treilis, “Two string theory flavours of generalised Eisenstein series,” JHEP 11 (2023) 102, arXiv:2307.07491 [hep-th].
  41. K. Fedosova, K. Klinger-Logan, and D. Radchenko, “Convolution identities for divisor sums and modular forms,” arXiv:2312.00722 [math.NT].
  42. G. V. Dunne and M. Unsal, “Deconstructing zero: resurgence, supersymmetry and complex saddles,” JHEP 12 (2016) 002, arXiv:1609.05770 [hep-th].
  43. C. Kozçaz, T. Sulejmanpasic, Y. Tanizaki, and M. Ünsal, “Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems,” Commun. Math. Phys. 364 (2018) no. 3, 835–878, arXiv:1609.06198 [hep-th].
  44. D. Dorigoni and P. Glass, “The grin of Cheshire cat resurgence from supersymmetric localization,” SciPost Phys. 4 (2018) no. 2, 012, arXiv:1711.04802 [hep-th].
  45. D. Dorigoni and P. Glass, “Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D 𝒩𝒩\mathcal{N}caligraphic_N = 2 field theories,” JHEP 12 (2019) 085, arXiv:1909.05262 [hep-th].
  46. T. Fujimori and P. Glass, “Resurgence in 2-dimensional Yang–Mills and a genus-altering deformation,” PTEP 2023 (2023) no. 5, 053B03, arXiv:2212.11988 [hep-th].
  47. C. Luo and Y. Wang, “Casimir energy and modularity in higher-dimensional conformal field theories,” JHEP 07 (2023) 028, arXiv:2212.14866 [hep-th].
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

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

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Ai Generate Text Spark Streamline Icon: https://streamlinehq.com

Paper Prompts

Sign up for free to create and run paper prompts using GPT-5.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up
Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

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

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets