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Asymptotic Symmetries for Logarithmic Soft Theorems in Gauge Theory and Gravity (2403.13053v2)

Published 19 Mar 2024 in hep-th

Abstract: Gauge theories and perturbative gravity in four dimensions are governed by a tower of infinite-dimensional symmetries which arise from tree-level soft theorems. However, aside from the leading soft theorems which are all-loop exact, subleading ones receive loop corrections due to long-range infrared effects which result in new soft theorems with logarithmic dependence on the energy of the soft particle. The conjectured universality of these logarithmic soft theorems to all loop orders cries out for a symmetry interpretation. In this letter we initiate a program to compute long-range infrared corrections to the charges that generate the asymptotic symmetries in (scalar) QED and perturbative gravity. For late-time fall-offs of the electromagnetic and gravitational fields which give rise to infrared dressings for the matter fields, we derive finite charge conservation laws and show that in the quantum theory they correspond precisely to the first among the infinite tower of logarithmic soft theorems. This symmetry interpretation, by virtue of being universal and all-loop exact, is a key element for a holographic principle in spacetimes with flat asymptotics.

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References (68)
  1. F. E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev. 110, 974 (1958).
  2. S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140, B516 (1965).
  3. F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem,   (2014), arXiv:1404.4091 [hep-th] .
  4. Y. Hamada and G. Shiu, Infinite Set of Soft Theorems in Gauge-Gravity Theories as Ward-Takahashi Identities, Phys. Rev. Lett. 120, 201601 (2018), arXiv:1801.05528 [hep-th] .
  5. Z.-Z. Li, H.-H. Lin, and S.-Q. Zhang, Infinite Soft Theorems from Gauge Symmetry, Phys. Rev. D 98, 045004 (2018), arXiv:1802.03148 [hep-th] .
  6. H. Elvang, C. R. T. Jones, and S. G. Naculich, Soft Photon and Graviton Theorems in Effective Field Theory, Phys. Rev. Lett. 118, 231601 (2017), arXiv:1611.07534 [hep-th] .
  7. D. Ghosh and B. Sahoo, Spin-dependent gravitational tail memory in D=4𝐷4D=4italic_D = 4, Phys. Rev. D 105, 025024 (2022), arXiv:2106.10741 [hep-th] .
  8. A. Laddha and A. Sen, Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity, JHEP 10, 065, arXiv:1706.00759 [hep-th] .
  9. H. Krishna and B. Sahoo, Universality of loop corrected soft theorems in 4d, JHEP 11, 233, arXiv:2308.16807 [hep-th] .
  10. A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07, 152, arXiv:1312.2229 [hep-th] .
  11. V. Lysov, S. Pasterski, and A. Strominger, Low’s Subleading Soft Theorem as a Symmetry of QED, Phys. Rev. Lett. 113, 111601 (2014), arXiv:1407.3814 [hep-th] .
  12. D. Kapec, M. Pate, and A. Strominger, New Symmetries of QED, Adv. Theor. Math. Phys. 21, 1769 (2017a), arXiv:1506.02906 [hep-th] .
  13. M. Campiglia and A. Laddha, Asymptotic symmetries of QED and Weinberg’s soft photon theorem, JHEP 07, 115, arXiv:1505.05346 [hep-th] .
  14. M. Campiglia and A. Laddha, Subleading soft photons and large gauge transformations, JHEP 11, 012, arXiv:1605.09677 [hep-th] .
  15. M. Campiglia and A. Laddha, Asymptotic symmetries of gravity and soft theorems for massive particles, JHEP 12, 094, arXiv:1509.01406 [hep-th] .
  16. M. Campiglia and A. Laddha, Asymptotic symmetries and subleading soft graviton theorem, Phys. Rev. D 90, 124028 (2014), arXiv:1408.2228 [hep-th] .
  17. Asymptotic symmetries in gauge theory are generically called large gauge transformations. In analogy to gravity, we refer to the leading one as superphaserotation.
  18. M. Campiglia and A. Laddha, Asymptotic charges in massless QED revisited: A view from Spatial Infinity, JHEP 05, 207, arXiv:1810.04619 [hep-th] .
  19. L. Freidel, D. Pranzetti, and A.-M. Raclariu, Higher spin dynamics in gravity and w1+∞\infty∞ celestial symmetries, Phys. Rev. D 106, 086013 (2022), arXiv:2112.15573 [hep-th] .
  20. A.-M. Raclariu, Lectures on Celestial Holography,   (2021), arXiv:2107.02075 [hep-th] .
  21. S. Pasterski, Lectures on celestial amplitudes, Eur. Phys. J. C 81, 1062 (2021), arXiv:2108.04801 [hep-th] .
  22. T. McLoughlin, A. Puhm, and A.-M. Raclariu, The SAGEX review on scattering amplitudes chapter 11: soft theorems and celestial amplitudes, J. Phys. A 55, 443012 (2022), arXiv:2203.13022 [hep-th] .
  23. L. Donnay, Celestial holography: An asymptotic symmetry perspective,  (2023), arXiv:2310.12922 [hep-th] .
  24. J. de Boer and S. N. Solodukhin, A Holographic reduction of Minkowski space-time, Nucl. Phys. B 665, 545 (2003), arXiv:hep-th/0303006 .
  25. C. Cheung, A. de la Fuente, and R. Sundrum, 4D scattering amplitudes and asymptotic symmetries from 2D CFT, JHEP 01, 112, arXiv:1609.00732 [hep-th] .
  26. S. Pasterski, S.-H. Shao, and A. Strominger, Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere, Phys. Rev. D 96, 065026 (2017a), arXiv:1701.00049 [hep-th] .
  27. S. Pasterski and S.-H. Shao, Conformal basis for flat space amplitudes, Phys. Rev. D 96, 065022 (2017), arXiv:1705.01027 [hep-th] .
  28. S. Pasterski, S.-H. Shao, and A. Strominger, Gluon Amplitudes as 2d Conformal Correlators, Phys. Rev. D 96, 085006 (2017b), arXiv:1706.03917 [hep-th] .
  29. A. Nande, M. Pate, and A. Strominger, Soft Factorization in QED from 2D Kac-Moody Symmetry, JHEP 02, 079, arXiv:1705.00608 [hep-th] .
  30. L. Donnay, A. Puhm, and A. Strominger, Conformally Soft Photons and Gravitons, JHEP 01, 184, arXiv:1810.05219 [hep-th] .
  31. W. Fan, A. Fotopoulos, and T. R. Taylor, Soft Limits of Yang-Mills Amplitudes and Conformal Correlators, JHEP 05, 121, arXiv:1903.01676 [hep-th] .
  32. M. Pate, A.-M. Raclariu, and A. Strominger, Conformally Soft Theorem in Gauge Theory, Phys. Rev. D 100, 085017 (2019), arXiv:1904.10831 [hep-th] .
  33. T. Adamo, L. Mason, and A. Sharma, Celestial amplitudes and conformal soft theorems, Class. Quant. Grav. 36, 205018 (2019), arXiv:1905.09224 [hep-th] .
  34. A. Puhm, Conformally Soft Theorem in Gravity, JHEP 09, 130, arXiv:1905.09799 [hep-th] .
  35. A. Guevara, Notes on Conformal Soft Theorems and Recursion Relations in Gravity,   (2019), arXiv:1906.07810 [hep-th] .
  36. D. Kapec and P. Mitra, A d𝑑ditalic_d-Dimensional Stress Tensor for Minkd+2𝑑2{}_{d+2}start_FLOATSUBSCRIPT italic_d + 2 end_FLOATSUBSCRIPT Gravity, JHEP 05, 186, arXiv:1711.04371 [hep-th] .
  37. L. Donnay, S. Pasterski, and A. Puhm, Asymptotic Symmetries and Celestial CFT, JHEP 09, 176, arXiv:2005.08990 [hep-th] .
  38. D. Kapec and P. Mitra, Shadows and soft exchange in celestial CFT, Phys. Rev. D 105, 026009 (2022), arXiv:2109.00073 [hep-th] .
  39. S. Pasterski, A. Puhm, and E. Trevisani, Celestial Diamonds: Conformal Multiplets in Celestial CFT,   (2021), arXiv:2105.03516 [hep-th] .
  40. L. Donnay, S. Pasterski, and A. Puhm, Goldilocks modes and the three scattering bases, JHEP 06, 124, arXiv:2202.11127 [hep-th] .
  41. Y. Pano, A. Puhm, and E. Trevisani, Symmetries in Celestial CFTd𝑑{}_{d}start_FLOATSUBSCRIPT italic_d end_FLOATSUBSCRIPT, JHEP 07, 076, arXiv:2302.10222 [hep-th] .
  42. M. Geiller, Celestial w1+∞subscript𝑤1w_{1+\infty}italic_w start_POSTSUBSCRIPT 1 + ∞ end_POSTSUBSCRIPT charges and the subleading structure of asymptotically-flat spacetimes,   (2024), arXiv:2403.05195 [hep-th] .
  43. R. Penrose, Nonlinear Gravitons and Curved Twistor Theory, Gen. Rel. Grav. 7, 31 (1976).
  44. Note that in D>4𝐷4D>4italic_D > 4 dimensions these soft theorems are all-loop exact.
  45. Z. Bern, S. Davies, and J. Nohle, On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons, Phys. Rev. D 90, 085015 (2014), arXiv:1405.1015 [hep-th] .
  46. B. Sahoo and A. Sen, Classical and Quantum Results on Logarithmic Terms in the Soft Theorem in Four Dimensions, JHEP 02, 086, arXiv:1808.03288 [hep-th] .
  47. A. P. Saha, B. Sahoo, and A. Sen, Proof of the classical soft graviton theorem in D𝐷Ditalic_D = 4, JHEP 06, 153, arXiv:1912.06413 [hep-th] .
  48. B. Sahoo, Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions, JHEP 12, 070, arXiv:2008.04376 [hep-th] .
  49. M. Campiglia and A. Laddha, Loop Corrected Soft Photon Theorem as a Ward Identity, JHEP 10, 287, arXiv:1903.09133 [hep-th] .
  50. S. Atul Bhatkar, Ward identity for loop level soft photon theorem for massless QED coupled to gravity, JHEP 10, 110, arXiv:1912.10229 [hep-th] .
  51. We thank E. Trevisani for discussion on this point.
  52. Related recent work includes [78, 79].
  53. L. Donnay, K. Nguyen, and R. Ruzziconi, Loop-corrected subleading soft theorem and the celestial stress tensor, JHEP 09, 063, arXiv:2205.11477 [hep-th] .
  54. S. Choi, A. Laddha, and A. Puhm,   (in preparation).
  55. Note that a ln⁡τ𝜏\ln\tauroman_ln italic_τ term in (5) is possible, but we will show in [63] that this term is pure gauge (even though it diverges as τ→∞→𝜏\tau\to\inftyitalic_τ → ∞) and hence does not contribute to the charges.
  56. M. Campiglia, Null to time-like infinity Green’s functions for asymptotic symmetries in Minkowski spacetime, JHEP 11, 160, arXiv:1509.01408 [hep-th] .
  57. J. Peraza, Renormalized electric and magnetic charges for O(rn𝑛{}^{n}start_FLOATSUPERSCRIPT italic_n end_FLOATSUPERSCRIPT) large gauge symmetries, JHEP 01, 175, arXiv:2301.05671 [hep-th] .
  58. In the literature, LGTs with divergent (“overleading”) gauge parameters are sometimes referred to as overleading LGTs; here we instead we refer to them as subleading LGTs since they are related to subleading soft theorems.
  59. D. Christodoulou, The global initial value problem in general relativity, Proceedings of the MGIX MM Meeting. Held 2-8 July 2000 in The University of Rome ”La Sapienza”,  (Pub Date: December 2002 DOI:).
  60. L. M. A. Kehrberger, The Case Against Smooth Null Infinity I: Heuristics and Counter-Examples, Annales Henri Poincare 23, 829 (2022), arXiv:2105.08079 [gr-qc] .
  61. M. Geiller and C. Zwikel, The partial Bondi gauge: Further enlarging the asymptotic structure of gravity, SciPost Phys. 13, 108 (2022).
  62. M. Geiller and C. Zwikel, The partial Bondi gauge: Gauge fixings and asymptotic charges,   (2024).
  63. As the gravitational soft theorems have been derived in harmonic gauge, we believe that the logarithmic divergence of the superrotation charge is a physical effect referred to as tail to the memory in [76].
  64. A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory,  (2017), arXiv:1703.05448 [hep-th] .
  65. A. Laddha and A. Sen, Observational Signature of the Logarithmic Terms in the Soft Graviton Theorem, Phys. Rev. D 100, 024009 (2019), arXiv:1806.01872 [hep-th] .
  66. S. Choi, A. Laddha, and A. Puhm,   (work in progress).
  67. H. Krishna, Celestial gluon and graviton OPE at loop level,   (2023), arXiv:2310.16687 [hep-th] .
  68. R. Bhardwaj and A. Yelleshpur Srikant, Celestial soft currents at one-loop and their OPEs,  (2024), arXiv:2403.10443 [hep-th] .
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