Papers
Topics
Authors
Recent
2000 character limit reached

BRST Covariant Phase Space and Holographic Ward Identities (2405.18898v3)

Published 29 May 2024 in hep-th

Abstract: This paper develops an enlarged BRST framework to treat the large gauge transformations of a given quantum field theory. It determines the associated infinitely many Noether charges stemming from a gauge fixed and BRST invariant Lagrangian, a result that cannot be obtained from Noether's second theorem. The geometrical significance of this result is highlighted by the construction of a trigraded BRST covariant phase space, allowing a BRST invariant gauge fixing procedure. This provides an appropriate framework for determining the conserved BRST Noether current of the global BRST symmetry and the associated global Noether charges. The latter are found to be equivalent with the usual classical corner charges of large gauge transformations. It allows one to prove the gauge independence of their physical effects at the perturbative quantum level. In particular, the underlying BRST fundamental canonical relation provides the same graded symplectic brackets as in the classical covariant phase space. A unified Lagrangian Ward identity for small and large gauge transformations is built. It consistently decouples into a bulk part for small gauge transformations, which is the standard BRST--BV quantum master equation, and a boundary part for large gauge transformations. The boundary part provides a perturbation theory origin for the invariance of the Hamiltonian physical $\mathcal{S}$-matrix under asymptotic symmetries. Holographic anomalies for the boundary Ward identity are studied and found to be solutions of a codimension one Wess--Zumino consistency condition. Such solutions are studied in the context of extended BMS symmetry. Their existence clarifies the status of the $1$-loop correction to the subleading soft graviton theorem.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (71)
  1. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, “Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems”, Proc. Roy. Soc. Lond. A 269 (1962) 21–52.
  2. R. Sachs, “Asymptotic symmetries in gravitational theory”, Phys. Rev. 128 (1962) 2851–2864.
  3. A. Strominger, “Asymptotic Symmetries of Yang-Mills Theory”, JHEP 07 (2014)a 151, arXiv:1308.0589.
  4. A. Strominger, “On BMS Invariance of Gravitational Scattering”, JHEP 07 (2014)b 152, arXiv:1312.2229.
  5. G. Barnich and C. Troessaert, “Aspects of the BMS/CFT correspondence”, JHEP 05 (2010) 062, arXiv:1001.1541.
  6. D. Kapec, V. Lysov, S. Pasterski, and A. Strominger, “Semiclassical Virasoro symmetry of the quantum gravity 𝒮𝒮\mathcal{S}caligraphic_S-matrix”, JHEP 08 (2014) 058, arXiv:1406.3312.
  7. M. Campiglia and A. Laddha, “Asymptotic symmetries and subleading soft graviton theorem”, Phys. Rev. D 90 (2014), no. 12, 124028, arXiv:1408.2228.
  8. S. Weinberg, “Infrared photons and gravitons”, Phys. Rev. 140 Oct (1965) B516–B524.
  9. F. Cachazo and A. Strominger, “Evidence for a New Soft Graviton Theorem”, arXiv:1404.4091.
  10. S. Pasterski, “Asymptotic Symmetries and Electromagnetic Memory”, JHEP 09 (2017) 154, arXiv:1505.00716.
  11. A. Strominger and A. Zhiboedov, “Gravitational Memory, BMS Supertranslations and Soft Theorems”, JHEP 01 (2016) 086, arXiv:1411.5745.
  12. S. Pasterski, A. Strominger, and A. Zhiboedov, “New Gravitational Memories”, JHEP 12 (2016) 053, arXiv:1502.06120.
  13. A. Strominger, “Lectures on the Infrared Structure of Gravity and Gauge Theory”, arXiv:1703.05448.
  14. T. He, V. Lysov, P. Mitra, and A. Strominger, “BMS supertranslations and Weinberg’s soft graviton theorem”, JHEP 05 (2015) 151, arXiv:1401.7026.
  15. M. Campiglia and A. Laddha, “Asymptotic symmetries of QED and Weinberg’s soft photon theorem”, JHEP 07 (2015) 115, arXiv:1505.05346.
  16. E. Noether, “Invariant variation problems”, Transport Theory and Statistical Physics 1 (1971), no. 3, 186–207.
  17. G. Compère and A. Fiorucci, “Advanced Lectures on General Relativity”, arXiv:1801.07064.
  18. L. Ciambelli, “From Asymptotic Symmetries to the Corner Proposal”, 12 2022. arXiv:2212.13644.
  19. C. Crnkovic and E. Witten, “COVARIANT DESCRIPTION OF CANONICAL FORMALISM IN GEOMETRICAL THEORIES”, 9 1986.
  20. J. Lee and R. M. Wald, “Local symmetries and constraints”, J. Math. Phys. 31 (1990) 725–743.
  21. R. M. Wald and A. Zoupas, “A General definition of ’conserved quantities’ in general relativity and other theories of gravity”, Phys. Rev. D 61 (2000) 084027, gr-qc/9911095.
  22. G. Barnich and F. Brandt, “Covariant theory of asymptotic symmetries, conservation laws and central charges”, Nucl. Phys. B 633 (2002) 3–82, hep-th/0111246.
  23. D. Harlow and J.-Q. Wu, “Covariant phase space with boundaries”, JHEP 10 (2020) 146, arXiv:1906.08616.
  24. J. D. Brown and M. Henneaux, “Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity”, Commun. Math. Phys. 104 (1986) 207–226.
  25. G. Barnich and C. Troessaert, “BMS charge algebra”, JHEP 12 (2011) 105, arXiv:1106.0213.
  26. M. Campiglia and J. Peraza, “Generalized BMS charge algebra”, Phys. Rev. D 101 (2020), no. 10, 104039, arXiv:2002.06691.
  27. G. Compère, A. Fiorucci, and R. Ruzziconi, “The ΛΛ\Lambdaroman_Λ-BMS4 charge algebra”, JHEP 10 (2020) 205, arXiv:2004.10769.
  28. L. Freidel, R. Oliveri, D. Pranzetti, and S. Speziale, “The Weyl BMS group and Einstein’s equations”, JHEP 07 (2021)a 170, arXiv:2104.05793.
  29. L. Freidel, R. Oliveri, D. Pranzetti, and S. Speziale, “Extended corner symmetry, charge bracket and Einstein’s equations”, JHEP 09 (2021)b 083, arXiv:2104.12881.
  30. L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part I. Corner potentials and charges”, JHEP 11 (2020) 026, arXiv:2006.12527.
  31. L. Ciambelli, R. G. Leigh, and P.-C. Pai, “Embeddings and Integrable Charges for Extended Corner Symmetry”, Phys. Rev. Lett. 128 (2022) arXiv:2111.13181.
  32. L. Donnay and R. Ruzziconi, “BMS flux algebra in celestial holography”, JHEP 11 (2021) 040, arXiv:2108.11969.
  33. A. Rignon-Bret and S. Speziale, “Centerless-BMS charge algebra”, arXiv:2405.01526.
  34. L. Baulieu and J. Thierry-Mieg, “The Principle of BRS Symmetry: An Alternative Approach to Yang-Mills Theories”, Nucl. Phys. B 197 (1982) 477–508.
  35. L. Alvarez-Gaume and L. Baulieu, “The Two Quantum Symmetries Associated With a Classical Symmetry”, Nucl. Phys. B 212 (1983) 255–267.
  36. S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT”, Phys. Rev. Lett. 96 (2006) 181602, hep-th/0603001.
  37. I. Anderson, “Introduction to the variational bicomplex”, 1992.
  38. P. Mnev, M. Schiavina, and K. Wernli, “Towards holography in the BV-BFV setting”, Annales Henri Poincare 21 (2019), no. 3, 993–1044, arXiv:1905.00952.
  39. D. L. Karatas and K. L. Kowalski, “NOETHER’S THEOREM FOR LOCAL GAUGE TRANSFORMATIONS”, Am. J. Phys. 58 (1990) 123–131.
  40. S. G. Avery and B. U. W. Schwab, “Noether’s second theorem and Ward identities for gauge symmetries”, JHEP 02 (2016) 031, arXiv:1510.07038.
  41. N. Miller, “From Noether’s Theorem to Bremsstrahlung: a pedagogical introduction to large gauge transformations and classical soft theorems”, arXiv:2112.05289.
  42. W. Donnelly and L. Freidel, “Local subsystems in gauge theory and gravity”, JHEP 09 (2016) 102, arXiv:1601.04744.
  43. L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part II. Corner metric and Lorentz charges”, JHEP 11 (2020) 027, arXiv:2007.03563.
  44. L. Freidel, M. Geiller, and D. Pranzetti, “Edge modes of gravity. Part III. Corner simplicity constraints”, JHEP 01 (2021) 100, arXiv:2007.12635.
  45. A. J. Speranza, “Local phase space and edge modes for diffeomorphism-invariant theories”, JHEP 02 (2018) 021, arXiv:1706.05061.
  46. A. Ball, A. Law, and G. Wong, “Dynamical Edge Modes and Entanglement in Maxwell Theory”, arXiv:2403.14542.
  47. L. Freidel, “A canonical bracket for open gravitational system”, arXiv:2111.14747.
  48. L. Ciambelli and R. G. Leigh, “Isolated surfaces and symmetries of gravity”, Phys. Rev. D 104 (2021), no. 4, 046005, arXiv:2104.07643.
  49. F. Hopfmüller and L. Freidel, “Null Conservation Laws for Gravity”, Phys. Rev. D 97 (2018), no. 12, 124029, arXiv:1802.06135.
  50. V. Chandrasekaran and A. J. Speranza, “Anomalies in gravitational charge algebras of null boundaries and black hole entropy”, JHEP 01 (2021) 137, arXiv:2009.10739.
  51. G. Odak, A. Rignon-Bret, and S. Speziale, “Wald-Zoupas prescription with soft anomalies”, Phys. Rev. D 107 (2023), no. 8, 084028, arXiv:2212.07947.
  52. H. Gomes and A. Riello, “The observer’s ghost: notes on a field space connection”, JHEP 05 (2017) 017, arXiv:1608.08226.
  53. A. Riello, “Soft charges from the geometry of field space”, JHEP 05 (2020) 125, arXiv:1904.07410.
  54. A. Alekseev, L. D. Faddeev, and S. L. Shatashvili, “Quantization of symplectic orbits of compact Lie groups by means of the functional integral”, J. Geom. Phys. 5 (1988) 391–406.
  55. A. Alekseev and S. L. Shatashvili, “Path Integral Quantization of the Coadjoint Orbits of the Virasoro Group and 2D Gravity”, Nucl. Phys. B 323 (1989) 719–733.
  56. G. Barnich, K. Nguyen, and R. Ruzziconi, “Geometric action for extended Bondi-Metzner-Sachs group in four dimensions”, JHEP 12 (2022) 154, arXiv:2211.07592.
  57. L. Baulieu, “Anomalies and Gauge Symmetry”, Nucl. Phys. B 241 (1984) 557–588.
  58. L. Baulieu, B. Grossman, and R. Stora, “Gauged BRST Symmetry and the Occurrence of Higher Cocycles in Quantum Field Theory”, Phys. Lett. B 180 (1986) 95–100.
  59. P. P. Kulish and L. D. Faddeev, “Asymptotic conditions and infrared divergences in quantum electrodynamics”, Theor. Math. Phys. 4 (1970) 745.
  60. G. Compère, S. E. Gralla, and H. Wei, “An asymptotic framework for gravitational scattering”, Class. Quant. Grav. 40 (2023), no. 20, 205018, arXiv:2303.17124.
  61. G. Barnich, “Centrally extended BMS4 Lie algebroid”, JHEP 06 (2017) 007, arXiv:1703.08704.
  62. L. Baulieu and T. Wetzstein, “BRST BMS4 symmetry and its cocycles from horizontality conditions”, JHEP 07 (2023) 130, arXiv:2304.12369.
  63. L. Baulieu, “Leaf of Leaf Foliation and Beltrami Parametrization in d>2𝑑2d>2italic_d > 2 dimensional Gravity”, arXiv:2109.06681.
  64. M. Geiller and C. Zwikel, “The partial Bondi gauge: Further enlarging the asymptotic structure of gravity”, SciPost Phys. 13 (2022) 108, arXiv:2205.11401.
  65. S. Ananth, L. Brink, and S. Majumdar, “BMS algebra from residual gauge invariance in light-cone gravity”, JHEP 11 (2021) 008, arXiv:2101.00019.
  66. M. Geiller and C. Zwikel, “The partial Bondi gauge: Gauge fixings and asymptotic charges”, SciPost Phys. 16 (2024) 076, arXiv:2401.09540.
  67. G. Compère, A. Fiorucci, and R. Ruzziconi, “Superboost transitions, refraction memory and super-Lorentz charge algebra”, JHEP 11 (2018) 200, arXiv:1810.00377, [Erratum: JHEP 04, 172 (2020)].
  68. L. Donnay, K. Nguyen, and R. Ruzziconi, “Loop-corrected subleading soft theorem and the celestial stress tensor”, JHEP 09 (2022) 063, arXiv:2205.11477.
  69. M. Campiglia and A. Laddha, “BMS Algebra, Double Soft Theorems, and All That”, arXiv:2106.14717.
  70. Z. Bern, S. Davies, and J. Nohle, “On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons”, Phys. Rev. D 90 (2014), no. 8, 085015, arXiv:1405.1015.
  71. S. He, Y.-t. Huang, and C. Wen, “Loop Corrections to Soft Theorems in Gauge Theories and Gravity”, JHEP 12 (2014) 115, arXiv:1405.1410.
Citations (1)
View on Semantic Scholar

Summary

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

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

Whiteboard

Paper to Video (Beta)

Open Problems

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

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

Continue Learning

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

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

Collections

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

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

Tweets

Sign up for free to view the 2 tweets with 13 likes about this paper.

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