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Soft Particles and Infinite-Dimensional Geometry (2210.00606v2)
Published 2 Oct 2022 in hep-th
Abstract: In the sigma model, soft insertions of moduli scalars enact parallel transport of $S$-matrix elements about the finite-dimensional moduli space of vacua, and the antisymmetric double-soft theorem calculates the curvature of the vacuum manifold. We explore the analogs of these statements in gauge theory and gravity in asymptotically flat spacetimes, where the relevant moduli spaces are infinite-dimensional. These models have spaces of vacua parameterized by (trivial) flat connections at spatial infinity, and soft insertions of photons, gluons, and gravitons parallel transport $S$-matrix elements about these infinite-dimensional manifolds. We argue that the antisymmetric double-soft gluon theorem in $d+2$ bulk dimensions computes the curvature of a connection on the infinite-dimensional space Map$(Sd,G)/G$. The analogous metrics in abelian gauge theory and gravity are flat, as indicated by the vanishing of the antisymmetric double-soft theorems in those models. In other words, Feynman diagram calculations not only know about the vacuum manifold of Yang-Mills theory, they can also be used to compute its curvature. The results have interesting implications for flat holography.
- Andrew Strominger, ‘‘On BMS Invariance of Gravitational Scattering,” JHEP 07, 152 (2014), arXiv:1312.2229 [hep-th]
- Andrew Strominger, “Asymptotic Symmetries of Yang-Mills Theory,” JHEP 07, 151 (2014), arXiv:1308.0589 [hep-th]
- Daniel Kapec, Vyacheslav Lysov, Sabrina Pasterski, and Andrew Strominger, “Semiclassical Virasoro symmetry of the quantum gravity 𝒮𝒮\mathcal{S}caligraphic_S-matrix,” JHEP 08, 058 (2014), arXiv:1406.3312 [hep-th]
- Daniel Kapec, Vyacheslav Lysov, and Andrew Strominger, “Asymptotic Symmetries of Massless QED in Even Dimensions,” Adv. Theor. Math. Phys. 21, 1747–1767 (2017), arXiv:1412.2763 [hep-th]
- Clifford Cheung, Andreas Helset, and Julio Parra-Martinez, “Geometric soft theorems,” JHEP 04, 011 (2022), arXiv:2111.03045 [hep-th]
- Daniel Kapec, Y. T. Albert Law, and Sruthi A. Narayanan, “Soft Scalars and the Geometry of the Space of Celestial CFTs,” (5 2022), arXiv:2205.10935 [hep-th]
- Nima Arkani-Hamed, Freddy Cachazo, and Jared Kaplan, “What is the Simplest Quantum Field Theory?.” JHEP 09, 016 (2010), arXiv:0808.1446 [hep-th]
- Temple He, Prahar Mitra, and Andrew Strominger, “2D Kac-Moody Symmetry of 4D Yang-Mills Theory,” JHEP 10, 137 (2016), arXiv:1503.02663 [hep-th]
- Daniel Kapec and Prahar Mitra, “A d𝑑ditalic_d-Dimensional Stress Tensor for Minkd+2𝑑2{}_{d+2}start_FLOATSUBSCRIPT italic_d + 2 end_FLOATSUBSCRIPT Gravity,” JHEP 05, 186 (2018), arXiv:1711.04371 [hep-th]
- Daniel Kapec and Prahar Mitra, ‘‘Shadows and soft exchange in celestial CFT,” Phys. Rev. D 105, 026009 (2022), arXiv:2109.00073 [hep-th]
- Laura Donnay, Andrea Puhm, and Andrew Strominger, “Conformally Soft Photons and Gravitons,” JHEP 01, 184 (2019), arXiv:1810.05219 [hep-th]
- Monica Pate, Ana-Maria Raclariu, and Andrew Strominger, “Conformally Soft Theorem in Gauge Theory,” Phys. Rev. D 100, 085017 (2019), arXiv:1904.10831 [hep-th]
- Temple He and Prahar Mitra, “Asymptotic symmetries and Weinberg’s soft photon theorem in Minkd+2𝑑2{}_{d+2}start_FLOATSUBSCRIPT italic_d + 2 end_FLOATSUBSCRIPT,” JHEP 10, 213 (2019), arXiv:1903.02608 [hep-th]
- Anjalika Nande, Monica Pate, and Andrew Strominger, “Soft Factorization in QED from 2D Kac-Moody Symmetry,” JHEP 02, 079 (2018), arXiv:1705.00608 [hep-th]
- A. Bassetto, M. Ciafaloni, and G. Marchesini, “Jet Structure and Infrared Sensitive Quantities in Perturbative QCD,” Phys. Rept. 100, 201–272 (1983)
- Ilya Feige and Matthew D. Schwartz, “Hard-Soft-Collinear Factorization to All Orders,” Phys. Rev. D 90, 105020 (2014), arXiv:1403.6472 [hep-ph]
- Matthew D. Schwartz, Quantum Field Theory and the Standard Model (Cambridge University Press, 2014) ISBN 978-1-107-03473-0, 978-1-107-03473-0
- Temple He and Prahar Mitra, “Covariant Phase Space and Soft Factorization in Non-Abelian Gauge Theories,” JHEP 03, 015 (2021), arXiv:2009.14334 [hep-th]
- Daniel Kapec, Vyacheslav Lysov, Sabrina Pasterski, and Andrew Strominger, “Higher-dimensional supertranslations and Weinberg’s soft graviton theorem,” Ann. Math. Sci. Appl. 02, 69–94 (2017), arXiv:1502.07644 [gr-qc]
- Thomas Klose, Tristan McLoughlin, Dhritiman Nandan, Jan Plefka, and Gabriele Travaglini, “Double-Soft Limits of Gluons and Gravitons,” JHEP 07, 135 (2015), arXiv:1504.05558 [hep-th]
- Temple He and Prahar Mitra, “Asymptotic Structure of Higher Dimensional Yang-Mills Theory,” (6 2023), arXiv:2306.04571 [hep-th]
- Frits A. Berends and W. T. Giele, “Multiple Soft Gluon Radiation in Parton Processes,” Nucl. Phys. B 313, 595–633 (1989)
- Stefano Catani and Massimiliano Grazzini, “Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond,” Nucl. Phys. B 570, 287–325 (2000), arXiv:hep-ph/9908523
- Andrew J. Larkoski, Duff Neill, and Iain W. Stewart, “Soft Theorems from Effective Field Theory,” JHEP 06, 077 (2015), arXiv:1412.3108 [hep-th]
- Glenn Barnich and Cedric Troessaert, “Aspects of the BMS/CFT correspondence,” JHEP 05, 062 (2010), arXiv:1001.1541 [hep-th]
- Miguel Campiglia and Alok Laddha, “Asymptotic symmetries and subleading soft graviton theorem,” Phys. Rev. D 90, 124028 (2014), arXiv:1408.2228 [hep-th]
- Andrew Strominger, “w1+∞subscript𝑤1w_{1+\infty}italic_w start_POSTSUBSCRIPT 1 + ∞ end_POSTSUBSCRIPT Algebra and the Celestial Sphere: Infinite Towers of Soft Graviton, Photon, and Gluon Symmetries,” Phys. Rev. Lett. 127, 221601 (2021)
- Elizabeth Himwich, Monica Pate, and Kyle Singh, “Celestial operator product expansions and w1+∞subscript𝑤1w_{1+\infty}italic_w start_POSTSUBSCRIPT 1 + ∞ end_POSTSUBSCRIPT symmetry for all spins,” JHEP 01, 080 (2022), arXiv:2108.07763 [hep-th]
- Tim Adamo, Lionel Mason, and Atul Sharma, “Celestial w1+∞subscript𝑤1w_{1+\infty}italic_w start_POSTSUBSCRIPT 1 + ∞ end_POSTSUBSCRIPT Symmetries from Twistor Space,” SIGMA 18, 016 (2022), arXiv:2110.06066 [hep-th]
- Clifford Cheung, Andreas Helset, and Julio Parra-Martinez, “Geometry-kinematics duality,” Phys. Rev. D 106, 045016 (2022), arXiv:2202.06972 [hep-th]
- David Kutasov, “Geometry on the Space of Conformal Field Theories and Contact Terms,” Phys. Lett. B 220, 153–158 (1989)
- Johannes Jisse Duistermaat and Johan AC Kolk, Lie groups (Springer Science & Business Media, 2012)