Quantum corrections to generic branes: DBI, NLSM, and more. (English) Zbl 1459.81091
Summary: We study quantum corrections to hypersurfaces of dimension \(d + 1 > 2\) embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
Keywords:
effective field theories; global symmetries; renormalization regularization and renormalons; space-time symmetriesReferences:
| [1] | Morgan, F., Colloquium: Soap bubble clusters, Rev. Mod. Phys., 79, 821 (2007) · Zbl 1205.53009 |
| [2] | Silverstein, E.; Tong, D., Scalar speed limits and cosmology: Acceleration from D-cceleration, Phys. Rev. D, 70, 103505 (2004) |
| [3] | Alishahiha, M.; Silverstein, E.; Tong, D., DBI in the sky, Phys. Rev. D, 70, 123505 (2004) |
| [4] | Langlois, D.; Renaux-Petel, S.; Steer, DA; Tanaka, T., Primordial fluctuations and non-Gaussianities in multi-field DBI inflation, Phys. Rev. Lett., 101 (2008) |
| [5] | Langlois, D.; Renaux-Petel, S.; Steer, DA; Tanaka, T., Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation, Phys. Rev. D, 78 (2008) |
| [6] | J. Polchinski, TASI lectures on D-branes, in Theoretical Advanced Study Institute in Elementary Particle Physics (TASI 96): Fields, Strings, and Duality, pp. 293-356, 1996 [hep-th/9611050] [INSPIRE]. |
| [7] | Maldacena, JM, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys., 38, 1113 (1999) · Zbl 0969.81047 |
| [8] | Cheung, C.; Kampf, K.; Novotny, J.; Trnka, J., Effective Field Theories from Soft Limits of Scattering Amplitudes, Phys. Rev. Lett., 114, 221602 (2015) |
| [9] | Cheung, C.; Kampf, K.; Novotny, J.; Shen, C-H; Trnka, J., A Periodic Table of Effective Field Theories, JHEP, 02, 020 (2017) · Zbl 1377.81123 |
| [10] | Elvang, H.; Hadjiantonis, M.; Jones, CRT; Paranjape, S., Soft Bootstrap and Supersymmetry, JHEP, 01, 195 (2019) · Zbl 1409.81146 |
| [11] | Low, I.; Yin, Z., Soft Bootstrap and Effective Field Theories, JHEP, 11, 078 (2019) · Zbl 1429.81049 |
| [12] | Arkani-Hamed, N.; Cachazo, F.; Kaplan, J., What is the Simplest Quantum Field Theory?, JHEP, 09, 016 (2010) · Zbl 1291.81356 |
| [13] | Cachazo, F.; He, S.; Yuan, EY, New Double Soft Emission Theorems, Phys. Rev. D, 92 (2015) |
| [14] | Cachazo, F.; Cha, P.; Mizera, S., Extensions of Theories from Soft Limits, JHEP, 06, 170 (2016) · Zbl 1388.81203 |
| [15] | Padilla, A.; Stefanyszyn, D.; Wilson, T., Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes, JHEP, 04, 015 (2017) · Zbl 1378.81147 |
| [16] | Guerrieri, AL; Huang, Y-t; Li, Z.; Wen, C., On the exactness of soft theorems, JHEP, 12, 052 (2017) · Zbl 1383.81323 |
| [17] | Li, Z-z; Lin, H-h; Zhang, S-q, On the Symmetry Foundation of Double Soft Theorems, JHEP, 12, 032 (2017) · Zbl 1383.81326 |
| [18] | Bogers, MP; Brauner, T., Geometry of Multiflavor Galileon-Like Theories, Phys. Rev. Lett., 121, 171602 (2018) |
| [19] | Bogers, MP; Brauner, T., Lie-algebraic classification of effective theories with enhanced soft limits, JHEP, 05, 076 (2018) · Zbl 1391.81139 |
| [20] | Rodina, L., Scattering Amplitudes from Soft Theorems and Infrared Behavior, Phys. Rev. Lett., 122 (2019) |
| [21] | Yin, Z., The Infrared Structure of Exceptional Scalar Theories, JHEP, 03, 158 (2019) · Zbl 1414.81164 |
| [22] | Roest, D.; Stefanyszyn, D.; Werkman, P., An Algebraic Classification of Exceptional EFTs, JHEP, 08, 081 (2019) · Zbl 1421.81080 |
| [23] | Bonifacio, J.; Hinterbichler, K.; Johnson, LA; Joyce, A.; Rosen, RA, Matter Couplings and Equivalence Principles for Soft Scalars, JHEP, 07, 056 (2020) · Zbl 1451.81320 |
| [24] | Z. Bern, J.J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The Duality Between Color and Kinematics and its Applications, arXiv:1909.01358 [INSPIRE]. |
| [25] | Cachazo, F.; He, S.; Yuan, EY, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP, 07, 149 (2015) · Zbl 1388.83196 |
| [26] | Cheung, C.; Shen, C-H; Wen, C., Unifying Relations for Scattering Amplitudes, JHEP, 02, 095 (2018) · Zbl 1387.81264 |
| [27] | Gerstein, IS; Jackiw, R.; Weinberg, S.; Lee, BW, Chiral loops, Phys. Rev. D, 3, 2486 (1971) |
| [28] | S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press (2005). · Zbl 1069.81501 |
| [29] | S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press (2013). · Zbl 1264.81010 |
| [30] | Abbott, LF, Introduction to the Background Field Method, Acta Phys. Polon. B, 13, 33 (1982) |
| [31] | Honerkamp, J., Chiral multiloops, Nucl. Phys. B, 36, 130 (1972) |
| [32] | Álvarez-Gaumé, L.; Freedman, DZ; Mukhi, S., The Background Field Method and the Ultraviolet Structure of the Supersymmetric Nonlinear Sigma Model, Annals Phys., 134, 85 (1981) |
| [33] | Bärvinsky, AO; Vilkovisky, GA, The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity, Phys. Rept., 119, 1 (1985) |
| [34] | P. Creminelli and A. Strumia, Collider signals of brane fluctuations, Nucl. Phys. B596 (2001) 125 [hep-ph/0007267] [INSPIRE]. |
| [35] | R. Contino, L. Pilo, R. Rattazzi and A. Strumia, Graviton loops and brane observables, JHEP06 (2001) 005 [hep-ph/0103104] [INSPIRE]. |
| [36] | J.A.R. Cembranos, A. Dobado and A.L. Maroto, Brane world dark matter, Phys. Rev. Lett.90 (2003) 241301 [hep-ph/0302041] [INSPIRE]. |
| [37] | K. Akama and T. Hattori, Brane Induced Gravity in the Curved Bulk, arXiv:1403.5633 [INSPIRE]. · Zbl 1276.83003 |
| [38] | Forini, V.; Puletti, VGM; Griguolo, L.; Seminara, D.; Vescovi, E., Remarks on the geometrical properties of semiclassically quantized strings, J. Phys. A, 48, 475401 (2015) · Zbl 1330.81156 |
| [39] | de León Ardón, R., Semiclassical p-branes in hyperbolic space, Class. Quant. Grav., 37, 237001 (2020) · Zbl 1479.83079 |
| [40] | Nielsen, NK, On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories, Nucl. Phys. B, 101, 173 (1975) |
| [41] | Fukuda, R.; Kugo, T., Gauge Invariance in the Effective Action and Potential, Phys. Rev. D, 13, 3469 (1976) |
| [42] | Aitchison, IJR; Fraser, CM, Gauge Invariance and the Effective Potential, Annals Phys., 156, 1 (1984) · Zbl 1216.81109 |
| [43] | Hart, CF, Theory and renormalization of the gauge invariant effective action, Phys. Rev. D, 28, 1993 (1983) |
| [44] | Georgi, H., On-shell effective field theory, Nucl. Phys. B, 361, 339 (1991) |
| [45] | G. Isidori, G. Ridolfi and A. Strumia, On the metastability of the standard model vacuum, Nucl. Phys. B609 (2001) 387 [hep-ph/0104016] [INSPIRE]. · Zbl 0971.81580 |
| [46] | Andreassen, A.; Frost, W.; Schwartz, MD, Consistent Use of Effective Potentials, Phys. Rev. D, 91 (2015) |
| [47] | Di Luzio, L.; Isidori, G.; Ridolfi, G., Stability of the electroweak ground state in the Standard Model and its extensions, Phys. Lett. B, 753, 150 (2016) |
| [48] | Andreassen, A.; Farhi, D.; Frost, W.; Schwartz, MD, Precision decay rate calculations in quantum field theory, Phys. Rev. D, 95 (2017) |
| [49] | Howe, PS; Papadopoulos, G.; Stelle, KS, The background field method and the non-linear σ-model, Nucl. Phys. B, 296, 26 (1988) |
| [50] | Mukhi, S., The Geometric Background Field Method, Renormalization and the Wess-Zumino Term in Nonlinear Sigma Models, Nucl. Phys. B, 264, 640 (1986) |
| [51] | Gilkey, PB, The spectral geometry of a Riemannian manifold, J. Diff. Geom., 10, 601 (1975) · Zbl 0316.53035 |
| [52] | I.G. Avramidi, Covariant methods for the calculation of the effective action in quantum field theory and investigation of higher derivative quantum gravity, Ph.D. Thesis, Moscow State University, (1986), [hep-th/9510140] [INSPIRE]. |
| [53] | Hinterbichler, K.; Trodden, M.; Wesley, D., Multi-field galileons and higher co-dimension branes, Phys. Rev. D, 82, 124018 (2010) |
| [54] | Pajer, E.; Stefanyszyn, D., Symmetric Superfluids, JHEP, 06, 008 (2019) · Zbl 1445.81051 |
| [55] | Grall, T.; Jazayeri, S.; Pajer, E., Symmetric Scalars, JCAP, 05, 031 (2020) · Zbl 1491.83021 |
| [56] | Cheung, C.; Mangan, J.; Shen, C-H, Hidden Conformal Invariance of Scalar Effective Field Theories, Phys. Rev. D, 102, 125009 (2020) |
| [57] | Goon, GL; Hinterbichler, K.; Trodden, M., Stability and superluminality of spherical DBI galileon solutions, Phys. Rev. D, 83 (2011) |
| [58] | de Rham, C.; Tolley, AJ, DBI and the Galileon reunited, JCAP, 05, 015 (2010) |
| [59] | Goon, G.; Hinterbichler, K.; Trodden, M., A New Class of Effective Field Theories from Embedded Branes, Phys. Rev. Lett., 106, 231102 (2011) |
| [60] | Goon, G.; Hinterbichler, K.; Joyce, A.; Trodden, M., Galileons as Wess-Zumino Terms, JHEP, 06, 004 (2012) |
| [61] | Creminelli, P.; Serone, M.; Trevisan, G.; Trincherini, E., Inequivalence of Coset Constructions for Spacetime Symmetries, JHEP, 02, 037 (2015) · Zbl 1388.83040 |
| [62] | de Rham, C.; Ribeiro, RH, Riding on irrelevant operators, JCAP, 11, 016 (2014) |
| [63] | Appelquist, T.; Bernard, CW, The Nonlinear σ Model in the Loop Expansion, Phys. Rev. D, 23, 425 (1981) |
| [64] | Boulware, DG; Brown, LS, Symmetric space scalar field theory, Annals Phys., 138, 392 (1982) |
| [65] | Akhoury, R.; Yao, Y-P, The Nonlinear σ Model as an Effective Lagrangian, Phys. Rev. D, 25, 3361 (1982) |
| [66] | Gasser, J.; Leutwyler, H., Chiral Perturbation Theory to One Loop, Annals Phys., 158, 142 (1984) |
| [67] | Gaillard, MK, The Effective One Loop Lagrangian With Derivative Couplings, Nucl. Phys. B, 268, 669 (1986) |
| [68] | Costa, KM; Liebrand, F., Normal Coordinate Methods and Heavy Higgs Effects, Phys. Rev. D, 40, 2014 (1989) |
| [69] | Alonso, R.; Jenkins, EE; Manohar, AV, Geometry of the Scalar Sector, JHEP, 08, 101 (2016) |
| [70] | J.M. Martín-García, xAct, Efficient tensor computer algebra for the Wolfram Language. http://www.xact.es/. |
| [71] | Nutma, T., xTras: A field-theory inspired xAct package for mathematica, Comput. Phys. Commun., 185, 1719 (2014) · Zbl 1348.70003 |
| [72] | S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1, Phys. Rev.177 (1969) 2239 [INSPIRE]. |
| [73] | C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2, Phys. Rev.177 (1969) 2247 [INSPIRE]. |
| [74] | Low, I.; Rodina, L.; Yin, Z., Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons, Phys. Rev. D, 103 (2021) |
| [75] | S. Bellucci, E. Ivanov and S. Krivonos, AdS/CFT equivalence transformation, Phys. Rev. D66 (2002) 086001 [Erratum ibid.67 (2003) 049901] [hep-th/0206126] [INSPIRE]. |
| [76] | Elvang, H.; Freedman, DZ; Hung, L-Y; Kiermaier, M.; Myers, RC; Theisen, S., On renormalization group flows and the a-theorem in 6d, JHEP, 10, 011 (2012) · Zbl 1397.81179 |
| [77] | Hinterbichler, K.; Joyce, A.; Khoury, J.; Miller, GEJ, DBI Realizations of the Pseudo-Conformal Universe and Galilean Genesis Scenarios, JCAP, 12, 030 (2012) |
| [78] | Di Vecchia, P.; Marotta, R.; Mojaza, M., Double-soft behavior of the dilaton of spontaneously broken conformal invariance, JHEP, 09, 001 (2017) · Zbl 1382.81177 |
| [79] | Aharony, O.; Gubser, SS; Maldacena, JM; Ooguri, H.; Oz, Y., Large N field theories, string theory and gravity, Phys. Rept., 323, 183 (2000) · Zbl 1368.81009 |
| [80] | C.V. Johnson, D-branes, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2005), [DOI] [INSPIRE]. |
| [81] | D. Baumann and L. McAllister, Inflation and String Theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press (5, 2015), [DOI] [arXiv:1404.2601] [INSPIRE]. · Zbl 1339.83003 |
| [82] | A. Altland and B. Simons, Condensed matter field theory, Cambridge University Press (2006). · Zbl 1141.81017 |
| [83] | Akhoury, R.; Alfakih, A., Invariant background field method for chiral Lagrangians including Wess-Zumino terms, Annals Phys., 210, 81 (1991) · Zbl 0875.47007 |
| [84] | Curtright, TL; Zachos, CK, Geometry, Topology and Supersymmetry in Nonlinear Models, Phys. Rev. Lett., 53, 1799 (1984) |
| [85] | J. Gates, S. J., C.M. Hull and M. Roček, Twisted Multiplets and New Supersymmetric Nonlinear Sigma Models, Nucl. Phys. B248 (1984) 157 [INSPIRE]. |
| [86] | Shmakova, M., One loop corrections to the D3-brane action, Phys. Rev. D, 62, 104009 (2000) |
| [87] | Wen, C.; Zhang, S-Q, D3-Brane Loop Amplitudes from M5-Brane Tree Amplitudes, JHEP, 07, 098 (2020) · Zbl 1451.83103 |
| [88] | H. Elvang, M. Hadjiantonis, C.R.T. Jones and S. Paranjape, Electromagnetic Duality and D3-Brane Scattering Amplitudes Beyond Leading Order, arXiv:2006.08928 [INSPIRE]. · Zbl 1462.81154 |
| [89] | Klein, R.; Malek, E.; Roest, D.; Stefanyszyn, D., No-go theorem for a gauge vector as a spacetime Goldstone mode, Phys. Rev. D, 98 (2018) |
| [90] | Cheung, C.; Kampf, K.; Novotny, J.; Shen, C-H; Trnka, J.; Wen, C., Vector Effective Field Theories from Soft Limits, Phys. Rev. Lett., 120, 261602 (2018) |
| [91] | Novotny, J., Geometry of special Galileons, Phys. Rev. D, 95 (2017) |
| [92] | Přeučil, F.; Novotný, J., Special Galileon at one loop, JHEP, 11, 166 (2019) · Zbl 1429.81051 |
| [93] | Poisson, E.; Pound, A.; Vega, I., The motion of point particles in curved spacetime, Living Rev. Rel., 14, 7 (2011) · Zbl 1316.83024 |
| [94] | DeWitt, BS; Stora, R., Relativity, groups and topology: Proceedings, 40th Summer School of Theoretical Physics — Session 40: Les Houches, France, June 27 - August 4, 1983 (1984), Amsterdam, The Netherlands: North-holland, Amsterdam, The Netherlands |
| [95] | Brown, LS, Stress Tensor Trace Anomaly in a Gravitational Metric: Scalar Fields, Phys. Rev. D, 15, 1469 (1977) |
| [96] | Brown, LS; Cassidy, JP, Stress Tensor Trace Anomaly in a Gravitational Metric: General Theory, Maxwell Field, Phys. Rev. D, 15, 2810 (1977) |
| [97] | Hinterbichler, K.; Joyce, A., Hidden symmetry of the Galileon, Phys. Rev. D, 92 (2015) |
| [98] | de Rham, C.; Fasiello, M.; Tolley, AJ, Galileon Duality, Phys. Lett. B, 733, 46 (2014) · Zbl 1370.70054 |
| [99] | De Rham, C.; Keltner, L.; Tolley, AJ, Generalized galileon duality, Phys. Rev. D, 90 (2014) |
| [100] | Kampf, K.; Novotny, J., Unification of Galileon Dualities, JHEP, 10, 006 (2014) |
| [101] | Noller, J.; Scargill, JHC, The decoupling limit of Multi-Gravity: Multi-Galileons, Dualities and More, JHEP, 05, 034 (2015) · Zbl 1388.83600 |
| [102] | Heisenberg, L.; Steinwachs, CF, Geometrized quantum Galileons, JCAP, 02, 031 (2020) · Zbl 1489.83089 |
| [103] | Heisenberg, L.; Noller, J.; Zosso, J., Horndeski under the quantum loupe, JCAP, 10, 010 (2020) · Zbl 1494.83012 |
| [104] | D. Roest, The Special Galileon as Goldstone of Diffeomorphisms, arXiv:2004.09559 [INSPIRE]. · Zbl 1459.81078 |
| [105] | Bärvinsky, AO; Vilkovisky, GA, The generalized Schwinger-De Witt technique and the unique effective action in quantum gravity, Phys. Lett. B, 131, 313 (1983) |
| [106] | A.O. Bärvinsky and G.A. Vilkovisky, Covariant perturbation theory. 2: Second order in the curvature. General algorithms, Nucl. Phys. B333 (1990) 471 [INSPIRE]. |
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