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.
F. Morgan, Colloquium: Soap bubble clusters, Rev. Mod. Phys. 79 (2007) 821 [INSPIRE].
D. Langlois, S. Renaux-Petel, D.A. Steer and T. Tanaka, Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation, Phys. Rev. D 78 (2008) 063523 [arXiv:0806.0336] [INSPIRE].
I.S. Gerstein, R. Jackiw, S. Weinberg and B.W. Lee, Chiral loops, Phys. Rev. D 3 (1971) 2486 [INSPIRE].
S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press (2005).
S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, Cambridge University Press (2013).
L.F. Abbott, Introduction to the Background Field Method, Acta Phys. Polon. B 13 (1982) 33.
J. Honerkamp, Chiral multiloops, Nucl. Phys. B 36 (1972) 130 [INSPIRE].
L. Álvarez-Gaumé, D.Z. Freedman and S. Mukhi, The Background Field Method and the Ultraviolet Structure of the Supersymmetric Nonlinear Sigma Model, Annals Phys. 134 (1981) 85 [INSPIRE].
A.O. Bärvinsky and G.A. Vilkovisky, The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity, Phys. Rept. 119 (1985) 1 [INSPIRE].
V. Forini, V.G.M. Puletti, L. Griguolo, D. Seminara and E. Vescovi, Remarks on the geometrical properties of semiclassically quantized strings, J. Phys. A 48 (2015) 475401 [arXiv:1507.01883] [INSPIRE].
N.K. Nielsen, On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories, Nucl. Phys. B 101 (1975) 173 [INSPIRE].
R. Fukuda and T. Kugo, Gauge Invariance in the Effective Action and Potential, Phys. Rev. D 13 (1976) 3469 [INSPIRE].
I.J.R. Aitchison and C.M. Fraser, Gauge Invariance and the Effective Potential, Annals Phys. 156 (1984) 1 [INSPIRE].
C.F. Hart, Theory and renormalization of the gauge invariant effective action, Phys. Rev. D 28 (1983) 1993 [INSPIRE].
H. Georgi, On-shell effective field theory, Nucl. Phys. B 361 (1991) 339 [INSPIRE].
P.S. Howe, G. Papadopoulos and K.S. Stelle, The background field method and the non-linear σ-model, Nucl. Phys. B 296 (1988) 26 [INSPIRE].
S. Mukhi, The Geometric Background Field Method, Renormalization and the Wess-Zumino Term in Nonlinear Sigma Models, Nucl. Phys. B 264 (1986) 640 [INSPIRE].
P.B. Gilkey, The spectral geometry of a Riemannian manifold, J. Diff. Geom. 10 (1975) 601 [INSPIRE].
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].
T. Appelquist and C.W. Bernard, The Nonlinear σ Model in the Loop Expansion, Phys. Rev. D 23 (1981) 425 [INSPIRE].
D.G. Boulware and L.S. Brown, Symmetric space scalar field theory, Annals Phys. 138 (1982) 392 [INSPIRE].
R. Akhoury and Y.-P. Yao, The Nonlinear σ Model as an Effective Lagrangian, Phys. Rev. D 25 (1982) 3361 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory to One Loop, Annals Phys. 158 (1984) 142 [INSPIRE].
M.K. Gaillard, The Effective One Loop Lagrangian With Derivative Couplings, Nucl. Phys. B 268 (1986) 669 [INSPIRE].
K.M. Costa and F. Liebrand, Normal Coordinate Methods and Heavy Higgs Effects, Phys. Rev. D 40 (1989) 2014 [INSPIRE].
J.M. Martín-García, xAct, Efficient tensor computer algebra for the Wolfram Language. http://www.xact.es/.
S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1, Phys. Rev. 177 (1969) 2239 [INSPIRE].
C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2, Phys. Rev. 177 (1969) 2247 [INSPIRE].
C.V. Johnson, D-branes, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2005), [DOI] [INSPIRE].
A. Altland and B. Simons, Condensed matter field theory, Cambridge University Press (2006).
R. Akhoury and A. Alfakih, Invariant background field method for chiral Lagrangians including Wess-Zumino terms, Annals Phys. 210 (1991) 81 [INSPIRE].
T.L. Curtright and C.K. Zachos, Geometry, Topology and Supersymmetry in Nonlinear Models, Phys. Rev. Lett. 53 (1984) 1799 [INSPIRE].
J. Gates, S. J., C.M. Hull and M. Roček, Twisted Multiplets and New Supersymmetric Nonlinear Sigma Models, Nucl. Phys. B 248 (1984) 157 [INSPIRE].
B.S. DeWitt and R. Stora, eds., Relativity, groups and topology: Proceedings, 40th Summer School of Theoretical Physics — Session 40: Les Houches, France, June 27 – August 4, 1983, vol. 2, North-holland, Amsterdam, The Netherlands (1984).
L.S. Brown, Stress Tensor Trace Anomaly in a Gravitational Metric: Scalar Fields, Phys. Rev. D 15 (1977) 1469 [INSPIRE].
L.S. Brown and J.P. Cassidy, Stress Tensor Trace Anomaly in a Gravitational Metric: General Theory, Maxwell Field, Phys. Rev. D 15 (1977) 2810 [INSPIRE].
A.O. Bärvinsky and G.A. Vilkovisky, The generalized Schwinger-De Witt technique and the unique effective action in quantum gravity, Phys. Lett. B 131 (1983) 313 [INSPIRE].
A.O. Bärvinsky and G.A. Vilkovisky, Covariant perturbation theory. 2: Second order in the curvature. General algorithms, Nucl. Phys. B 333 (1990) 471 [INSPIRE].
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ArXiv ePrint: 2010.05913
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Goon, G., Melville, S. & Noller, J. Quantum corrections to generic branes: DBI, NLSM, and more. J. High Energ. Phys. 2021, 159 (2021). https://doi.org/10.1007/JHEP01(2021)159
- Effective Field Theories
- Global Symmetries
- Renormalization Regularization and Renormalons
- Space-Time Symmetries