We compute the one-loop beta functions of the cosmological constant, Newton’s constant and the topological mass in topologically massive supergravity in three dimensions. We use a variant of the proper time method supplemented by a simple choice of cutoff function. We also employ two different analytic continuations of AdS 3 and consider harmonic expansions on the 3-sphere as well as a 3-hyperboloid, and then show that they give the same results for the beta functions. We find that the dimensionless coefficient of the Chern-Simons term, ν, has vanishing beta function. The flow of the cosmological constant and Newton’s constant depends on ν; we study analytically the structure of the flow and its fixed points in the limits of small and large ν.
S. Deser, R. Jackiw and S. Templeton, Topologically Massive Gauge Theories, Annals Phys. 140 (1982) 372 [Erratum ibid. 185 (1988) 406] [INSPIRE].
S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General Relativity: An Einstein Centenary Survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge, U.K. (1979), pp. 790-831.
M. Niedermaier and M. Reuter, The asymptotic safety scenario in quantum gravity, Living Rev. Relativity 9 (2006) 5.
R. Percacci, Asymptotic Safety, in D. Oriti ed., Approaches to Quantum Gravity: Towards a New Understanding of Space, Time and Matter, Cambridge University Press, Cambridge, U.K. (2009) [arXiv:0709.3851] [INSPIRE].
M. Roček and P. van Nieuwenhuizen, N ≥ 2 supersymmetric Chern-Simons terms as D = 3 extended conformal supergravity, Class. Quant. Grav. 3 (1986) 43 [INSPIRE].
S. Deser and J.H. Kay, Topologically massive supergravity, Phys. Lett. B 120 (1983) 97 [INSPIRE].
S. Deser, Cosmological topological supergravity, in S.M. Christensen ed., Quantum Theory Of Gravity, Adam Hilger, London, U.K. (1984) 374.
T. Uematsu, Structure of N = 1 Conformal and Poincaré Supergravity in (1 + 1)-dimensions and (2 + 1)-dimensions, Z. Phys. C 29 (1985) 143 [INSPIRE].
G.W. Gibbons, S.W. Hawking and M.J. Perry, Path Integrals and the Indefiniteness of the Gravitational Action, Nucl. Phys. B 138 (1978) 141 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys. B 201 (1982) 469 [INSPIRE].
Z. Bern, E. Mottola and S.K. Blau, General covariance of the path integral for quantum gravity, Phys. Rev. D 43 (1991) 1212 [INSPIRE].
N.K. Nielsen, Ghost Counting in Supergravity, Nucl. Phys. B 140 (1978) 499 [INSPIRE].
P. Van Nieuwenhuizen, Supergravity, Phys. Rept. 68 (1981) 189 [INSPIRE].
R.E. Kallosh, Modified Feynman Rules in Supergravity, Nucl. Phys. B 141 (1978) 141 [INSPIRE].
S.M. Christensen, M.J. Duff, G.W. Gibbons and M. Roček, Vanishing One Loop β-function in Gauged N > 4 Supergravity, Phys. Rev. Lett. 45 (1980) 161 [INSPIRE].
I.N. McArthur, Super b 4 Coefficients in Supergravity, Class. Quant. Grav. 1 (1984) 245 [INSPIRE].
R. Percacci, On the Topological Mass in Three-dimensional Gravity, Annals Phys. 177 (1987) 27 [INSPIRE].
S. Deser and Z. Yang, Is topologically massive gravity renormalizable?, Class. Quant. Grav. 7 (1990) 1603 [INSPIRE].
B. Keszthelyi and G. Kleppe, Renormalizability of D = 3 topologically massive gravity, Phys. Lett. B 281 (1992) 33 [INSPIRE].
E.S. Fradkin and A.A. Tseytlin, One Loop Effective Potential in Gauged O(4) Supergravity, Nucl. Phys. B 234 (1984) 472 [INSPIRE].
A.A. Bytsenko, S.D. Odintsov and S. Zerbini, The Effective action in gauged supergravity on hyperbolic background and induced cosmological constant, Phys. Lett. B 336 (1994) 355 [hep-th/9408095] [INSPIRE].
S. Weinberg, Critical Phenomena for Field Theorists, lectures presented at International School of Subnuclear Physics, Ettore Majorana Foundation, Erice, Sicily, 23July - 8 August 1976, published in Erice Subnuclear Physics (1976) 1.
R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [INSPIRE].
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ArXiv ePrint: 1302.0868
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Percacci, R., Perry, M.J., Pope, C.N. et al. Beta functions of topologically massive supergravity. J. High Energ. Phys. 2014, 83 (2014). https://doi.org/10.1007/JHEP03(2014)083
- Field Theories in Lower Dimensions
- Supergravity Models
- Renormalization Group