Abstract
The standard lore about the sum over topological sectors in quantum field theory is that locality and cluster decomposition uniquely determine the sum over such sectors, thus leading to the usual θ-vacua. We show that without changing the local degrees of freedom, a theory can be modified such that the sum over instantons should be restricted; e.g. one should include only instanton numbers which are divisible by some integer p. This conclusion about the configuration space of quantum field theory allows us to carefully reconsider the quantization of parameters in supergravity. In particular, we show that FI-terms and nontrivial Kähler forms are quantized. This analysis also leads to a new derivation of recent results about linearized supergravity.
Similar content being viewed by others
References
Z. Komargodski and N. Seiberg, Comments on the Fayet-Iliopoulos term in field theory and supergravity, JHEP 06 (2009) 007 [arXiv:0904.1159] [SPIRES].
Z. Komargodski and N. Seiberg, Comments on supercurrent multiplets, supersymmetric field theories and supergravity, JHEP 07 (2010) 017 [arXiv:1002.2228] [SPIRES].
D.Z. Freedman, Supergravity with axial gauge invariance, Phys. Rev. D 15 (1977) 1173 [SPIRES].
R. Barbieri, S. Ferrara, D.V. Nanopoulos and K.S. Stelle, Supergravity, R invariance and spontaneous supersymmetry breaking, Phys. Lett. B 113 (1982) 219 [SPIRES].
R. Kallosh, L. Kofman, A.D. Linde and A. Van Proeyen, Superconformal symmetry, supergravity and cosmology, Class. Quant. Grav. 17 (2000) 4269 [Erratum ibid. 21 (2004) 5017] [hep-th/0006179] [SPIRES].
G. Dvali, R. Kallosh and A. Van Proeyen, D-term strings, JHEP 01 (2004) 035 [hep-th/0312005] [SPIRES].
K.R. Dienes and B. Thomas, On the inconsistency of Fayet-Iliopoulos terms in supergravity theories, Phys. Rev. D 81 (2010) 065023 [arXiv:0911.0677] [SPIRES].
S.M. Kuzenko, The Fayet-Iliopoulos term and nonlinear self-duality, Phys. Rev. D 81 (2010) 085036 [arXiv:0911.5190] [SPIRES].
S.M. Kuzenko, Variant supercurrent multiplets, JHEP 04 (2010) 022 [arXiv:1002.4932] [SPIRES].
E. Witten and J. Bagger, Quantization of Newton’s constant in certain supergravity theories, Phys. Lett. B 115 (1982) 202 [SPIRES].
G. Girardi, R. Grimm, M. Muller and J . Wess, Antisymmetric tensor gauge potential in curved superspace and a (16 + 16) supergravity multiplet, Phys. Lett. B 147 (1984) 81 [SPIRES].
W. Lang, J. Louis and B.A. Ovrut, (16+ 16) supergravity coupled to matter: the low-energy limit of the superstring, Phys. Lett. B 158 (1985) 40 [SPIRES].
W. Siegel, 16/16 supergravity, Class. Quant. Grav. 3 (1986) L47 [SPIRES].
M. Dine, N. Seiberg and E. Witten, Fayet-Iliopoulos terms in string theory, Nucl. Phys. B 289 (1987) 589 [SPIRES].
B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1 [SPIRES].
S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [SPIRES].
S.R. Coleman, More about the massive Schwinger model, Ann. Phys. 101 (1976) 239 [SPIRES].
T. Banks, M. Dine and N. Seiberg, Irrational axions as a solution of the strong CP problem in an eternal universe, Phys. Lett. B 273 (1991) 105 [hep-th/9109040] [SPIRES].
G.T. Horowitz, Exactly soluble diffeomorphism invariant theories, Commun. Math. Phys. 125 (1989) 417 [SPIRES].
T. Pantev and E. Sharpe, Notes on gauging noneffective group actions, hep-th/0502027 [SPIRES].
T. Pantev and E. Sharpe, GLSM’s for gerbes (and other toric stacks), Adv. Theor. Math. Phys. 10 (2006) 77 [hep-th/0502053] [SPIRES].
A. Caldararu, J. Distler, S. Hellerman, T. Pantev and E. Sharpe, Non-birational twisted derived equivalences in abelian GLSMs, Commun. Math. Phys. 294 (2010) 605 [arXiv:0709.3855] [SPIRES].
E. Witten, unpublished.
J. Distler and B. Wecht, unpublished, mentioned in http://golem.ph.utexas.edu/∼distler/blog/archives/002180.html.
A.H. Chamseddine and H.K. Dreiner, Anomaly free gauged R symmetry in local supersymmetry, Nucl. Phys. B 458 (1996) 65 [hep-ph/9504337] [SPIRES].
D.J. Castano, D.Z. Freedman and C. Manuel, Consequences of supergravity with gauged U(1) R symmetry, Nucl. Phys. B 461 (1996) 50 [hep-ph/9507397] [SPIRES].
P. Binetruy, G. Dvali, R. Kallosh and A. Van Proeyen, Fayet-Iliopoulos terms in supergravity and cosmology, Class. Quant. Grav. 21 (2004) 3137 [hep-th/0402046] [SPIRES].
H. Elvang, D.Z. Freedman and B. Körs, Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings, JHEP 11 (2006) 068 [hep-th/0606012] [SPIRES].
T. Kugo and T.T. Yanagida, Coupling supersymmetric nonlinear σ-models to supergravity, arXiv:1003.5985 [SPIRES].
V.P. Akulov, D.V. Volkov and V.A. Soroka, On the general covariant theory of calibrating poles in superspace, Theor. Math. Phys. 31 (1977) 285 [Teor. Mat. Fiz. 31 (1977) 12] [SPIRES].
M.F. Sohnius and P.C. West, An alternative minimal off-shell version of N = 1 supergravity, Phys. Lett. B 105 (1981) 353 [SPIRES].
N.D. Lambert and G.W. Moore, Distinguishing off-shell supergravities with on-shell physics, Phys. Rev. D 72 (2005) 085018 [hep-th/0507018] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1005.0002
Rights and permissions
About this article
Cite this article
Seiberg, N. Modifying the sum over topological sectors and constraints on supergravity. J. High Energ. Phys. 2010, 70 (2010). https://doi.org/10.1007/JHEP07(2010)070
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2010)070