Abstract
We analyse the constraints from supersymmetry on ∇4 R 4 type corrections to the effective action in \( \mathcal{N}=2 \) supergravity in eight dimensions. We prove that there are two classes of invariants that descend respectively from type IIA and type IIB supergravity. We determine the first class as d-closed superforms in superspace in eight dimensions, whereas we obtain the second class by dimensional reduction down to four dimensions, in which there is a single class of invariants transforming in the next to minimal unitary representation of E 7(7).
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References
M.B. Green and M. Gutperle, Effects of D instantons, Nucl. Phys. B 498 (1997) 195 [hep-th/9701093] [INSPIRE].
M.B. Green, M. Gutperle and P. Vanhove, One loop in eleven-dimensions, Phys. Lett. B 409 (1997) 177 [hep-th/9706175] [INSPIRE].
E. Kiritsis and B. Pioline, On R 4 threshold corrections in IIB string theory and (p, q) string instantons, Nucl. Phys. B 508 (1997) 509 [hep-th/9707018] [INSPIRE].
E. D’Hoker and D.H. Phong, Two-loop superstrings VI: Non-renormalization theorems and the 4-point function, Nucl. Phys. B 715 (2005) 3 [hep-th/0501197] [INSPIRE].
M.B. Green, J.G. Russo and P. Vanhove, Low energy expansion of the four-particle genus-one amplitude in type-II superstring theory, JHEP 02 (2008) 020 [arXiv:0801.0322] [INSPIRE].
H. Gomez and C.R. Mafra, The closed-string 3-loop amplitude and S-duality, JHEP 10 (2013) 217 [arXiv:1308.6567] [INSPIRE].
M.B. Green, S.D. Miller and P. Vanhove, SL(2, \( \mathrm{\mathbb{Z}} \))-invariance and D-instanton contributions to the D 6 R 4 interaction, arXiv:1404.2192 [INSPIRE].
E. D’Hoker, M.B. Green, B. Pioline and R. Russo, Matching the D 6 R 4 interaction at two-loops, JHEP 01 (2015) 031 [arXiv:1405.6226] [INSPIRE].
M.B. Green, H.-h. Kwon and P. Vanhove, Two loops in eleven-dimensions, Phys. Rev. D 61 (2000) 104010 [hep-th/9910055] [INSPIRE].
A. Basu, Constraining non-BPS interactions from counterterms in three loop maximal supergravity, arXiv:1408.0094 [INSPIRE].
M.B. Green, J.G. Russo and P. Vanhove, Automorphic properties of low energy string amplitudes in various dimensions, Phys. Rev. D 81 (2010) 086008 [arXiv:1001.2535] [INSPIRE].
M.B. Green and S. Sethi, Supersymmetry constraints on type IIB supergravity, Phys. Rev. D 59 (1999) 046006 [hep-th/9808061] [INSPIRE].
A. Sinha, The Ĝ 4 λ 16 term in IIB supergravity, JHEP 08 (2002) 017 [hep-th/0207070] [INSPIRE].
A. Basu, Supersymmetry constraints on the R 4 multiplet in type IIB on T 2, Class. Quant. Grav. 28 (2011) 225018 [arXiv:1107.3353] [INSPIRE].
N.A. Obers and B. Pioline, Eisenstein series and string thresholds, Commun. Math. Phys. 209 (2000) 275 [hep-th/9903113] [INSPIRE].
M.B. Green and P. Vanhove, Duality and higher derivative terms in M-theory, JHEP 01 (2006) 093 [hep-th/0510027] [INSPIRE].
A. Basu, The D 4 R 4 term in type IIB string theory on T 2 and U-duality, Phys. Rev. D 77 (2008) 106003 [arXiv:0708.2950] [INSPIRE].
A. Basu, The D 6 R 4 term in type IIB string theory on T 2 and U-duality, Phys. Rev. D 77 (2008) 106004 [arXiv:0712.1252] [INSPIRE].
B. Pioline, H. Nicolai, J. Plefka and A. Waldron, R 4 couplings, the fundamental membrane and exceptional theta correspondences, JHEP 03 (2001) 036 [hep-th/0102123] [INSPIRE].
D. Kazhdan, B. Pioline and A. Waldron, Minimal representations, spherical vectors and exceptional theta series, Commun. Math. Phys. 226 (2002) 1 [hep-th/0107222] [INSPIRE].
B. Pioline and A. Waldron, The Automorphic membrane, JHEP 06 (2004) 009 [hep-th/0404018] [INSPIRE].
B. Pioline, R 4 couplings and automorphic unipotent representations, JHEP 03 (2010) 116 [arXiv:1001.3647] [INSPIRE].
M.B. Green, S.D. Miller, J.G. Russo and P. Vanhove, Eisenstein series for higher-rank groups and string theory amplitudes, Commun. Num. Theor. Phys. 4 (2010) 551 [arXiv:1004.0163] [INSPIRE].
M.B. Green, S.D. Miller and P. Vanhove, Small representations, string instantons and Fourier modes of Eisenstein series (with an appendix by D. Ciubotaru and P. Trapa), arXiv:1111.2983 [INSPIRE].
P. Fleig, A. Kleinschmidt and D. Persson, Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors, Commun. Num. TheorPhys. 08 (2014) 41 [arXiv:1312.3643] [INSPIRE].
G. Bossard and V. Verschinin, Minimal unitary representations from supersymmetry, JHEP 10 (2014) 008 [arXiv:1406.5527] [INSPIRE].
A. Joseph, Minimal realizations and spectrum generating algebras, Commun. Math. Phys. 36 (1974) 325 [INSPIRE].
A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained \( \mathcal{N}=2 \) Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav. 1 (1984) 469 [INSPIRE].
N. Berkovits, Construction of R 4 terms in \( \mathcal{N}=2 \) D = 8 superspace, Nucl. Phys. B 514 (1998) 191 [hep-th/9709116] [INSPIRE].
J.M. Drummond, P.J. Heslop, P.S. Howe and S.F. Kerstan, Integral invariants in \( \mathcal{N}=4 \) SYM and the effective action for coincident D-branes, JHEP 08 (2003) 016 [hep-th/0305202] [INSPIRE].
G. Bossard, P.S. Howe and K.S. Stelle, The Ultra-violet question in maximally supersymmetric field theories, Gen. Rel. Grav. 41 (2009) 919 [arXiv:0901.4661] [INSPIRE].
T. Voronov, Geometric integration theory on supermanifolds, Sov. Sci. Rev. C 9 (1992) 1.
S.J. Gates Jr., Ectoplasm has no topology: The Prelude, hep-th/9709104 [INSPIRE].
S.J. Gates Jr., M.T. Grisaru, M.E. Knutt-Wehlau and W. Siegel, Component actions from curved superspace: Normal coordinates and ectoplasm, Phys. Lett. B 421 (1998) 203 [hep-th/9711151] [INSPIRE].
J.M. Drummond, P.J. Heslop and P.S. Howe, A note on N = 8 counterterms, arXiv:1008.4939 [INSPIRE].
M.B. Green, J.H. Schwarz and L. Brink, \( \mathcal{N}=4 \) Yang-Mills and \( \mathcal{N}=8 \) Supergravity as Limits of String Theories, Nucl. Phys. B 198 (1982) 474 [INSPIRE].
M.B. Green, J.G. Russo and P. Vanhove, String theory dualities and supergravity divergences, JHEP 06 (2010) 075 [arXiv:1002.3805] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar, M. Perelstein and J.S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998) 401 [hep-th/9802162] [INSPIRE].
G.G. Hartwell and P.S. Howe, (N, p, q) harmonic superspace, Int. J. Mod. Phys. A 10 (1995) 3901 [hep-th/9412147] [INSPIRE].
S. Krutelevich, Jordan algebras, exceptional groups, and Bhargava composition, J. Algebra 314 (2007) 924977 [math/0411104].
S. Ferrara and J.M. Maldacena, Branes, central charges and U duality invariant BPS conditions, Class. Quant. Grav. 15 (1998) 749 [hep-th/9706097] [INSPIRE].
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Bossard, G., Verschinin, V. ε∇4 R 4 type invariants and their gradient expansion. J. High Energ. Phys. 2015, 89 (2015). https://doi.org/10.1007/JHEP03(2015)089
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DOI: https://doi.org/10.1007/JHEP03(2015)089