E 7(7) symmetry in perturbatively quantised $ \mathcal{N} = 8 $ supergravity

Bossard, Guillaume; Hillmann, Christian; Nicolai, Hermann

doi:10.1007/jhep12(2010)052

Cited by 64 publications

(134 citation statements)

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“…The SU(8) subgroup of E 7(7) was shown to be non-anomalous at oneloop long ago [41]. More recently, Bossard, Hillmann and Nicolai [42], using a formulation for the vector fields that has manifest electric-magnetic duality, but is not Lorentz covariant, have extended this result to the full E 7(7) symmetry, and to all orders in perturbation theory.…”

Section: Counterterm Constraintsmentioning

confidence: 93%

Amplitudes and ultraviolet behavior of N = 8 supergravity

Bern¹,

Carrasco²,

Dixon³

et al. 2011

Fortschritte der Physik

107

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Section: Counterterm Constraintsmentioning

confidence: 93%

Amplitudes and ultraviolet behavior of N = 8 supergravity

Bern¹,

Carrasco²,

Dixon³

et al. 2011

Fortschritte der Physik

107

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“…Upon using these identities and summing over all permutations we find that the UV pole has the form, 20) where M tree 4 is the four-point tree-level supergravity amplitude, and…”

Section: B N = 8 Supergravity Vacuum Graphs At Four Loopsmentioning

confidence: 99%

“…Subsequently it was realized [19] that this counterterm is forbidden in D = 4 by the E 7(7) duality symmetry [12]. Other analyses have extended the finiteness constraints from E 7 (7) and linearized supersymmetry, such that the first potential divergence in D = 4 is now at seven loops [20][21][22][23]. Finiteness until this loop order happens to agree with an earlier naive power-counting, based on the assumption of an off-shell N = 8 superspace [24].…”

mentioning

confidence: 99%

Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes

et al. 2012

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We use the duality between color and kinematics to simplify the construction of the complete four-loop four-point amplitude of N = 4 super-Yang-Mills theory, including the nonplanar contributions. The duality completely determines the amplitude's integrand in terms of just two planar graphs. The existence of a manifestly dual gauge-theory amplitude trivializes the construction of the corresponding N = 8 supergravity integrand, whose graph numerators are double copies (squares) of the N = 4 super-Yang-Mills numerators. The success of this procedure provides further nontrivial evidence that the duality and double-copy properties hold at loop level. The new form of the four-loop four-point supergravity amplitude makes manifest the same ultraviolet power counting as the corresponding N = 4 super-Yang-Mills amplitude. We determine the amplitude's ultraviolet pole in the critical dimension of D = 11/2, the same dimension as for N = 4 super-Yang-Mills theory. Strikingly, exactly the same combination of vacuum integrals (after simplification) describes the ultraviolet divergence of N = 8 supergravity as the subleading-in-1/N 2 c single-trace divergence in N = 4 super-Yang-Mills theory.

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“…Perturbative finiteness of d = 4 N = 8 SUGRA is possible only if its E 7(7) symmetry is anomalyfree [26,27,28,29]. Even when the symmetry is anomalous, as in pure N = 4 SUGRA, its Ward identities can restrict counterterms [30,31,32].…”

Section: Introductionmentioning

confidence: 99%

Iwasawa nilpotency degree of non compact symmetric cosets in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} $\end{document}‐extended supergravity

Cacciatori

Cerchiai

Ferrara

et al. 2014

Fortschritte der Physik

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We analyze the polynomial part of the Iwasawa realization of the coset representative of non compact symmetric Riemannian spaces. We start by studying the role of Kostant's principal SU (2) P subalgebra of simple Lie algebras, and how it determines the structure of the nilpotent subalgebras. This allows us to compute the maximal degree of the polynomials for all faithful representations of Lie algebras. In particular the metric coefficients are related to the scalar kinetic terms while the representation of electric and magnetic charges is related to the coupling of scalars to vector field strengths as they appear in the Lagrangian.We consider symmetric scalar manifolds in N−extended supergravity in various space-time dimensions, elucidating various relations with the underlying Jordan algebras and normed Hurwitz algebras. For magic supergravity theories, our results are consistent with the Tits-Satake projection of symmetric spaces and the nilpotency degree turns out to depend only on the space-time dimension of the theory.These results should be helpful within a deeper investigation of the corresponding supergravity theory, e.g. in studying ultraviolet properties of maximal supergravity in various dimensions.

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E 7(7) symmetry in perturbatively quantised $ \mathcal{N} = 8 $ supergravity

Cited by 64 publications

References 50 publications

Amplitudes and ultraviolet behavior of N = 8 supergravity

Amplitudes and ultraviolet behavior of N = 8 supergravity

Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes

Iwasawa nilpotency degree of non compact symmetric cosets in \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathcal{N} $\end{document}‐extended supergravity

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