Towards the full N = 4 conformal supergravity action

Ciceri, Franz; Sahoo, Bindusar

doi:10.1007/jhep01(2016)059

Cited by 15 publications

(35 citation statements)

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“…Here we will present its purely bosonic terms; full results will be reported elsewhere. When this function is constant these bosonic terms turn out to agree with a recent result derived by imposing supersymmetry on terms that are at most quadratic in the fermions [5].…”

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confidence: 83%

Construction of all N=4 conformal supergravities

et al. 2017

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All N = 4 conformal supergravities in four space-time dimensions are constructed. These are the only N = 4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1, 1)/U(1) coset space. When this function equals a constant the Lagrangian is invariant under continuous SU (1, 1) transformations. The construction of these higher-derivative invariants also opens the door to various applications for non-conformal theories.

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Construction of all N=4 conformal supergravities

et al. 2017

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“…As a final confirmation of this Lagrangian we compare it with the bosonic part of the action constructed by Ciceri and Sahoo for the same theory [165]. This version of the action contains additional gauge fields associated with the symmetries of the conformal group, which allow the full conformal symmetry (including conformal boosts) to be realized covariantly.…”

Section: (515)mentioning

confidence: 85%

“…The first of these has already been used to write down the covariant derivative (B.5c). One ultimately finds that which vanishes on support of the Maurer-Cartan equations associated with the SU(1,1)/U(1) coset space [127,165].…”

Section: B1 the Minimal Theorymentioning

confidence: 96%

“…Special conformal transformations are gauge fixed by setting b µ = 0, giving λ K,a = − 1 2 e a µ ∂ µ λ D . Then we use the following constraints on superconformal curvatures [165]: where F(φ α ) is the zeroth-degree homogeneous function introduced in the main text. When F = 1, by dropping total-derivative terms one may re-express this result as Ciceri and Sahoo's minimal Lagrangian (B.1).…”

Section: B1 the Minimal Theorymentioning

confidence: 99%

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Unraveling conformal gravity amplitudes

Johansson

Mogull

Teng

2018

J. High Energ. Phys.

100

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Conformal supergravity amplitudes are obtained from the double-copy construction using gauge-theory amplitudes, and compared to direct calculations starting from conformal supergravity Lagrangians. We consider several different theories: minimal N = 4 conformal supergravity, non-minimal N = 4 Berkovits-Witten conformal supergravity, mass-deformed versions of these theories, as well as supersymmetry truncations thereof. Coupling the theories to a Yang-Mills sector is also considered. For all cases we give the gravity Lagrangians that the double copy implicitly generates. The two main results are: we determine a Lagrangian for the non-minimal Berkovits-Witten theory, and we uncover the double-copy prescription for the minimal N = 4 conformal supergravity.

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“…This would suggest that either (i) a "non-minimal" theory does not exist as non-minimal scalar couplings are inconsistent with N = 4 supersymmetry, or (ii) a "non-minimal" N = 4 CSG exists but its UV divergences and thus anomalies are the same (i.e. non-vanishing) as in the "minimal" theory.It is the "minimal" N = 4 CSG that appeared (as the coefficient of the log cutoff term) in the quantum effective action of N = 4 SYM coupled (in the standard SU (1, 1) covariant way [8]) to the conformal supergravity background [10,11,12] or in the classical action of the 5d N = 8 gauged supergravity evaluated on the solution of the AdS 5 Dirichlet boundary problem [10]. However, one reason to expect that there should be another inequivalent version of N = 4 CSG with a non-minimal coupling f = e 4ϕ was provided [7] by dimensional reduction to 4d from 10d conformal supergravity [13] (cf.…”

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On divergences in non-minimal ${ \newcommand{\N}{{{\mathcal N}}} \N=4}$ conformal supergravity

Tseytlin¹

2017

J. Phys. A: Math. Theor.

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We review the question of quantum consistency of N = 4 conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard ("minimal") conformal supergravity where the complex scalar ϕ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to N = 4 super Yang-Mills with gauge group of dimension 4. The same turns out to be true also for the "non-minimal" N = 4 conformal supergravity with the action (recently constructed in arXiv:1609.09083) depending on an arbitrary holomorphic function f (ϕ). The special case of the "non-minimal" conformal supergravity with f = e 2ϕ appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function f and thus can be cancelled just as in the "minimal" f = 1 case by coupling the theory to four N = 4 vector multiplets.1 Also at Lebedev Institute, Moscow. tseytlin@imperial.ac.uk Conformal supergravities (CSGs) are N ≤ 4 supersymmetric extensions of the (C mnkl ) 2 Weyl gravity in 4 dimensions [1,2]. They are formally power-counting renormalizable with one coupling constant. The corresponding one-loop beta-functions were found to be non-zero [3] implying non-vanishing conformal anomaly. As the Weyl symmetry here is gauged, this means quantum inconsistency [4]. The same conclusion was reached also from the analysis of chiral SU (4) R-symmetry gauge anomalies [5], in agreement with the fact that all anomalies should belong to the same N = 4 superconformal multiplet.Remarkably, it was observed that the standard N = 4 CSG theory of [2] can be made UV finite [4,6,7] and thus anomaly-free [5] by coupling it [8] to exactly four N = 4 super Maxwell multiplets (e.g., to U (2) N = 4 super YM theory). This was shown directly at the one-loop order but should be true to all orders as the beta-function in N > 1 conformal supergravity and conformal anomaly of SYM may receive contributions only from the first loop (as follows from formal superspace arguments as in the SYM case, see [7]). In the present case of N = 4 there is also another reason for one-loop exactness: the conformal anomaly is tied by supersymmetry with SU (4) chiral anomaly which has one-loop origin.In the SU (1, 1) invariant N = 4 CSG of [2] the 4-derivative complex scalar ϕ = φ + iψ did not couple to Weyl graviton and SU (4) gauge field kinetic terms. It was conjectured in [4, 6, 7] that there may exist a "non-standard" (non SU (1, 1) invariant) version of N = 4 CSG. If one assumes that ϕ may "non-minimally" couple to Weyl term, f (ϕ)(C mnkl ) 2 + ... = (1 + k 1 φ + k 2 φ 2 + ...)(C mnkl ) 2 + ..., then there will be additional contributions to the beta-function that may cancel against the "minimal" N = 4 CSG beta-function. This finiteness conjecture was, however, in an apparent contradiction with the chiral anomaly count [5] as "non-minimal" couplings should not contribute to the chiral anomaly (see, e.g., [9]).This would suggest that either (i) a "non-minimal" theory does not exist as non-minimal scalar couplings are inc...

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Towards the full N = 4 conformal supergravity action

Abstract: Based on the known non-linear transformation rules of the Weyl multiplet fields, the action of N = 4 conformal supergravity is constructed up to terms quadratic in the fermion fields. The bosonic sector corrects a recent result in the literature.

Cited by 15 publications

References 17 publications

Construction of all N=4 conformal supergravities

Construction of all N=4 conformal supergravities

Unraveling conformal gravity amplitudes

On divergences in non-minimal ${ \newcommand{\N}{{{\mathcal N}}} \N=4}$ conformal supergravity

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