Arguments Against a Finite N=8 Supergravity

T. Banks

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Arguments Against a Finite N=8 Supergravity

T. Banks

High Energy Physics - Theory · Submitted 25 May 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim I present arguments based on dispersion theory and the existence of charged BPS states of small charge, that maximally supersymmetric SUGRA is not a finite theory.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.31 · compares with prior results 0.52 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

I present arguments based on dispersion theory and the existence of charged BPS states of small charge, that maximally supersymmetric SUGRA is not a finite theory. The essence of the argument is that the perturbative construction of the theory implies that scattering amplitudes are invariant under a continuous SU(8) global symmetry, which is broken by contributions from virtual BPS states. Conventional estimates of the contributions of those states above production threshold, shows that they should be order one. If the amplitude satisfies a dispersion relation with a finite number of subtractions, as has recently been argued by Giddings and Porto [1], then SU(8) violating amplitudes appear at finite orders in the low energy expansion. We also make a brief remark about the inconsistency of the idea of classicalization in non-gravitational theories.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	I present arguments based on dispersion theory and the existence of charged BPS states of small charge, that maximally supersymmetric SUGRA is not a finite theory.	result 0.63	0.88	0.95	asserted 1.00
s1	The essence of the argument is that the perturbative construction of the theory implies that scattering amplitudes are invariant under a continuous SU(8) global symmetry, which is broken by contributions from virtual BPS states.	method 0.40	0.43	0.10	asserted 1.00
s2	Conventional estimates of the contributions of those states above production threshold, shows that they should be order one.	result 0.59	0.47	0.03	asserted 0.86
s3	If the amplitude satisfies a dispersion relation with a finite number of subtractions, as has recently been argued by Giddings and Porto [1], then SU(8) violating amplitudes appear at finite orders in the low energy expansion.	result 0.63	0.19	0.14	asserted 0.64
s4	We also make a brief remark about the inconsistency of the idea of classicalization in non-gravitational theories.	contribution 0.75	0.61	0.02	asserted 0.85

What kind of paper the classifier reports this is: position or commentary 0.81 · evidence from argument 0.98.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

I present arguments based on dispersion theory and the existence of charged BPS states of small charge, that maximally supersymmetric SUGRA is not a finite theory. The essence of the argument is that the perturbative construction of the theory implies that scattering amplitudes are invariant under a continuous SU(8) global symmetry, which is broken by contributions from virtual BPS states. Conventional estimates of the contributions of those states above production threshold, shows that they should be order one. If the amplitude satisfies a dispersion relation with a finite number of subtractions, as has recently been argued by Giddings and Porto [1], then SU(8) violating amplitudes appear at finite orders in the low energy expansion. We also make a brief remark about the inconsistency of the idea of classicalization in non-gravitational theories.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
hep-th 2012-10 accept novelty 7.0 of 10

Planar maximally supersymmetric Yang-Mills theory in five dimensions has a nonzero ultraviolet divergence at six loops, with coefficient 68.68 ± 0.17 in the paper's normalization, so the theory is not ultraviolet fini...
The Five-Loop Four-Point Amplitude of N=4 super-Yang-Mills Theory
hep-th 2012-07 accept novelty 7.0 of 10

The full five-loop four-point integrand of N=4 super-Yang-Mills is constructed, and its ultraviolet divergence in D=26/5 reduces to three positive vacuum integrals with no residual cancellations.
Nonlocal quantum gravity and M-theory
hep-th 2014-04 conditional novelty 6.0 of 10

A nonlocal 11-dimensional supergravity action, built from a string-field-theory form factor, is proposed as a candidate finite and unitary field-theory limit of M-theory.
Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
hep-th 2012-09 accept novelty 6.0 of 10

Half-maximal supergravity's ultraviolet cancellations at one and two loops are the same color-factor cancellations that remove forbidden color tensors from pure Yang-Mills divergences.
Scattering Amplitudes
hep-th 2013-08 accept novelty 2.0 of 10

A graduate-level textbook review that reconstructs the on-shell amplitudes program, from spinor helicity and BCFW recursion through superamplitudes, twistors, Grassmannians, and polytopes, with worked examples and exercises.

How the literature uses it

10 arXiv papers cite this in 13 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 11 sentences without a confident label

Cites it as support 1 paper

A more explicit and general argument supporting unsubtracted dispersion relations is that, as argued in Refs. [ref] (see also [ref] ), the gravitational 2-body elastic scattering amplitude $f(s,t)$ of any theory obeying Hermitian unitarity and crossing symmetry is polynomially bound in the complex-$s$ upper half plane for fixed Mandelstam variable $t$.

New Sum Rules from Low Energy Compton Scattering on Arbitrary Spin Target · A Puzzle with $N=8$ Supergravity and a Possible Solution · 1.00

Cites it as background 1 paper

Since gravity is perturbatively non-renormalisable, its naive quantisation leads to divergent amplitudes unless some unexpected cancellation takes place.[This is only conjectured to happen for highly symmetric theories such as $𝒩=8$ supergravity (see [ref] as well as references therein for recent arguments in favour of and against this possibility).] Amplitudes in string theory, on the other hand, are believed to be finite.

Backreaction of Localised Sources in String Compactifications · Introduction · 0.88

What it cites · 14 sentences without a confident label

Cites as support 1 paper

Green, Ooguri and Schwarz [ref] have shown that there are no limits of string theory in which all the BPS states decouple.

Decoupling Supergravity from the Superstring · Introduction · 0.98

Cites as background 1 paper

There has been a lot of interest in recent years in the question of whether $N=8$ supergravity (SUGRA) has a finite S-matrix in perturbation theory [ref] .

Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity · Introduction · 1.00

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