N = 4 Yang-Mills and N = 8 supergravity as limits of string theories

Green, Michael; Schwarz, John H.; Brink, Lars

doi:10.1016/0550-3213(82)90336-4

Cited by 512 publications

(571 citation statements)

References 6 publications

Supporting

Mentioning

529

Contrasting

Unclassified

Order By: Relevance

“…It was shown that a squaring relation exists for the coefficients of various multi-loop integrals appearing in the two answers, similar to a relation found at one loop [7,8]. This result was obtained for all terms in the two-loop amplitudes, and for some of the terms in higher-loop amplitudes (those that can be reconstructed entirely from two-particle unitarity cuts).…”

Section: Introductionsupporting

confidence: 59%

Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

Dixon¹

1998

View full text Add to dashboard Cite

By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the 'maximally helicity-violating' amplitudes in N = 8 supergravity, and the 'all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n ≤ 6, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found 'dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N = 4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n ≤ 6 N = 8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations.

show abstract

Section: Introductionsupporting

confidence: 59%

Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

Dixon¹

1998

View full text Add to dashboard Cite

show abstract

“…In particular, it has been confirmed that the duality holds for the three-loop four-point amplitude of N = 4 sYM theory [30]. (The one-and two-loop four-point amplitudes [8,52,53] in this theory also manifestly satisfy the duality). Similarly, the duality-satisfying five-point one-, two-and three-loop amplitudes of N = 4 sYM theory have recently been constructed [33].…”

Section: A Duality Between Color and Kinematicsmentioning

confidence: 74%

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

et al. 2012

View full text Add to dashboard Cite

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.

show abstract

“…In §III, we divide up the integration over moduli of the torus -including the positions of the vertex operators -into 3 inequivalent regions which transform into one another under duality [11,14]. We exhibit a formal equivalence of the amplitudes with an infinite sum over φ 3 quantum field theory box diagrams in which each propagator can have a different mass.…”

Section: Introductionmentioning

confidence: 99%

The box graph in superstring theory

D’Hoker

Phong

1995

Nuclear Physics B

View full text Add to dashboard Cite

In theories of closed oriented superstrings, the one loop amplitude is given by a single diagram, with the topology of a torus. Its interpretation had remained obscure, because it was formally real, converged only for purely imaginary values of the Mandelstam variables, and had to account for the singularities of both the box graph and the one particle reducible graphs in field theories. We present in detail an analytic continuation method which resolves all these difficulties. It is based on a reduction to certain minimal amplitudes which can themselves be expressed in terms of double and single dispersion relations, with explicit spectral densities. The minimal amplitudes correspond formally to an infinite superposition of box graphs on φ 3 like field theories, whose divergence is responsible for the poles in the string amplitudes.

show abstract

N = 4 Yang-Mills and N = 8 supergravity as limits of string theories

Cited by 512 publications

References 6 publications

Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

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

The box graph in superstring theory

Contact Info

Product

Resources

About