Non-renormalisation conditions in type II string theory and maximal supergravity

By M. Green, Jorge G. Russo, Pierre Vanhove. 2006

152 citations recorded by the source corpus.

This paper considers general features of the derivative expansion of Feynman diagram contributions to the four-graviton scattering amplitude in eleven-dimensional supergravity compactified on a two-torus. These are translated into statements about interactions of the form D2kR4 in type II superstring theories, assuming the standard M-theory/string theory duality relationships, which provide powerful constraints on the effective interactions. In the ten-dimensional IIA limit we find that there can be no perturbative contributions beyond k string loops (for k>0). Furthermore, the genus h = k contributions are determined exactly by the one-loop eleven-dimensional supergravity amplitude for all values of k. A plausible interpretation of these observations is that the sum of h-loop Feynman diagrams of maximally extended supergravity is less divergent than might be expected and could be ultraviolet finite in dimensions d<4+6/h – the same bound as for N = 4 Yang-Mills.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f17329e8a0e8a4ae58ed3a412ada820d8a6ef06c

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Citations in the corpus

Low energy expansion of the four-particle genus-one amplitude in type II superstring theory (2008, methodology): “The logarithmic singularities characteristic of ten dimensions are recovered in the ten-dimensional limit by a condensation of these Kaluza–Klein thresholds [7].”
Taming tree amplitudes in general relativity (2007, background): “A surprising example of this, now at the loop level, is the work of [25, 26, 27] where N = 8 supergravity has been shown to possess a remarkably good ultraviolet behavior even though a direct power counting argument indicates that bad divergencies must be present.”
Automorphic properties of low energy string amplitudes in various dimensions (2010, background): “The term proportional to r3 contains the requisite D = 8 coefficient together with a r3 log r3 term that is essential for cancelling a similar term in the sum of the infinite series of (s r2 3) m terms that reproduces the eight-dimensional s log(−l(2)8 s)R4 threshold behaviour (as described in [4, 1”