Cancellation of divergences up to three loops in exceptional field theory

Abstract

We consider the tetrahedral three-loop diagram in $E_d$ exceptional field theory evaluated as a scalar diagram for four external gravitons. At lowest order in momenta, this diagram contributes to the ${\nabla }^6{R}^4$ term in the low-energy effective action for M-theory. We evaluate explicitly the sums over the discrete exceptional field theory loop momenta that become sums over 1/2-BPS states in the compact exceptional space. These sums can be rewritten as Eisenstein series that solve the homogeneous differential equations that supersymmetry implies for the ${\nabla }^6{R}^4$ coupling. We also show how our results, even though sums over 1/2-BPS states, are consistent with expected 1/4-BPS contributions to the couplings.

40 pages

References in corpus (13)

• Generalised Geometry for M-Theory
• Three-Loop Superfiniteness of N=8 Supergravity
• Generalized Geometry and M theory
• Exceptional Field Theory III: E${}_{8(8)}$
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Generalised diffeomorphisms for E${}_9$
• $D^6{R}^4$ amplitudes in various dimensions
• Minimal unitary representations from supersymmetry
• Protected couplings and BPS dyons in half-maximal supersymmetric string vacua
• The D^6 R^4 term from three loop maximal supergravity

Cited by in corpus (13)

• The Geometry, Branes and Applications of Exceptional Field Theory
• D-instantons, String Field Theory and Two Dimensional String Theory
• Normalization of Type IIB D-instanton Amplitudes
• AdS${}_7$ Black-Hole Entropy and 5D $\mathcal{N}=2$ Yang-Mills
• On supersymmetric E11 exceptional field theory
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• The Forced Soliton Equation and Semiclassical Soliton Form Factors
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Accelerating Solitons
• Worldsheet (anti)instanton bound states in type II on $T^2$
• Computation of the leading order contributions to the Lamb shift for the H atom using spectral regularization
• The canonical formulation of E${}_{6(6)}$ exceptional field theory