Loops in exceptional field theory

Abstract

We study certain four-graviton amplitudes in exceptional field theory in dimensions $D\ge 4$ up to two loops. As the formulation is manifestly invariant under the U-duality group $E_{11-D}(\mathbb{Z})$, our resulting expressions can be expressed in terms of automorphic forms. In the low energy expansion, we find terms in the M-theory effective action of type $R^4$, ${\nabla }^4{R}^4$ and ${\nabla }^6{R}^4$ with automorphic coefficient functions in agreement with independent derivations from string theory. This provides in particular an explicit integral formula for the exact string theory ${\nabla }^6{R}^4$ threshold function. We exhibit moreover that the usual supergravity logarithmic divergences cancel out in the full exceptional field theory amplitude, within an appropriately defined dimensional regularisation scheme. We also comment on terms of higher derivative order and the role of the section constraint for possible counterterms.

1+78 pages: v2: Added references and typos corrected. Version accepted by JHEP. v3: corrected discussion of associativity in EFT and other typos

References in corpus (25)

• Double Field Theory
• Generalised Geometry for M-Theory
• Generalized Geometry and M theory
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• Exceptional Field Theory III: E${}_{8(8)}$
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• T-duality and ${\alpha }^{\prime }$-corrections
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Modular properties of two-loop maximal supergravity and connections with string theory
• $D^6{R}^4$ amplitudes in various dimensions
• Minimal unitary representations from supersymmetry
• Enhanced Coset Symmetries and Higher Derivative Corrections
• Curvature corrections and Kac-Moody compatibility conditions
• The two D6R4 type invariants and their higher order generalisation
• Aspects of higher curvature terms and U-duality
• Exceptional geometry and Borcherds superalgebras
• Supergravity divergences, supersymmetry and automorphic forms
• The D^6 R^4 term from three loop maximal supergravity
• Infrared divergences and harmonic anomalies in the two-loop superstring effective action
• E11 and exceptional field theory
• Finite Transformations in Doubled and Exceptional Space
• Twistors and supertwistors for exceptional field theory

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• Beyond E11
• One-loop Finiteness of Chiral Higher Spin Gravity
• D-instantons, String Field Theory and Two Dimensional String Theory
• Extended geometries
• E${}_9$ exceptional field theory I. The potential
• Normalization of Type IIB D-instanton Amplitudes
• A master exceptional field theory
• AdS${}_7$ Black-Hole Entropy and 5D $\mathcal{N}=2$ Yang-Mills
• On supersymmetric E11 exceptional field theory
• Higher Derivative Supergravities in Diverse Dimensions
• Poisson equation for the three loop ladder diagram in string theory at genus one
• E${}_{7(7)}$ Exceptional Field Theory in Superspace
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• Cancellation of divergences up to three loops in exceptional field theory
• The Forced Soliton Equation and Semiclassical Soliton Form Factors
• New classes of bi-axially symmetric solutions to four-dimensional Vasiliev higher spin gravity
• Emergence of $R^4$-terms in M-theory
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Accelerating Solitons
• Finite Gauge Transformations and Geometry in Extended Field Theory
• Non--analytic terms from nested divergences in maximal supergravity
• Reductions of Exceptional Field Theories
• Canonical analysis of E${}_{6(6)}(\mathbb{R})$ invariant five dimensional (super-)gravity
• Exotic Aspects of Extended Field Theories
• Worldsheet (anti)instanton bound states in type II on $T^2$
• Symmetries of non-maximal supergravities with higher-derivative corrections
• The canonical formulation of E${}_{6(6)}$ exceptional field theory