Infrared divergences and harmonic anomalies in the two-loop superstring effective action

Abstract

We analyze the pertubative contributions to the $D^4{R}^4$ and $D^6{R}^4$ couplings in the low-energy effective action of type II string theory compactified on a torus $T^d$, with particular emphasis on two-loop corrections. In general, it is necessary to introduce an infrared cut-off $\Lambda$ to separate local interactions from non-local effects due to the exchange of massless states. We identify the degenerations of the genus-two Riemann surface which are responsible for power-like dependence on $\Lambda$, and give an explicit prescription for extracting the $\Lambda$-independent effective couplings. These renormalized couplings are then shown to be eigenmodes of the Laplace operator with respect to the torus moduli, up to computable anomalous source terms arising in the presence of logarithmic divergences, in precise agreement with predictions from U-duality. Our results for the two-loop $D^6{R}^4$ contribution also probe essential properties of the Kawazumi-Zhang invariant

23 pages

References in corpus (13)

• 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
• Modular properties of two-loop maximal supergravity and connections with string theory
• $D^6{R}^4$ amplitudes in various dimensions
• Constraining Higher Derivative Supergravity with Scattering Amplitudes
• Johnson's homomorphisms and the Arakelov-Green function
• Minimal unitary representations from supersymmetry
• A Theta lift representation for the Kawazumi-Zhang and Faltings invariants of genus-two Riemann surfaces
• The two D6R4 type invariants and their higher order generalisation
• Supergravity divergences, supersymmetry and automorphic forms
• The D^6 R^4 term from three loop maximal supergravity
• SL(2,Z)-invariance and D-instanton contributions to the $D^6{R}^4$ interaction
• $\mathcal{E}{\nabla }^4{R}^4$ type invariants and their gradient expansion

Cited by in corpus (12)

• Eisenstein series and automorphic representations
• Loops in exceptional field theory
• On exponential suppression of the cosmological constant in non-SUSY strings at two loops and beyond
• Poisson equation for the Mercedes diagram in string theory at genus one
• A Theta lift representation for the Kawazumi-Zhang and Faltings invariants of genus-two Riemann surfaces
• Poisson equation for the three loop ladder diagram in string theory at genus one
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Perturbative type II amplitudes for BPS interactions
• Supergravity limit of genus two modular graph functions in the worldline formalism
• Non--analytic terms from nested divergences in maximal supergravity
• Worldsheet (anti)instanton bound states in type II on $T^2$