The closed-string 3-loop amplitude and S-duality

Abstract

The low-energy limit of the four-point 3-loop amplitude (including its overall coefficient) is computed in both type IIA and IIB superstring theories using the pure spinor formalism. The result is shown to agree with the prediction of the coefficient for the type IIB $D^6{R}^4$ interaction made by Green and Vanhove based on S-duality considerations.

26 pages, harvmac. v3: factor of 3 in section 3.3 corrected, updated abstract and dropped Z_3-symmetry argument

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• Constraining Higher Derivative Supergravity with Scattering Amplitudes
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• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
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• Superstring loop amplitudes from the field theory limit
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• Modular Forms and $SL(2,\mathbb{Z})$-covariance of type IIB superstring theory
• The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals
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• The two-loop superstring five-point amplitude and S-duality
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• Integrated Massive Vertex Operator in Pure Spinor Formalism
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• One-loop superstring six-point amplitudes and anomalies in pure spinor superspace
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• Hierarchy of Modular Graph Identities
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• Non-analytic terms of string amplitudes from partial waves
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