The D^4 R^4 term in type IIB string theory on T^2 and U-duality

Abstract

We propose a manifestly U-duality invariant modular form for the D^4 R^4 interaction in type IIB string theory compactified on T^2. It receives perturbative contributions upto two loops, and non-perturbative contributions from D-instantons and (p,q) string instantons wrapping T^2. We provide evidence for this modular form by showing that the coefficients at tree level and at one loop precisely match those obtained using string perturbation theory. Using duality, parts of the perturbative amplitude are also shown to match exactly the results obtained from eleven dimensional supergravity compactified on T^3 at one loop. Decompactifying the theory to nine dimensions, we obtain a U-duality invariant modular form, whose coefficients at tree level and at one loop agree with string perturbation theory.

25 pages, LaTeX

References in corpus (27)

• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Effects of D-instantons
• U-duality and M-Theory
• One loop in eleven dimensions
• Three-Loop Superfiniteness of N=8 Supergravity
• Supersymmetry Constraints on Type IIB Supergravity
• On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons
• Duality and higher derivative terms in M theory
• D-instantons, Strings and M-theory
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Two loops in eleven dimensions
• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• The low energy expansion of the one-loop type II superstring amplitude
• Heterotic / type I duality and D-brane instantons
• Two-loop superstrings and S-duality
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• New Higher-Derivative $R^4$ Theorems
• Eisenstein Series and String Thresholds
• On Brillouin Zones
• A note on non-perturbative R^4 couplings
• One-loop four-graviton amplitude in eleven-dimensional supergravity
• $R^4$ couplings, the fundamental membrane and exceptional theta correspondences
• U-duality and D-brane Combinatorics
• Eisenstein Series in String Theory
• Connections between M-theory and superstrings

Cited by in corpus (46)

• On the modular structure of the genus-one Type II superstring low energy expansion
• Automorphic properties of low energy string amplitudes in various dimensions
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• $R^4$ couplings and automorphic unipotent representations
• Small representations, string instantons, and Fourier modes of Eisenstein series (with an appendix by D. Ciubotaru and P. Trapa)
• Eisenstein series and automorphic representations
• Loops in exceptional field theory
• $D^6{R}^4$ amplitudes in various dimensions
• Poisson equation for the Mercedes diagram in string theory at genus one
• D-instantons, String Field Theory and Two Dimensional String Theory
• Normalization of Type IIB D-instanton Amplitudes
• Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes
• Minimal unitary representations from supersymmetry
• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• The two D6R4 type invariants and their higher order generalisation
• Poisson equation for the three loop ladder diagram in string theory at genus one
• The D^6 R^4 term in type IIB string theory on T^2 and U-duality
• S-matrix elements from T-duality
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• Perturbation Theory From 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
• Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
• Constraining the D3-brane effective action
• Supersymmetry constraints on the R^4 multiplet in type IIB on T^2
• Ramond-Ramond corrections to type II supergravity at order ${\alpha }^{\prime 3}$
• Cancellation of divergences up to three loops in exceptional field theory
• On S-duality of D${}_3$-brane S-matrix
• Sphere-level Ramond-Ramond couplings in Ramond-Neveu-Schwarz formalism
• SL(2,Z)-invariance and D-instanton contributions to the $D^6{R}^4$ interaction
• S-duality of tree-level S-matrix elements in D${}_3$-brane effective action
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• Perturbative type II amplitudes for BPS interactions
• S-duality invariant dilaton couplings at order ${\alpha }^{\prime 3}$
• Higher derivative type II string effective actions, automorphic forms and E11
• S-duality constraint on higher-derivative couplings
• S-duality of color-ordered amplitudes
• Perturbative higher-derivative terms in N=6 asymmetric orbifolds
• Light cone quantization and interactions of a new closed bosonic string inspired to D1 string
• Non--analytic terms from nested divergences in maximal supergravity
• Transcendentality violation in type IIB string amplitudes
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity
• Poisson equations, higher derivative automorphic forms and string parameter limits
• Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
• Worldsheet (anti)instanton bound states in type II on $T^2$
• Symmetries of non-maximal supergravities with higher-derivative corrections