On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons

Abstract

We obtain the exact non-perturbative thresholds of $R^4$ terms in IIB string theory compactified to eight and seven dimensions. These thresholds are given by the perturbative tree-level and one-loop results together with the contribution of the D-instantons and of the (p,q)-string instantons. The invariance under U-duality is made manifest by rewriting the sum as a non-holomorphic modular function of the corresponding discrete U-duality group. In the eight-dimensional case, the threshold is the sum of a order-1 Eisenstein series for SL(2,Z) and a order-3/2 Eisenstein series for SL(3,Z). The seven-dimensional result is given by the order-3/2 Eisenstein series for SL(5,Z). We also conjecture formulae for the non-perturbative thresholds in lower dimensional compactifications and discuss the relation with M-theory.

24 pages; v6: Eqs 5.27, 5.28 fixed, refs updated, see note added

Cited by in corpus (147)

• U-duality and M-Theory
• Aspects of Quadratic Gravity
• R^4 terms in 11 dimensions and conformal anomaly of (2,0) theory
• Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace
• Two-loop superstrings and S-duality
• On the modular structure of the genus-one Type II superstring low energy expansion
• Automorphic properties of low energy string amplitudes in various dimensions
• Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
• String theory dualities and supergravity divergences
• Non-compact Calabi--Yau Manifolds and Localized Gravity
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• D-instantons and twistors
• M-Theory and U-duality on T^d with Gauge Backgrounds
• Interconnections between type II superstrings, M theory and N=4 supersymmetric Yang--Mills
• $R^4$ couplings and automorphic unipotent representations
• Minimal representations, spherical vectors, and exceptional theta series I
• A note on non-perturbative R^4 couplings
• Automorphic Forms and Fermion Masses
• Small representations, string instantons, and Fourier modes of Eisenstein series (with an appendix by D. Ciubotaru and P. Trapa)
• Low-Scale Closed Strings and their Duals
• On α' corrections in N=1 F-theory compactifications
• On a supersymmetric completion of the R^4 term in IIB supergravity
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• One-Loop BPS amplitudes as BPS-state sums
• Eisenstein series and automorphic representations
• Type IIB $R^4{H}^{4g-4}$ Conjectures
• Topological $R^4$ Inflation
• Logarithmic loop corrections, moduli stabilisation and de Sitter vacua in string theory
• Higher Derivative Couplings and Heterotic-Type I Duality in Eight Dimensions
• Nonlinear multidimensional cosmological models with form fields: stabilization of extra dimensions and the cosmological constant problem
• Instantons in N=2 magnetized D-brane worlds
• D-instanton partition functions
• Loops in exceptional field theory
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• Higher derivatives in Type II and M-theory on Calabi-Yau threefolds
• On higher-order corrections in M theory
• Poisson equation for the Mercedes diagram in string theory at genus one
• $D^6{R}^4$ amplitudes in various dimensions
• R^2 Corrections for 5D Black Holes and Rings
• D-instantons, String Field Theory and Two Dimensional String Theory
• Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry
• Subleading Corrections and Central Charges in the AdS/CFT Correspondence
• Calculable e^{-1/λ} Effects
• On M-theory fourfold vacua with higher curvature terms
• Duality completion of higher derivative corrections
• Normalization of Type IIB D-instanton Amplitudes
• Construction of $R^4$ Terms in N=2 D=8 Superspace
• Toward the Determination of R^3F^2 Terms in M-theory
• Systematics of the ${\alpha }^{\prime }$ Expansion in F-Theory
• Minimal unitary representations from supersymmetry
• IIA String Theory on Calabi-Yau Fourfolds with Background Fluxes
• $1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver
• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• Fluxed M5-instantons in F-theory
• Tetrahedral modular graph functions
• Fuzzball geometries and higher derivative corrections for extremal holes
• From maximal to minimal supersymmetry in string loop amplitudes
• Summing up D-instantons in N=2 supergravity
• Eisenstein Series in String Theory
• The two D6R4 type invariants and their higher order generalisation
• Duality Groups, Automorphic Forms and Higher Derivative Corrections
• Duality group actions on fermions
• Type II string theory and modularity
• Higher Derivative Supergravities in Diverse Dimensions
• On a supersymmetric completion of the $R^4$ term in type IIB supergravity
• Poisson equation for the three loop ladder diagram in string theory at genus one
• On the supersymmetric completion of the $R^4$ term in M-theory
• T-Duality, and the K-Theoretic Partition Function of TypeIIA Superstring Theory
• The Automorphic Membrane
• The effective action of warped M-theory reductions with higher-derivative terms - Part II
• Species scale, worldsheet CFTs and emergent geometry
• The One-Loop H^2R^3 and H^2(DH)^2R Terms in the Effective Action
• Eisenstein series for infinite-dimensional U-duality groups
• R^4 Corrections to Eleven Dimensional Supergravity via Supersymmetry
• Supergravity divergences, supersymmetry and automorphic forms
• The D^6 R^4 term in type IIB string theory on T^2 and U-duality
• S-matrix elements from T-duality
• Two Conjectures on Gauge Theories, Gravity, and Infinite Dimensional Kac-Moody Groups
• Stabilising all Kähler moduli in perturbative LVS
• U-duality Twists and Possible Phase Transitions in 2+1D Supergravity
• Perturbation Theory From Automorphic Forms
• Infrared divergences and harmonic anomalies in the two-loop superstring effective action
• The D^6 R^4 term from three loop maximal supergravity
• Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
• U-duality covariant membranes
• Supersymmetry constraints on the R^4 multiplet in type IIB on T^2
• Strong Coupling Effects in non-commutative spaces from OM Theory and supergravity
• S and U-duality Constraints on IIB S-matrices
• Exact ${\nabla }^4{R}^4$ couplings and helicity supertraces
• Ramond-Ramond corrections to type II supergravity at order ${\alpha }^{\prime 3}$
• On S-duality of D${}_3$-brane S-matrix
• Cancellation of divergences up to three loops in exceptional field theory
• Notes on Soliton Bound-State Problems in Gauge Theory and String Theory
• Sphere-level Ramond-Ramond couplings in Ramond-Neveu-Schwarz formalism
• U-Duality and the Compactified Gauss-Bonnet Term
• Note on de Sitter vacua from perturbative and non-perturbative dynamics in type IIB/F-theory compactifications
• Type II and heterotic one loop string effective actions in four dimensions
• Emergent/Composite axions
• Low momentum expansion of one loop amplitudes in heterotic string theory
• Exact thresholds and instanton effects in D=3 string theories
• Non-derivative Axionic Couplings to Nucleons at large and small N
• S-duality of tree-level S-matrix elements in D${}_3$-brane effective action
• D-instanton and polyinstanton effects from type I' D0-brane loops
• U-duality from Matrix Membrane Partition Function
• Emergence of $R^4$-terms in M-theory
• Remarks on the effects of quantum corrections on moduli stabilization and de Sitter vacua in type IIB string theory
• The automorphic NS5-brane
• DLCQ of M-Theory as the Light-Like Limit
• Arithmetic and Hyperbolic Structures in String Theory
• On string one-loop correction to the Einstein-Hilbert term and its implications on the Kahler potential
• Connections between M-theory and superstrings
• Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories
• $D^6{R}^4$ curvature corrections, modular graph functions and Poincaré series
• Tree-level S-matrix elements from S-duality
• 1/8-BPS Couplings and Exceptional Automorphic Functions
• U-duality p-Branes in Diverse Dimensions
• Seeking de-Sitter Vacua in the String Landscape
• D1/D5 systems in $\mathcal{N}=4$ string theories
• S-duality invariant dilaton couplings at order ${\alpha }^{\prime 3}$
• Perturbative type II amplitudes for BPS interactions
• Axion RG flows and the holographic dynamics of instanton densities
• S-duality of color-ordered amplitudes
• Functional determinants, index theorems, and exact quantum black hole entropy
• Higher derivative type II string effective actions, automorphic forms and E11
• S-duality constraint on higher-derivative couplings
• Fivebrane instantons and higher derivative couplings in type I theory
• Discrete anomalies in supergravity and consistency of string backgrounds
• Static solutions in the R^4 brane world
• Two Ramond-Ramond corrections to type II supergravity via field-theory amplitude
• Perturbative higher-derivative terms in N=6 asymmetric orbifolds
• Light cone quantization and interactions of a new closed bosonic string inspired to D1 string
• On four-derivative terms in IIB Calabi-Yau orientifold reductions
• $R^2$ Dark Energy in the Laboratory
• Transcendentality violation in type IIB string amplitudes
• Non--analytic terms from nested divergences in maximal supergravity
• Parameters, limits and higher derivative type II string corrections
• Poisson equations, higher derivative automorphic forms and string parameter limits
• Constraining non--BPS interactions from counterterms in three loop maximal supergravity
• Effects of D-instantons in string amplitudes
• Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
• Saturating unitarity bounds at U-duality symmetric points
• Minimal gauge invariant couplings at order ${\ell }_p^6$ in M-theory
• Worldsheet (anti)instanton bound states in type II on $T^2$
• Symmetries of non-maximal supergravities with higher-derivative corrections
• Domain Walls in AdS-Einstein-scalar Gravity
• Some finite terms from ladder diagrams in three and four loop maximal supergravity
• U-duality and M-theory, an algebraic approach