Two-loop superstrings and S-duality

Abstract

The two-loop contribution to the Type IIB low energy effective action term $D^4{R}^4$, predicted by SL(2,Z) duality, is compared with that of the two-loop 4-point function derived recently in superstring perturbation theory through the method of projection onto super period matrices. For this, the precise overall normalization of the 4-point function is determined through factorization. The resulting contributions to $D^4{R}^4$ match exactly, thus providing an indirect check of SL(2,Z) duality. The two-loop Heterotic low energy term $D^2{F}^4$ is evaluated in string perturbation theory; its form is closely related to the $D^4{R}^4$ term in Type II, although its significance to duality is an open issue.

44 pages, LaTeX, epsfig, 1 figure

References in corpus (49)

• String Theory Dynamics In Various Dimensions
• Unity of Superstring Dualities
• Evidence for Heterotic - Type I String Duality
• Effects of D-instantons
• Some Comments On String Dynamics
• One loop in eleven dimensions
• Supersymmetry Constraints on Type IIB Supergravity
• On $R^4$ threshold corrections in IIB string theory and (p,q) string instantons
• D-instantons, Strings and M-theory
• Lectures on D-branes
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Two loops in eleven dimensions
• The low energy expansion of the one-loop type II superstring amplitude
• Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace
• Ten Dimensional Heterotic String as a Soliton
• Two-Loop Superstrings I, Main Formulas
• Two-Loop Superstrings II, The Chiral Measure on Moduli Space
• Two-Loop Superstrings IV, The Cosmological Constant and Modular Forms
• Heterotic - type I superstring duality and low-energy effective actions
• String-String Duality in Ten Dimensions
• On Brillouin Zones
• Eisenstein Series and String Thresholds
• Sixteen-fermion and related terms in M-theory on T**2
• Two-Loop Superstrings III, Slice Independence and Absence of Ambiguities
• Two-Loop Superstrings V: Gauge Slice Independence of the N-Point Function
• Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II): Nonrenormalization Theorems
• A note on non-perturbative R^4 couplings
• One-loop four-graviton amplitude in eleven-dimensional supergravity
• The Box Graph In Superstring Theory
• Lectures on Two-Loop Superstrings
• On a supersymmetric completion of the R^4 term in IIB supergravity
• Type IIB $R^4{H}^{4g-4}$ Conjectures
• Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude
• Light-cone Quantum Mechanics of the Eleven-dimensional Superparticle
• On SO(32) heterotic - type I superstring duality in ten dimensions
• Construction of $R^4$ Terms in N=2 D=8 Superspace
• Explicit Modular Invariant Two-Loop Superstring Amplitude Relevant for R^4
• Trilepton Events and B_s -> mu^+ mu^- : No-lose for mSUGRA at the Tevatron?
• Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (I): Heterotic F^6 Terms at Two Loops
• Eisenstein Series in String Theory
• Dispersion Relations in String Theory
• Lectures on Heterotic-Type I Duality
• Two-Loop Superstrings in Hyperelliptic Language I: the Main Results
• Two-Loop Superstrings in Hyperelliptic Language II: the Vanishing of the Cosmological Constant and the Non-Renormalization Theorem
• Construction of SL(2,Z) invariant amplitudes in type IIB superstring theory
• Two-Loop Superstrings in Hyperelliptic Language III: the Four-Particle Amplitude
• Comments on Two-Loop Four-Particle Amplitude in Superstring Theory
• An ansatz for a non-perturbative four-graviton amplitude in type IIB superstring theory
• Factorization of the Two Loop Four-Particle Amplitude in Superstring Theory Revisited

Cited by in corpus (89)

• Duality and higher derivative terms in M theory
• On the modular structure of the genus-one Type II superstring low energy expansion
• The closed-string 3-loop amplitude and S-duality
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• The Structure of n-Point One-Loop Open Superstring Amplitudes
• Genus-One String Amplitudes from Conformal Field Theory
• Far Beyond the Planar Limit in Strongly-Coupled $\mathcal{N}=4$ SYM
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Genus-2 Holographic Correlator on $Ad{S}_5\times S^5$ from Localization
• Multiparticle one-loop amplitudes and S-duality in closed superstring theory
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• Higher genus modular graph functions, string invariants, and their exact asymptotics
• Tropical Amplitudes
• The D^4 R^4 term in type IIB string theory on T^2 and U-duality
• Eisenstein series and automorphic representations
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Superstring Scattering Amplitudes with the Pure Spinor Formalism
• The Overall Coefficient of the Two-loop Superstring Amplitude Using Pure Spinors
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• Pure Spinor Superspace Identities for Massless Four-point Kinematic Factors
• Tree-level amplitudes from the pure spinor superstring
• Exploring transcendentality in superstring amplitudes
• $D^6{R}^4$ amplitudes in various dimensions
• Poisson equation for the Mercedes diagram in string theory at genus one
• Higher genus superstring amplitudes from the geometry of moduli spaces
• Four-Point One-Loop Amplitude Computation in the Pure Spinor Formalism
• Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes
• PSS: A FORM Program to Evaluate Pure Spinor Superspace Expressions
• Superstring loop amplitudes from the field theory limit
• An R^4 non-renormalisation theorem in N=4 supergravity
• 6d (2,0) and M-theory at 1-loop
• Tetrahedral modular graph functions
• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality
• On Genus Two Riemann Surfaces Formed from Sewn Tori
• Poisson equation for the three loop ladder diagram in string theory at genus one
• 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
• One-loop Superstring Amplitude From Integrals on Pure Spinors Space
• Superstring measure and non-renormalization of the three-point amplitude
• Getting superstring amplitudes by degenerating Riemann surfaces
• The D^{10} R^4 term in type IIB string theory
• The two-loop superstring five-point amplitude and S-duality
• NSR Superstring Measures Revisited
• Two-loop vacuum energy for Calabi-Yau orbifold models
• Protected couplings and BPS dyons in half-maximal supersymmetric string vacua
• The D^6 R^4 term in type IIB string theory on T^2 and U-duality
• S-matrix elements from T-duality
• Holomorphic subgraph reduction of higher-point modular graph forms
• Type I/heterotic duality and M-theory amplitudes
• Two-loop superstring five-point amplitudes III, construction via the RNS formulation: even spin structures
• On S-duality of D${}_3$-brane S-matrix
• NSR measures on hyperelliptic locus and non-renormalization of 1,2,3-point functions
• Ramond-Ramond corrections to type II supergravity at order ${\alpha }^{\prime 3}$
• Sphere-level Ramond-Ramond couplings in Ramond-Neveu-Schwarz formalism
• Eigenvalue equation for genus two modular graphs
• Low momentum expansion of one loop amplitudes in heterotic string theory
• S-duality of tree-level S-matrix elements in D${}_3$-brane effective action
• The Super Period Matrix with Ramond Punctures in the supergravity formulation
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Relations between elliptic modular graphs
• Factorization of the Two Loop Four-Particle Amplitude in Superstring Theory Revisited
• Tree-level S-matrix elements from S-duality
• Topics in Two-Loop Superstring Perturbation Theory
• Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
• S-duality invariant dilaton couplings at order ${\alpha }^{\prime 3}$
• Perturbative type II amplitudes for BPS interactions
• S-duality of color-ordered amplitudes
• Asymptotics of the $D^8{R}^4$ genus-two string invariant
• S-duality constraint on higher-derivative couplings
• Hierarchy of Modular Graph Identities
• Cyclic products of Szegö kernels and spin structure sums I: hyper-elliptic formulation
• Modular Invariant Regularization of String Determinants and the Serre GAGA Principle
• Supergravity limit of genus two modular graph functions in the worldline formalism
• Factorization and Unitarity in Superstring Theory
• Scattering equations, supergravity integrands, and pure spinors
• Identities among higher genus modular graph tensors
• Pure spinor formulation of the superstring and its applications
• Non-analytic terms of string amplitudes from partial waves
• Poisson equation for genus two string invariants: a conjecture
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• Integrability in String Theories
• Non--analytic terms from nested divergences in maximal supergravity
• Transcendentality violation in type IIB string amplitudes
• Boundary contributions to three loop superstring amplitudes
• Finite Strings From Non-Chiral Mumford Forms
• Symmetry Algebra of IIB Superstring Scattering
• Integrating simple genus two string invariants over moduli space
• Symmetries of non-maximal supergravities with higher-derivative corrections