N=2 Type II- Heterotic duality and Higher derivative F-terms

Abstract

We test the recently conjectured duality between $N=2$ supersymmetric type II and heterotic string models by analysing a class of higher dimensional interactions in the respective low-energy Lagrangians. These are $F$-terms of the form $F_g{W}^{2g}$ where $W$ is the gravitational superfield. On the type II side these terms are generated at the $g$-loop level and in fact are given by topological partition functions of the twisted Calabi-Yau sigma model. We show that on the heterotic side these terms arise at the one-loop level. We study in detail a rank 3 example and show that the corresponding couplings $F_g$ satisfy the same holomorphic anomaly equations as in the type II case. Moreover we study the leading singularities of $F_g$'s on the heterotic side, near the enhanced symmetry point and show that they are universal poles of order $2g-2$ with coefficients that are given by the Euler number of the moduli space of genus-$g$ Riemann surfaces. This confirms a recent conjecture that the physics near conifold singularity is governed by $c=1$ string theory at the self-dual point.

33 pages, latex, no figures

Cited by in corpus (100)

• Geometric Engineering of Quantum Field Theories
• Superstrings and Topological Strings at Large N
• Knot Invariants and Topological Strings
• U-duality and M-Theory
• Self-Dual Strings and N=2 Supersymmetric Field Theory
• Black Holes and Solitons in String Theory
• Precision Counting of Small Black Holes
• Classical and quantum N=2 supersymmetric black holes
• Direct Integration of the Topological String
• Topological String Partition Functions as Polynomials
• Counting higher genus curves in a Calabi-Yau manifold
• Introduction to Seiberg-Witten Theory and its Stringy Origin
• Duality Between the Webs of Heterotic and Type II Vacua
• Heterotic - type I superstring duality and low-energy effective actions
• Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
• Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
• Toric Geometry and Enhanced Gauge Symmetry of F-Theory/Heterotic Vacua
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Strong Coupling Singularities and Non-abelian Gauge Symmetries in $N=2$ String Theory
• Long-distance interactions of branes: correspondence between supergravity and super Yang-Mills descriptions
• Threshold effects in open-string theory
• Non-Perturbative Properties of Heterotic String Vacua Compactified on $K3\times T^2$
• Deformed Topological Partition Function and Nekrasov Backgrounds
• N=2 Electric-magnetic duality in a chiral background
• The Emergence Proposal in Quantum Gravity and the Species Scale
• New Higgs Transitions between Dual N=2 String Models
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Type IIB $R^4{H}^{4g-4}$ Conjectures
• Two-loop N=4 Super Yang Mills effective action and interaction between D3-branes
• Higher Derivative Couplings and Heterotic-Type I Duality in Eight Dimensions
• Holomorphic Couplings in String Theory
• N=2 symplectic reparametrizations in a chiral background
• Little String Theory and Heterotic/Type II Duality
• Special geometry in hypermultiplets
• Worldsheet Realization of the Refined Topological String
• On the Duality between the Heterotic String and F-Theory in 8 Dimensions
• Perturbative Couplings and Modular Forms in N=2 String Models with a Wilson Line
• $N=2$ heterotic string threshold correction, $K3$ surface and generalized Kac-Moody superalgebra
• A Class of N=1 Dual String Pairs and its Modular Superpotential
• Modular Symmetries of N=2 Black Holes
• Counting BPS states on the Enriques Calabi-Yau
• Calculable e^{-1/λ} Effects
• Topological Amplitudes in Heterotic Superstring Theory
• Non-Perturbative Nekrasov Partition Function from String Theory
• Fricke S-duality in CHL models
• String Duality and Modular Forms
• Instanton Numbers and Exchange Symmetries in $N=2$ Dual String Pairs
• Duality in String Theory
• Global Properties of Topological String Amplitudes and Orbifold Invariants
• Mathieu Moonshine and N=2 String Compactifications
• Black Holes and Large Order Quantum Geometry
• Higher-Order Gravitational Couplings and Modular Forms in $N=2,D=4$ Heterotic String Compactifications
• Lectures on Heterotic-Type I Duality
• Instantons, Hypermultiplets and the Heterotic String
• Conifold Transitions and Mirror Symmetries
• Threshold corrections, generalised prepotentials and Eichler integrals
• Higher Derivative F-terms in N=2 Strings
• Construction of SL(2,Z) invariant amplitudes in type IIB superstring theory
• N=4 Topological Amplitudes and String Effective Action
• Harmonicity in N=4 supersymmetry and its quantum anomaly
• Classical and Quantum Aspects of BPS Black Holes in N=2, D=4 Heterotic String Compactifications
• N=2 Type I-Heterotic Duality and Higher Derivative F-Terms
• Comments on A,B,C Chains of Heterotic and Type II Vacua
• Topological Amplitudes and Physical Couplings in String Theory
• String Vacua with N=2 Supersymmetry in Four Dimensions
• Aspects of Type I - Type II - Heterotic Triality in Four Dimensions
• Perturbative gravitational couplings and Siegel modular forms in $D=4,N=2$ string models
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Topological Amplitudes in Heterotic Strings with Wilson Lines
• Borcherds Algebras and N=4 Topological Amplitudes
• F-Theory Duals of Nonperturbative Heterotic E8xE8 Vacua in Six Dimensions
• Probing the Moduli Dependence of Refined Topological Amplitudes
• BPS states and supersymmetric index in N=2 type I string vacua
• D1/D5 systems in $\mathcal{N}=4$ string theories
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• D-branes and the Conifold Singularity
• The low-energy effective action for perturbative heterotic strings on $K_3\times T^2$ and the d=4 N=2 vector-tensor multiplet
• Towards Refining the Topological Strings on Compact Calabi-Yau 3-folds
• Heterotic-Type II duality in the hypermultiplet sector
• N=4 Topological Amplitudes and Black Hole Entropy
• Solving the Topological String on K3 Fibrations
• The Ruled Vertex and D-E Degenerations
• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• Fivebrane instantons and higher derivative couplings in type I theory
• Witten Anomaly in 4d Heterotic Compactificaitons with N = 2 Supersymmetry
• Black Hole Entropy, Quantum Corrections and EFT Transitions
• On Mathieu moonshine and Gromov-Witten invariants
• Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
• A string realisation of $\Omega$-deformed Abelian $\mathcal{N}=2^{\ast }$ theory
• Heterotic strings on $(K3\times T^2)/{\mathbb{Z}}_3$ and their dual Calabi-Yau threefolds
• The String Geometry Behind Topological Amplitudes
• Gravitational couplings in $\mathcal{N}=2$ heterotic compactifications with Wilson lines
• Refined Topological Amplitudes from the $\Omega$-Background in String Theory
• On Heterotic/Type I Duality in d=8
• $\Omega$ versus Graviphoton
• Moduli spaces of non-geometric type II/heterotic dual pairs
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Direct Computation of Monodromy Matrices and Classification of 4d N=2 Heterotic--IIA Dual Vacua
• Noncritical-Topological Correspondence: Disc Amplitudes and Noncompact Branes
• Real topological string amplitudes