Heterotic/Type II Triality and Instantons on $K_3$

Abstract

A detailed understanding of instanton effects for half-BPS couplings is pursued in theories with 16 supersymmetries. In particular, we investigate the duality between heterotic string on $T^4$ and type IIA on $K_3$ at the $T^4/Z_2$ orbifold point, as well as their higher and lower dimensional versions. We present a remarkably clean quantitative test of the duality at the level of $F^4$ couplings, by completely matching a purely one-loop heterotic amplitude to a purely tree-level type II result. The triality of SO(4,4) and several other miracles are shown to be crucial for the duality to hold. Exact non-perturbative new results for type I', F on $K_3$, M on $K_3$, and IIB on $K_3$ are found, and the general form of D-instanton contributions in type IIA or B on $T^4/Z_2$ is obtained. We also analyze the NS5-brane contributions in type II on $K_3\times T^2$, and predict the value $\mu (N)={\sum }_{d|N}(1/d^3)$ for the bulk contribution to the index of the NS5-brane world-volume theory on $K_3\times T^2$.

52 pages, uses JHEP.cls; v2: minor corrections and 2 refs added. Final version for JHEP

References in corpus (6)

• Superpotentials and Membrane Instantons
• A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6
• Duality and Instantons in String Theory
• Instantons in $\mathcal{N}=2$ $Sp(N)$ Superconformal Gauge Theories and the AdS/CFT Correspondence
• Type I' and Real Algebraic Geometry
• Heterotic/type I duality, D-instantons and an N=2 AdS/CFT correspondence

Cited by in corpus (45)

• Brane-World Gravity
• Precision Counting of Small Black Holes
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Breaking GUT Groups in F-Theory
• A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6
• Minimal representations, spherical vectors, and exceptional theta series I
• D-branes in Standard Model building, Gravity and Cosmology
• Exotic instanton counting and heterotic/type I' duality
• Little String Theory and Heterotic/Type II Duality
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• String instantons, fluxes and moduli stabilization
• Update of D3/D7-Brane Inflation on K3 x T^2/Z_2
• $D^6{R}^4$ amplitudes in various dimensions
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• Invariants and divergences in half-maximal supergravity theories
• Stringy instanton corrections to N=2 gauge couplings
• N=4 Superconformal Bootstrap of the K3 CFT
• Fivebrane Instanton Corrections to the Universal Hypermultiplet
• On symmetries of N=(4,4) sigma models on T^4
• N=4 Topological Amplitudes and String Effective Action
• Mirror Symmetry on Kummer Type K3 Surfaces
• Non-perturbative Vacuum Destabilization and D-brane Dynamics
• Unoriented D-brane Instantons vs Heterotic worldsheet Instantons
• Four-derivative couplings and BPS dyons in heterotic CHL orbifolds
• Exact thresholds and instanton effects in D=3 string theories
• An Entropy-Weighted Sum over Non-Perturbative Vacua
• Inside an Enhancon: Monopoles and Dual Yang-Mills Theory
• Supersymmetry Constraints and String Theory on K3
• Borcherds Algebras and N=4 Topological Amplitudes
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Arithmetic and Hyperbolic Structures in String Theory
• Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• N=4 BPS black holes and octonionic twistors
• Heterotic-Type II duality and wrapping rules
• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• String-String triality for d=4, Z_2 orbifolds
• Discrete anomalies in supergravity and consistency of string backgrounds
• Combinatorics, observables, and String Theory: part II
• K-theoretic matching of brane charges in S- and U-duality
• Gravitational couplings of orientifold planes
• Umbral Moonshine and String Duality
• One loop amplitude for Heterotic string on $T^2$
• D-instantons and Dualities in String Theory
• Notes on unoriented D-brane instantons