Anomaly Cancellation in Six Dimensions

Abstract

I show that anomaly cancellation conditions are sufficient to determine the two most important topological numbers relevant for Calabi-Yau compactification to six dimensions. This reflects the fact that K3 is the only non-trivial CY manifold in two complex dimensions. I explicitly construct the Green-Schwarz counterterms and derive sum rules for charges of additional enhanced U(1) factors and compare the results with all possible Abelian orbifold constructions of K3. This includes asymmetric orbifolds as well, showing that it is possible to regain a geometrical interpretation for this class of models. Finally, I discuss some models with a broken $E_7$ gauge group which will be useful for more phenomenological applications.

19 pages, UPR-0567T

References in corpus (2)

• No Mirror Symmetry in Landau-Ginzburg Spectra!
• Comment on the Generation Number in Orbifold Compactifications

Cited by in corpus (117)

• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Weak Scale Superstrings
• Comments on String Dynamics in Six Dimensions
• Towards a Naturally Small Cosmological Constant from Branes in 6D Supergravity
• Lectures on Superstring and M Theory Dualities
• Loop-Corrected Compactifications of the Heterotic String with Line Bundles
• F-Theory and the Mordell-Weil Group of Elliptically-Fibered Calabi-Yau Threefolds
• Anomaly polynomial of general 6d SCFTs
• Warped Brane Worlds in Six Dimensional Supergravity
• Global aspects of the space of 6D N = 1 supergravities
• New Phases of String Theory and 6d RG Fixed Points via Branes at Orbifold Singularities
• Anomaly Equations and Intersection Theory
• F-Theory Compactifications with Multiple U(1)-Factors: Constructing Elliptic Fibrations with Rational Sections
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Toric bases for 6D F-theory models
• (0,2) Heterotic Gauge Couplings and their M-Theory Origin
• Strings of Minimal 6d SCFTs
• Anomaly-Free Supersymmetric Models in Six Dimensions
• Mapping 6D N = 1 supergravities to F-theory
• General Axisymmetric Solutions and Self-Tuning in 6D Chiral Gauged Supergravity
• New Constraints (and Motivations) for Abelian Gauge Bosons in the MeV-TeV Mass Range
• Elliptic Fibrations with Rank Three Mordell-Weil Group: F-theory with U(1) x U(1) x U(1) Gauge Symmetry
• Type IIB Orientifolds with NS-NS Antisymmetric Tensor Backgrounds
• Chains of N=2, D=4 heterotic/type II duals
• SUSY Breaking and Moduli Stabilization from Fluxes in Gauged 6D Supergravity
• Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry
• Non-Perturbative Properties of Heterotic String Vacua Compactified on $K3\times T^2$
• MSLED: A Minimal Supersymmetric Large Extra Dimensions Scenario
• Resolutions of C^n/Z_n Orbifolds, their U(1) Bundles, and Applications to String Model Building
• From strings to the MSSM
• On the Hodge structure of elliptically fibered Calabi-Yau threefolds
• 6D supergravity without tensor multiplets
• Universal Features of BPS Strings in Six-dimensional SCFTs
• A bound on 6D N=1 supergravities
• Merging Heterotic Orbifolds and K3 Compactifications with Line Bundles
• UV Caps and Modulus Stabilization for 6D Gauged Chiral Supergravity
• General U(1)xU(1) F-theory Compactifications and Beyond: Geometry of unHiggsings and novel Matter Structure
• 4D Anomalous U(1)'s, their masses and their relation to 6D anomalies
• Brane webs, $5d$ gauge theories and $6d$ $\mathcal{N}$$=(1,0)$ SCFT's
• Non-Perturbative Heterotic D=6,4 Orbifold Vacua
• Calabi-Yau threefolds with large h^{2, 1}
• The frozen phase of F-theory
• Structure in 6D and 4D N=1 supergravity theories from F-theory
• Localized anomalies in orbifold gauge theories
• Chiral 2d Theories from N=4 SYM with Varying Coupling
• AdS${}_7$/CFT${}_6$ with orientifolds
• Non-Higgsable QCD and the Standard Model Spectrum in F-theory
• Putting string/string duality to the test
• Asymmetric Orbifolds and Higher Level Models
• Massive U(1)s and Heterotic Five-Branes on K3
• A systematic search for anomaly-free supergravities in six dimensions
• Non-Supersymmetric Orbifolds
• The 6D SuperSwirl
• Notes on Supersymmetric Gauge Theories in Five and Six Dimensions
• Anomalies of the SO(32) five-brane and their cancellation
• A New Anomaly-Free Gauged Supergravity in Six Dimensions
• Curvature squared invariants in six-dimensional $\mathcal{N}=(1,0)$ supergravity
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• Local SU(5) Unification from the Heterotic String
• Duality in String Theory
• On the Duality between Perturbative Heterotic Orbifolds and M-Theory on T^4/Z_N
• Proton Hexality in Local Grand Unification
• Split symmetries
• On elliptic genera of 6d string theories
• Anomaly-Free Brane Worlds in Seven Dimensions
• Algebraic Cycles and Local Anomalies in F-Theory
• Generic matter representations in 6D supergravity theories
• Dimensionless Coupling of Bulk Scalars at the LHC
• Anomaly Cancellation in Seven-Dimensional Supergravity with a Boundary
• Exotic matter on singular divisors in F-theory
• Large U(1) charges in F-theory
• Chiral fermions and anomaly cancellation on orbifolds with Wilson lines and flux
• Stable Vacua for Tachyonic Strings
• Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction
• Three-Index Symmetric Matter Representations of SU(2) in F-Theory from Non-Tate Form Weierstrass Models
• Abelian F-theory Models with Charge-3 and Charge-4 Matter
• Heterotic non-Abelian orbifolds
• The Geometry of the SU(2)$\times$ G${}_2$-model
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• A New Orientifold of C^2/Z_N and Six-dimensional RG Fixed Points
• Anomalies on Six Dimensional Orbifolds
• Matter in transition
• Localization of heterotic anomalies on various hyper surfaces of T^6/Z_4
• Gauged D=7 Supergravity on the S**1/Z_2 Orbifold
• Supersymmetric codimension-two branes and U(1)_R mediation in 6D gauged supergravity
• F-theory duals of singular heterotic K3 mode
• Charge completeness and the massless charge lattice in F-theory models of supergravity
• Gravity mediated supersymmetry breaking in six dimensions
• D-instanton and polyinstanton effects from type I' D0-brane loops
• Light Axiodilatons: Matter Couplings, Weak-Scale Completions and Long-Distance Tests of Gravity
• Global tensor-matter transitions in F-theory
• Chiral Generations on Intersecting 5-branes in Heterotic String Theory
• D=6, N=1 String Vacua and Duality
• An infinite swampland of U(1) charge spectra in 6D supergravity theories
• A note on T^5/Z_2 compactification of the M-theory matrix model
• Distributed SUSY Breaking: Dark Energy, Newton's Law and the LHC
• The Fate of Discrete 1-Form Symmetries in 6d
• Moduli Dependent Non-Holomorphic Contributions of Massive States to Gravitational Couplings and $C^2$-Terms in $Z_N$-Orbifold Compactifications
• Heterotic warped Eguchi-Hanson spectra with five-branes and line bundles
• de Sitter vacua and supersymmetry breaking in six-dimensional flux compactifications
• 6D Effective Action of Heterotic Compactification on K3 with nontrivial Gauge Bundles
• Constraint on Spinor-Vector Dualities in Six Dimensions
• F-theory models with $U(1)\times {\mathbb{Z}}_2,{\mathbb{Z}}_4$ and transitions in discrete gauge groups
• Flavor Symmetries and Automatic Enhancement in the 6d Supergravity Swampland
• Gauge Coupling Unification in Six Dimensions
• Discrete anomalies in supergravity and consistency of string backgrounds
• Generating functions for intersection products of divisors in resolved F-theory models
• Local Grand Unification in the Heterotic Landscape
• The Master Equation for the Prepotential-Pub
• Transitions of Orbifold Vacua
• Gauge Coupling Unification in a 6D SO(10) Orbifold GUT
• Orders of Vanishing and U(1) Charges in F-theory
• Anomaly Cancelations in Orientifolds with Quantized B Flux
• SO(8) and G_2 X G_2 N=1 Supergravities in D=6
• Assisted baryon number violation from $4k+2$ dimensions
• 6d $\mathcal{N}=(1,0)$ anomalies on $S^1$ and F-theory implications
• Anomalies, D-flatness and Small Instantons