Curvature squared invariants in six-dimensional $\mathcal{N}=(1,0)$ supergravity

Abstract

We describe the supersymmetric completion of several curvature-squared invariants for $\mathcal{N}=(1,0)$ supergravity in six dimensions. The construction of the invariants is based on a close interplay between superconformal tensor calculus and recently developed superspace techniques to study general off-shell supergravity-matter couplings. In the case of minimal off-shell Poincaré supergravity based on the dilaton-Weyl multiplet coupled to a linear multiplet as a conformal compensator, we describe off-shell supersymmetric completions for all the three possible purely gravitational curvature-squared terms in six dimensions: Riemann, Ricci, and scalar curvature squared. A linear combination of these invariants describes the off-shell completion of the Gauss-Bonnet term, recently presented in arXiv:1706.09330. We study properties of the Einstein-Gauss-Bonnet supergravity, which plays a central role in the effective low-energy description of ${\alpha }^{\prime }$-corrected string theory compactified to six dimensions, including a detailed analysis of the spectrum about the ${\mathrm{AdS}}_3\times {\mathrm{S}}^3$ solution. We also present a novel locally superconformal invariant based on a higher-derivative action for the linear multiplet. This invariant, which includes gravitational curvature-squared terms, can be defined both coupled to the standard-Weyl or dilaton-Weyl multiplet for conformal supergravity. In the first case, we show how the addition of this invariant to the supersymmetric Einstein-Hilbert term leads to a dynamically generated cosmological constant and non-supersymmetric (A)dS${}_6$ solutions. In the dilaton-Weyl multiplet, the new off-shell invariant includes Ricci and scalar curvature-squared terms and possesses a nontrivial dependence on the dilaton field.

V3: 70 pages, 2 tables; added comments and references; version published in JHEP

References in corpus (82)

• Evidence for F-Theory
• Compactifications of F-Theory on Calabi--Yau Threefolds -- II
• Compactifications of F-Theory on Calabi--Yau Threefolds -- I
• Comments on String Dynamics in Six Dimensions
• A Note on the Green - Schwarz Mechanism in Open - String Theories
• Towards a Naturally Small Cosmological Constant from Branes in 6D Supergravity
• Six-Dimensional Supergravity on S^3 X AdS_3 and 2d Conformal Field Theory
• Four Dimensional String/String/String Triality
• Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions
• R^4 Couplings in M and Type II Theories
• A field-theory motivated approach to symbolic computer algebra
• Anomaly Cancellation in Six Dimensions
• Low-Energy Analysis of $M$ and $F$ Theories on Calabi-Yau Threefolds
• Warped Brane Worlds in Six Dimensional Supergravity
• Spectrum of D=6, N=4b Supergravity on AdS_3 x S^3
• 3-Branes and Uniqueness of the Salam-Sezgin Vacuum
• String loop corrections to the universal hypermultiplet
• Supergravity couplings: a geometric formulation
• Introducing Cadabra: a symbolic computer algebra system for field theory problems
• Higher-derivative couplings in string theory: dualities and the B-field
• N=1 Conformal Superspace in Four Dimensions
• New Couplings of Six-Dimensional Supergravity
• Charge Lattices and Consistency of 6D Supergravity
• Off-shell supergravity-matter couplings in three dimensions
• 4D N = 2 Supergravity and Projective Superspace
• Anomaly-Free Supersymmetric Models in Six Dimensions
• Stable de Sitter Vacua from N=2 Supergravity
• Mapping 6D N = 1 supergravities to F-theory
• Tensor and Vector Multiplets in Six-Dimensional Supergravity
• String Theory Effects on Five-Dimensional Black Hole Physics
• General Axisymmetric Solutions and Self-Tuning in 6D Chiral Gauged Supergravity
• New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term
• Component Actions from Curved Superspace: Normal Coordinates and Ectoplasm
• On conformal supergravity and projective superspace
• 5D Supergravity and Projective Superspace
• Conformal supergravity in five dimensions: New approach and applications
• Conformal supergravity in three dimensions: New off-shell formulation
• N=2 Conformal Superspace in Four Dimensions
• Anomalous Magnetic Properties of Sr2YRuO6
• Super-Weyl invariance in 5D supergravity
• Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry
• A String and M-theory Origin for the Salam-Sezgin Model
• Conformal supergravity in three dimensions: Off-shell actions
• TASI Lectures on Supergravity and String Vacua in Various Dimensions
• All Couplings of Minimal Six-dimensional Supergravity
• All Off-Shell R^2 Invariants in Five Dimensional N=2 Supergravity
• Quantization of anomaly coefficients in 6D $\mathcal{N}=(1,0)$ supergravity
• Five-dimensional Superfield Supergravity
• Invariants for minimal conformal supergravity in six dimensions
• Ectoplasm Has No Topology
• Six-dimensional Supergravity and Projective Superfields
• N=6 superconformal gravity in three dimensions from superspace
• Structure in 6D and 4D N=1 supergravity theories from F-theory
• Couplings of self-dual tensor multiplet in six dimensions
• Higher Derivative Extension of 6D Chiral Gauged Supergravity
• The component structure of conformal supergravity invariants in six dimensions
• More anomaly-free models of six-dimensional gauged supergravity
• Gauss-Bonnet supergravity in six dimensions
• TASI Lectures on F-theory
• Component reduction in N=2 supergravity: the vector, tensor, and vector-tensor multiplets
• A systematic search for anomaly-free supergravities in six dimensions
• Supersymmetric Completion of Gauss-Bonnet Combination in Five Dimensions
• Off-shell N=(1,0), D=6 supergravity from superconformal methods
• A New Anomaly-Free Gauged Supergravity in Six Dimensions
• Fine Tuning and Six-Dimensional Gauged $N=(1,0)$ Supergravity Vacua
• Conformal supergravities as Chern-Simons theories revisited
• 2D N=(4,4) superspace supergravity and bi-projective superfields
• The three-form multiplet in N=2 superspace
• On curvature squared terms in N = 2 supergravity
• A new approach to curved projective superspace
• The linear multiplet and ectoplasm
• On 2D N=(4,4) superspace supergravity
• On supersymmetric Chern-Simons-type theories in five dimensions
• D=6, N=2, F(4)-Supergravity with supersymmetric de Sitter Background
• Off-Shell N=2 Linear Multiplets in Five Dimensions
• New superconformal multiplets and higher derivative invariants in six dimensions
• Superforms in Simple Six-dimensional Superspace
• N=2 Supergravity Counterterms, Off and On Shell
• Higher-derivative supergravity in U(1) superspace
• Spectrum of Higher Derivative 6D Chiral Supergravity
• Spinorial geometry, off-shell Killing spinor identities and higher derivative 5D supergravities
• Non-conformal supercurrents in six dimensions

Cited by in corpus (23)

• Higher Derivative Supergravities in Diverse Dimensions
• Superconformal geometries and local twistors
• On curvature-squared invariants of minimal five-dimensional supergravity from superspace
• New higher derivative action for tensor multiplet in N=2 conformal supergravity in four dimensions
• Hyper-Dilaton Weyl Multiplets of 5D and 6D Minimal Conformal Supergravity
• Improved Wald formalism and First Law of Dyonic Black Strings with Mixed Chern-Simons Terms
• Curvature squared action in four dimensional $N=2$ supergravity using the dilaton Weyl multiplet
• Negative Corrections to Black Hole Entropy from String Theory
• Dualization of Higher Derivative Heterotic Supergravities in $6D$ and $10D$
• Higher derivative couplings of hypermultiplets
• Dimensional reduction of higher derivative heterotic supergravity
• Symmetries of $\mathcal{N}=(1,0)$ supergravity backgrounds in six dimensions
• Attractor Mechanism and Non-Renormalization Theorem in 6D (1,0) Supergravity
• Rotating Strings in Six-Dimensional Higher-Derivative Supergravity
• Off-shell invariants of linearized $4D,\mathcal{N}=2$ supergravity in the harmonic approach
• Local supertwistors and conformal supergravity in six dimensions
• Dyonic Black Strings and the Charge Lattice in Salam-Sezgin model
• Force-free higher derivative Einstein-Maxwell theory and multi-centered black holes
• Off-Shell $\mathcal{N}=(1,0)$ Linear Multiplets in Six Dimensions
• Six-dimensional $\mathcal{N}=(2,0)$ Conformal Superspace
• ${\alpha }^{\prime }$-corrections to Near Extremal Dyonic Strings and Weak Gravity Conjecture
• Four-derivative Corrections to Minimal Gauged Supergravity in Five Dimensions
• Hyper-Dilaton Weyl Multiplet of 4D, $\mathcal{N}=2$ Conformal Supergravity