Structures on the Conformal Manifold in Six Dimensional Theories

Abstract

The tensors which may be defined on the conformal manifold for six dimensional CFTs with exactly marginal operators are analysed by considering the response to a Weyl rescaling of the metric in the presence of local couplings. It is shown that there are three symmetric two index tensors only one of which satisfies any positivity conditions. The general results are specialised to the six dimensional conformal theory defined by free two-forms and also to the interacting scalar ${\varphi }^3$ theory at two loops which preserves conformal invariance to this order. All three two index tensor contributions are present.

31 pages; v3: Result for Branson operator for general d added; v4: Minor additions, typos fixed

References in corpus (3)

• Conformal collider physics: Energy and charge correlations
• Holographic c-theorems in arbitrary dimensions
• A challenge to the $a$-theorem in six dimensions

Cited by in corpus (34)

• A Constraint on Defect and Boundary Renormalization Group Flows
• Anomalies, Conformal Manifolds, and Spheres
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• $C_T$ for Non-unitary CFTs in Higher Dimensions
• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• Einstein Gravity from Conformal Gravity in 6D
• On the conformal properties of topological terms in even dimensions
• Einstein-AdS action, renormalized volume/area and holographic Renyi entropies
• $C_T$ for higher derivative conformal fields and anomalies of (1,0) superconformal 6d theories
• Two-loop renormalization of multiflavor ${\varphi }^3$ theory in six dimensions and the trace anomaly
• Weyl Consistency Conditions in Non-Relativistic Quantum Field Theory
• Conformal renormalization of scalar-tensor theories
• Constraints on Perturbative RG Flows in Six Dimensions
• Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories
• The a-function in six dimensions
• Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly
• The a-function in three dimensions: beyond leading order
• Simple recipe for holographic Weyl anomaly
• Self-dual 6d 2-form fields coupled to non-abelian gauge field: quantum corrections
• Conformal Renormalization of topological black holes in AdS${}_6$
• Scheme invariants in phi^4 theory in four dimensions
• Partition functions of higher derivative conformal fields on conformally related spaces
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• Holographic Trace Anomaly and Local Renormalization Group
• $Q$-curvature and gravity
• The a-function for N=2 supersymmetric gauge theories in three dimensions
• Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all
• Conformally covariant operators of mixed-symmetry tensors and MAGs
• AdS/CFT and local renormalization group with gauge fields
• Covariantly Constant Anomalies on Conformal Manifolds
• Sphere free energy of scalar field theories with cubic interactions
• The local renormalization of super-Yang-Mills theories
• On heat coefficients, multiplicative anomaly and 4D Casimir energy for GJMS operators
• Holographic Weyl Anomaly and Kounterterms in AdS gravity