Central Charge Bounds in 4D Conformal Field Theory

Abstract

We derive model-independent lower bounds on the stress tensor central charge C_T in terms of the operator content of a 4-dimensional Conformal Field Theory. More precisely, C_T is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the CFT. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition.

16 pages, 6 figures

References in corpus (15)

• Large N Field Theories, String Theory and Gravity
• The String Landscape, Black Holes and Gravity as the Weakest Force
• Bounding scalar operator dimensions in 4D CFT
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Holography from Conformal Field Theory
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• The Exact Superconformal R-Symmetry Maximizes a
• Bounds on 4D Conformal and Superconformal Field Theories
• Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
• Universal Constraints on Conformal Operator Dimensions
• Rigorous Limits on the Interaction Strength in Quantum Field Theory
• Bounds for State Degeneracies in 2D Conformal Field Theory
• A counterexample to the a-'theorem'
• Extremal N=(2,2) 2D Conformal Field Theories and Constraints of Modularity

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