Irreversibility and higher-spin conformal field theory

Abstract

I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.

25 pages. Presentation reorganized, with the final section moved to the beginning. CQG in press

References in corpus (4)

• Higher-spin current multiplets in operator-product expansions
• Anomalies, Unitarity and Quantum Irreversibility
• Quantum irreversibility in arbitrary dimension
• Towards the classification of conformal field theories in arbitrary even dimension

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• Weyl Covariance and the Energy Momentum Tensors of Higher-Derivative Free Conformal Field Theories
• Quantum field theories of arbitrary-spin massive multiplets and Palatini quantum gravity
• Scale vs. Conformal Invariance at the IR Fixed Point of Quantum Gravity
• Scale and Conformal Invariance on (A)dS
• A universal flow invariant in quantum field theory
• A different kind of four dimensional brane for string theory
• Conformal gauge theory of vector-spinors and spin-3/2 particles