Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
Volume 28, Issue 31, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217751X13501662
Keywords
Renormalization group; beta functions
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Funding
- World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan
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We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta functions, Higgs-like relation among anomalous dimensions and a gradient property. We further conjecture that non-renormalization holds if and only if the vector operator is conserved. The local renormalization group analysis guarantees the first three within power counting renormalization. We verify all the conjectures in conformal perturbation theories and holography in the weakly coupled gravity regime.
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