Abstract
Effects of the θ parameter are studied in Witten’s model of holographic 4d Yang-Mills, where θ is the coefficient of the CP-breaking topological term. First, the gravity background, including the full backreaction of the RR form dual to the θ parameter, is revisited. Then, a number of observables are computed holographically: the ground-state energy density, the string tension, the ’t Hooft loop, the light scalar glueball mass, the baryon mass scale, the critical temperature for deconfinement — and thus the whole (T, θ) phase diagram — and the entanglement entropy. A simple rule is provided to derive the θ corrections to (at least) all the CP-neutral observables of the model. Some of the observables we consider can and have been in fact studied in pure 4d Yang-Mills on the lattice. In that framework the results, obtained in the small θ regime, are given up to very few powers of θ2. The corresponding holographic results agree qualitatively with available lattice data and signal an overall mass scale reduction by θ. Moreover, being exact in θ, they provide a benchmark for higher order corrections in Yang-Mills.
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Bigazzi, F., Cotrone, A.L. & Sisca, R. Notes on theta dependence in holographic Yang-Mills. J. High Energ. Phys. 2015, 90 (2015). https://doi.org/10.1007/JHEP08(2015)090
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DOI: https://doi.org/10.1007/JHEP08(2015)090