Notes on theta dependence in holographic Yang-Mills

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 θ 2 . 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