Abstract
In this contribution we review how holographic tools can be used to study the dependence on the CP-breaking θ parameter of various observables in a large Nc Yang-Mills model. Relevant examples are the ground-state energy density, the string tension, the glueball mass spectrum and the critical temperature for deconfinement. These observables have been also studied, in the small θ regime and up to very few powers of θ 2 , in pure Yang-Mills on the Lattice. The holographic results qualitatively agree with available Lattice data and, being exact in θ , provide benchmarks for higher order corrections.
Highlights
Instanton configurations naturally induce a topological term in the Lagrangian for a S U(Nc) Yang-Mills gauge theory
The use of numerical simulations on Euclidean Lattices is limited since the θ term is imaginary and Monte Carlo methods fail to converge
The above gravity background is regular and in particular, since g00(u0) 0, it describes a confining gauge theory. This will be made explicit in a moment when the string tension of the model will be computed
Summary
Instanton configurations naturally induce a topological term in the Lagrangian for a S U(Nc) Yang-. The map between a QFT and a theory of gravity is one-to-one, when the dual pairs are embedded into a consistent ten dimensional string theory model This feature is crucially based on the properties of the so called Dp-branes, p + 1 dimensional hyperplanes over which the open strings can end (here "D" stands for Dirichlet boundary conditions). The holographic model qualitatively agrees with available Lattice data in the small θ regime, confirming that mass scales get reduced by θ to leading order and providing possible benchmarks for higher order corrections As it is shown in [10], holographic tools allow to extract the θ-dependence of observables like the ’t Hooft loop, the baryon mass (vertex) and the entanglement entropy, which are not under control using other techniques. It is possible to introduce massive quarks and study the physics of the associated QCD-like holographic model, obtaining interesting results concerning for example the vacuum structure of the theory or the calculation of the neutron electric dipole moment [11]
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