# Spontaneous CP breaking and the axion potential: an effective Lagrangian approach

- Institution: CERN
- Department: TH String Theory Seminar
- Speaker: Gabriele Veneziano
- Year: 2017
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3010144)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

After a quick review of the U(1) and strong-CP problems in QCD I will turn to some recent work on spontaneous CP violation in QCD at vacuum angle $\theta = \pi$ and to its possible relevance for determining the axion potential at temperatures up to the deconfinement temperature $T_c$.

Using an effective Lagrangian approach, valid in the double large-N and chiral limit (with $r_i \sim m_i N/\Lambda$ fixed), we determine the regions in the multidimensional parameter space of the $r_i$ where CP is spontaneously broken/unbroken at $\theta=\pi$. The two regions are separated by an hypersurface on which lines of first order transitions end, there is a massless pseudoscalar meson (in spite of chiral symmetry being explicitly broken), and the topological susceptibility of QCD diverges.

When we add to the model a generic axion field (in order to ensure CP at all values of $\theta$) the above considerations have a bearing on the shape of the axion potential near the boundary of its periodicity interval. This may have implications on the calculation of axionic dark matter abundance if some $r_i$ have a marked temperature dependence as one approaches $T_c$. .

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## Lectures

1. [Spontaneous CP breaking and the axion potential: an effective Lagrangian approach](https://invisiblenetwork.ai/learn/cern/3010144/d72066018a98), 1 h 21 min (CERN's player)