Higgs Mechanism with Type-II Nambu-Goldstone Bosons at Finite Chemical Potential

Understand

When the spontaneous symmetry breaking occurs for systems without Lorentz covariance, there arises possible mismatch, $N_{\rm NG} < N_{\rm BG}$, between numbers of Nambu-Goldstone (NG) bosons ($N_{\rm NG}$) and the numbers of broken generators ($N_{\rm BG}$.

• In such a situation, so-called type-II NG bosons emerge.
• We study how the gauge bosons acquire masses through the Higgs mechanism under this mismatch by employing gauge theories with complex scalar field at finite chemical potential and by enforcing &#34;charge&#34; neutrality.
• To separate the physical spectra from unphysical ones, the $R_{\xi}$ gauge is adopted.