IISER MOHALI

Abstract: The phase structure of QCD at finite baryon chemical potential remains one of the most elusive problems in strongly coupled gauge theory. Low-temperature, high-density regimes are expected to host a hierarchy of order parameters such as quark bilinears, diquark pairings, and multi-quark condensates, but the lattice sign problem and the breakdown of perturbation theory obscure first-principles access to the resulting phase diagram. Effective field theories illuminate individual phases but cannot adjudicate the competition between them.

We address this question using gauge/gravity duality as a controlled nonperturbative laboratory. Building on the universal structure of holographic superconductor backgrounds, we study a five-dimensional bulk model with two charged scalars dual to operators carrying different baryon charges and scaling dimensions. Each scalar wants to condense at a finite chemical potential, and the question is what happens when they both can: does one win, or do they coexist?

Scanning the space of operator charges and dimensions and working in both confined and deconfined phases, we map the full phase diagram in the temperature and chemical potential plane. Coexistence appears in a finite region of parameter space. Elsewhere, one condensate generically suppresses the others. This suggests that the coexistence of multiple order parameters is rare and governed by simple selection rules on operator data, constraining symmetry-breaking patterns across a wide class of holographic systems with several charged sectors well beyond the QCD setting that motivated us.