Weak coupling large-N transitions at finite baryon density

Abstract

We study thermodynamics of free SU(N ) gauge theory with a large number of colours and flavours on a three-sphere, in the presence of a baryon number chemical potential. Reducing the system to a holomorphic large-N matrix integral, paying specific attention to theories with scalar flavours (squarks), we identify novel third-order deconfining phase transitions as a function of the chemical potential. These transitions in the complex large-N saddle point configurations are interpreted as "melting" of baryons into (s)quarks. They are triggered by the exponentially large (∼ e N ) degeneracy of light baryon-like states, which include ordinary baryons, adjoint-baryons and baryons made from different spherical harmonics of flavour fields on the three-sphere. The phase diagram of theories with scalar flavours terminates at a phase boundary where baryon number diverges, representing the onset of Bose condensation of squarks.

Phase transitions of a (super) quantum mechanical matrix model with a chemical potential

“…The D-dependence of the power b is obtained in The bosonic result can be compared with the phase diagram in figure 1 of ref. [34]. The power behavior (4.1) for 0 < b < 1 is consistent with figure 1 of ref.…”

“…The power behavior (4.1) for 0 < b < 1 is consistent with figure 1 of ref. [34] in that this curve is convex upward. On the other hand, the saw-tooth features at low temperature and µ > 0.5 could not be observed in the bosonic action (2.12), since |u 1 | simply increases monotonically with respect to µ at low temperature, as is indicated in fig.…”

Heavy quark density in $ \mathcal{N} $ = 4 SYM: from hedgehog to Lifshitz spacetimes

“…The Hawking-Page deconfinement transition at infinite 't Hooft coupling has its zero coupling analogue which is driven by the Hagedorn growth of states. For theories with fundamental flavours on S 3 , in the Veneziano large-N limit, continuous deconfinement transitions have been shown to exist at finite quark density, and these are driven by the exponentially large degeneracy (∼ e N ) of baryon-like states [46]. It would be extremely interesting to understand if there is any sign of this physics within the smeared string setup in global AdS 5 .…”

Complex saddle points and disorder lines in QCD at finite temperature and density

“…A useful expansion for βðm − μÞ ≫ 1 can be generated by expanding the logarithm in Eq. (18) and integrating term by term [37]. Such an expansion gives…”

“…If a single CK-symmetric saddle point dominates the effective potential, then the sign problem is solved, at least for a particular phenomenological model. Such CK-symmetric saddle points have been seen before in finite density calculations [16][17][18][19]. Going beyond a saddlepoint approximation will usually require a consideration of the properties of the integration contour under CK symmetry.…”