Thermodynamics of holographic defects

Abstract

Using the AdS/CFT correspondence, we study the thermodynamic properties and the phase diagram of matter fields on (2+1)-dimensional defects coupled to a (3+1)dimensional N = 4 SYM "heat bath". Considering a background magnetic field, (net) quark density, defect "magnitude" δN c and the mass of the matter, we study the defect contribution to the thermodynamic potentials and their first and second derivatives to map the phases and study their physical properties. We find some features that are qualitatively similar to other systems e.g. in (3+1) dimensions and a number of features that are particular to the defect nature, such as its magnetic properties, unexpected properties at T → 0 and finite density; and the finite δN c effects, e.g. a diverging susceptibility and vanishing density of states at small temperatures, a physically consistent negative heat capacity and new types of consistent phases. tities of the full (defect+bulk) field theory that are extrinsic in the area of the defect. Certainly, we will miss contributions that are extrinsic in the volume of the SYM, but these depend only on a "topological" parameter that is related to a difference in the level -2 -J T quantum critical point "ordered" quantum critical phase transition "Higgs" quantum critical phase / J s / J b T J bs u r f a c e t r a n s i t i o n extraordinary transition ordinary transition bulk + boundary "ordered" boundary "ordered" special point

Non-mean-field quantum critical points from holography

“…All of these transitions are typically first order at finite temperature and low quark density but continuous at large density (see [50][51][52] for the full phase diagrams of the D3/D5 and D3/D7 systems with magnetic field which we will study here. For thermodynamics see [53,54]). …”

Physical response functions of strongly coupled massive quantum liquids

“…At vanishing density, there is a critical temperature-mass ratio below which the probe branes do not extend down to the horizon [27,21]. At finite densities, unless one turns on the scalar in the z direction considered in [8,20], the branes always extend down to the horizon even though a phase transition may still be observed at small densities [20]. In the limit considered in this paper, however, this phase transition is of no concern.…”

“…We assume translational invariance along the flat directions and rotational invariance on the sphere. Hence, the pullback on D5-brane gives us one scalar field corresponding to the position in the z direction, which was extensively studied in [7,8], and another scalar which describes the size of the compact sphere and corresponds to turning on the mass of the fundamental matter, studied in [20,8] and more extensively in the similar D3-D7 system in [21,22,23,24,25]. Parametrizing the S 5 as dΩ 2 5 = dθ 2 + sin 2 θ dΩ 2 2 + cos 2 θ dΩ 2 2 and putting the branes on the first S 2 of the S 5 , the induced metric P [g] on the probe branes is given by…”

Holographic Wilson loops, dielectric interfaces, and topological insulators

“…Most importantly, the edge modes are apparent in the bulk: near the interface, the D7-branes bend and become extended along AdS 4 × S 4 [70]. Such D7-branes along AdS 4 × S 4 (in the absence of worldvolume gauge field flux) break all SUSY, and are dual to (2+1)-dimensional fermions alone, with no scalar superpartners, and with couplings only to the N = 4 SYM gauge field and one of the six real N = 4 SYM scalars, both restricted to the (2+1)-dimensional interface [76][77][78][79][80][81]. These (2+1)-dimensional fermions are the edge modes of the holographic fractional TI states described above.…”