Holographic $\mathrm{QCD}_{3}$ and Chern-Simons theory from anisotropic supergravity

Abstract

Based on the gauge-gravity duality, we study the three-dimensional QCD (QCD 3 ) and Chern-Simons theory by constructing the anisotropic black D3-brane solution in IIB supergravity. The deformed bulk geometry is obtained by performing a double Wick rotation and dimension reduction which becomes an anisotropic bubble configuration exhibiting confinement in the dual theory. And its anisotropy also reduces to a Chern-Simons term due to the presence of the dissolved D7-branes or the axion field in bulk. Using the bubble geometry, we investigate the the ground-state energy density, quark potential, entanglement entropy and the baryon vertex according to the standard methods in the AdS/CFT dictionary. Our calculation shows that the ground-state energy illustrates degenerate to the Chern-Simons coupling coefficient which is in agreement with the properties of the gauge Chern-Simons theory. The behavior of the quark tension, entanglement entropy and the embedding of the baryon vertex further implies strong anisotropy may destroy the confinement. Afterwards, we additionally introduce various D7-branes as flavor and Chern-Simons branes to include the fundamental matter and effective Chern-Simons level in the dual theory. By counting their orientation, we finally obtain the associated topological phase in the dual theory and the critical mass for the phase transition. Interestingly the formula of the critical mass reveals the flavor or chiral symmetry would be restored if the anisotropy increases greatly. As all of the analysis is consistent with characteristics of quark-gluon plasma, we therefore believe our framework provides a remarkable way to understand the features of Chern-Simons theory, the strong coupled nuclear matter and its deconfinement condition with anisotropy.

Holographic Schwinger effect and electric instability with anisotropy

“…Thus the pair production rate is increased/decreased by the anisotropy with the parallel/perpendicular electric field correspondingly. And this conclusion qualitatively agrees with the analysis of the quark potential in this system [21].…”

“…In the gauge-gravity duality, the bubble solution, as the gravity soliton, can be obtained by performing the double Wick rotation and compactification to the black brane solution as it is discussed in the famous [29,30]. Accordingly, the bubble solution associated to (2.2) reads [21],…”

“…Fortunately, the gauge-gravity duality and AdS/CFT may provide an alternative to study the strong coupled QFT [9,10], in particular, to evaluate Schwinger effect in holography [11,12,13,14,15,16,17,18,19]. Since the equivalence between the type IIB super string theory on AdS 5 × S 5 and the four-dimensional N = 4 SU (N c ) super Yang-Mills theory on N c D3-branes is the most famous example in gauge-gravity duality, the authors of [20,21] construct the solution in type IIB supergravity then obtain anisotropic black brane solution and bubble solution as gravity soliton in order to study anisotropic gauge theory at finite temperature and with confinement respectively. Accordingly, one of the motivation of this work is to investigate holographically the Schwinger effect with anisotropy in the backgrounds proposed in [20,21].…”

“…Since the equivalence between the type IIB super string theory on AdS 5 × S 5 and the four-dimensional N = 4 SU (N c ) super Yang-Mills theory on N c D3-branes is the most famous example in gauge-gravity duality, the authors of [20,21] construct the solution in type IIB supergravity then obtain anisotropic black brane solution and bubble solution as gravity soliton in order to study anisotropic gauge theory at finite temperature and with confinement respectively. Accordingly, one of the motivation of this work is to investigate holographically the Schwinger effect with anisotropy in the backgrounds proposed in [20,21]. So in the first part of this work, we compute the critical electric field for Schwinger effect, perform the potential analysis then evaluate the pair production rate numerically by solving the equation of motion for a fundamental string in bulk with respect to the black brane background and bubble background.…”

“…The outline of this manuscript is as follows. In Section 2, we review the anisotropic solutions in IIB supergravity proposed in [20,21]. In Section 3, we evaluate the critical electric field then perform the potential analysis for Schwinger effect.…”