Abstract
By constructing the configuration of D3-branes with D(-1)-branes as D-instantons, we study the three-dimensional Yang-Mills Chern-Simons theory in holography. Due to the presence of the D-instantons, the D7-branes with discrepant embedding functions are able to be introduced in order to include the fundamental fermions (as flavors) and the Chern-Simons term (at very low energy) in the dual theory. The vacuum structure at zero temperature is studied in the soliton background and it illustrates the topological phase transition in the presence of instantons. Moreover, since the confinement/deconfinement phase transition could be holographically identified as the Hawking-Page transition in the bulk, we accordingly calculate the critical temperature of the deconfinement phase transition by collecting the bulk onshell action as the thermodynamical free energy. On the other hand, we evaluate the difference of the entanglement entropy in slab configuration by using the RT formula since the confinement may also be characterized by the entanglement entropy. Altogether we find the behavior of the critical temperature is in qualitative agreement with the behavior of the critical length determined by the entanglement entropy which implies the entanglement entropy could indeed be a character of the confinement in our setup and the D3-D(-1) system would be a remarkable approach to study the three-dimensional gauge theory.
Highlights
In the past decade, a specific class of three-dimensional (3D) Chern-Simons (CS) theory involving fundamental matters with Nf flavors attracts many interests and the large N ’t Hooft limit of such theories with a UðNÞ gauge symmetry has been studied in detail [1,2,3,4,5,6,7]
On the other hand, very interesting to evaluate the critical temperature of the deconfinement phase transition to examine whether it is consistent with the analyses of the entanglement entropy in holography
To obtain the critical temperature of the deconfinement in the dual theory, we should compute the associated free energy F in holography, which is the summary of the Euclidean version of the on-shell action (2.1) denoted as SEIIB, Gibbons-Hawking term SGH, and holographic counterterm Sbctulk in bulk, since the deconfinement phase transition is suggested to be identified as the Hawking-Page transition in the bulk [35,36,37,38]
Summary
A specific class of three-dimensional (3D) Chern-Simons (CS) theory involving fundamental matters with Nf flavors attracts many interests and the large N ’t Hooft limit of such theories with a UðNÞ gauge symmetry has been studied in detail [1,2,3,4,5,6,7]. Hawking-Page transition, in the bulk which is very suggestive of the deconfinement transition [35,36,37,38] Following this idea, we collect the total on-shell action as the holographic free energy consisted of the bulk fields (as the color sector), the flavor and the CS branes, in the soliton and black brane background respectively. Using the Ryu-Takayanagi (RT) formula [43] with the slab geometry, the holographic entanglement entropy can be obtained, and it exhibits a first order phase transition at a critical length which behaves as the critical temperature evaluated by the thermodynamics In this sense, we believe the configuration of D3-branes with D-instantons would be a remarkable approach to study 3D gauge theory.
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