Topological or rotational non-Abelian gauge fields from Einstein-Skyrme holography

Abstract

We report analytically known states at non-zero temperature which may serve as a powerful tool to reveal common topological and thermodynamic properties of systems ranging from the QCD phase diagram to topological phase transitions in condensed matter materials. In the holographically dual gravity theory, these are analytic solutions to a five-dimensional non-linear-sigma (Skyrme) model dynamically coupled to Einstein gravity. This theory is shown to be holographically dual to $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory coupled to an SU(2)-current. All solutions are fully backreacted asymptotically Anti-de Sitter (AdS) black branes or holes. One family of global AdS black hole solutions contains non-Abelian gauge field configurations with positive integer Chern numbers and finite energy density. Larger Chern numbers increase the Hawking-Page transition temperature. In the holographically dual field theory this indicates a significant effect on the deconfinement phase transition. Black holes with one Hawking temperature can have distinct Chern numbers, potentially enabling topological transitions. A second family of analytic solutions, rotating black branes, is also provided. These rotating solutions induce states with propagating charge density waves in the dual field theory. We compute the Hawking temperature, entropy density, angular velocity and free energy for these black holes/branes. These correspond to thermodynamic data in the dual field theory. For these states the energy-momentum tensor, (non-)conserved current, and topological charge are interpreted.

Topological confinement in Skyrme holography

“…(2.7) we first compute the Komar integral. Inserting the energy momentum tensor as found in [1] into this expression we find…”

“…In [1] an analytic solution to the Einstein-Skyrme equations of motions was discovered. There, the authors demonstrated that the solution could be mapped to a solution of the massless SU (2) Einstein-Yang-Mills theory.…”

“…Via the holographic (AdS/CFT) correspondence, the H -P transition was found to be dual to the (de-)confinement transition of the N = 4 SYM field theory [3]. In [1], the Skyrme coupling and Skyrme field were shown to correspond to SU (2)-gauge fields and their coupling to N = 4 SYM theory, respectively. The results of our work form the foundation of a more generalized treatment of topological phases of matter at strong coupling, as our technique allows for an analytic study of such transitions.…”

“…In [1] an analytic solution of the Einstein equations for such a black hole endowed with a Skyrme field was obtained and shown to be holographically [2] dual to an N = 4 Super-Yang-Mills (SYM) gauge field theory. For a large Skyrme coupling constant the Skyrme field can significantly alter the temperature at which the gravitational system undergoes a Hawking -Page (H -P) transition between thermal AdS and an AdS black hole.…”

Topological structures in a non-canonical perturbative dynamics of a cuscuton-like model

“…In recent years several researchers have turned their attention to the study of these structures [14][15][16][17], in particular, kinks and vortices [12]. Part of this interest is motivated by the fact that such structures discussed in field theory have direct applications in condensed matter physics [18], since they are similar.…”