Flavours and Infra-red Instability in Holography

Within a phenomenological holographic model in $(4+1)$-bulk dimensions, defined by Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld and a Chern-Simons term, we explore the fate of BF-bound violation for a probe scalar field and a fluctuation mode of the corresponding geometry. We assume this simple model to capture the dynamics of a strongly coupled SU$(N_c)$ gauge theory with $N_f$ fundamental matter, which in the limit ${\cal O} \left( N_c \right) \sim {\cal O}\left(N_f\right)$ and with a non-vanishing matter density, is holographically described by an AdS$_2$-geometry in the IR. We demonstrate that, superconductor/superfluid instabilities are facilitated and spontaneous breaking of translational invariance is inhibited with increasing values of $\left(N_f / N_c \right)$. This is similar, in spirit, with known results in large $N_c$ Quantum Chromodynamics with $N_f$ quarks and a non-vanishing density, in which the chiral density wave phase becomes suppressed and superconducting instabilities become favoured as the number of quarks is increased.Comment: 24 pages, 2 figure

Effective Temperature in Steady-state Dynamics from Holography

We argue that, within the realm of gauge-gravity duality, for a large class of systems in a steady-state there exists an effective thermodynamic description. This description comes equipped with an effective temperature and a free energy, but no well-defined notion of entropy. Such systems are described by probe degrees of freedom propagating in a much larger background, e.g. $N_f$ number of ${\cal N} =2$ hypermultiplets in ${\cal N}=4$ $SU(N_c)$ super Yang-Mills theory, in the limit $N_f \ll N_c$. The steady-state is induced by exciting an external electric field that couples to the hypermultiplets and drives a constant current. With various stringy examples, we demonstrate that an open string equivalence principle determines a unique effective temperature for all fluctuations in the probe-sector. We further discuss various properties of the corresponding open string metric that determines the effective geometry which the probe degrees of freedom are coupled to. We also comment on the non-Abelian generalization, where the effective temperature depends on the corresponding sector of the fluctuation modes.Comment: 48 pages, 2 figure

Holographic Entanglement in a Noncommutative Gauge Theory

In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties.Comment: 28 pages, multiple figures; minor changes, conclusions unchange

External Fields and Chiral Symmetry Breaking in the Sakai-Sugimoto Model

Using the Sakai-Sugimoto model we study the effect of an external magnetic field on the dynamics of fundamental flavours in both the confined and deconfined phases of a large N_c gauge theory. We find that an external magnetic field promotes chiral symmetry breaking, consistent with the "magnetic catalysis" observed in the field theory literature, and seen in other studies using holographic duals. The external field increases the separation between the deconfinement temperature and the chiral symmetry restoring temperature. In the deconfined phase we investigate the temperature-magnetic field phase diagram and observe, for example, there exists a maximum critical temperature (at which symmetry is restored) for very large magnetic field. We find that this and certain other phenomena persist for the Sakai-Sugimoto type models with probe branes of diverse dimensions. We comment briefly on the dynamics in the presence of an external electric field.Comment: 26 pages. LaTeX, minor change

Fundamental flavours, fields and fixed points: a brief account

In this article we report on a preliminary study, {\it via} Holography, of infrared fixed points in a putative strongly coupled SU$(N_c)$ gauge theory, with $N_f$ fundamental matter, in the presence of additional fields in the fundamental sector, e.g. density or a magnetic field. In an inherently {\it effective} or a {\it bottom up} approach, we work with a simple system: Einstein-gravity with a negative cosmological constant, coupled to a Dirac-Born-Infeld (DBI) matter. We obtain a class of exact solutions, dual to candidate grounds states in the infrared (IR), with a scaling ansatz for various fields. These solutions are of two kinds: AdS$_m \times {\mathbb R}^n$--type, and AdS$_m \times$EAdS$_n$--type, where $m$ and $n$ are suitable integers. Both these classes of solutions are {\it non-perturbative} in back-reaction. The AdS$_m \times$EAdS$_n$--type contains examples of Bianchi type-V solutions. We also construct explicit numerical flows from an AdS$_5$ ultraviolet to both an AdS$_2$ and an AdS$_3$ IR.Comment: 32 pages, 6 figures, references added, published versio