Confining D-Instanton Background in an External Electric Field

Using holography, we discuss the effects of an external static electric field on the D3/D-instanton theory at zero-temperature, which is a quasi-confining theory, with confined quarks and deconfined gluons. We introduce the quarks to the theory by embedding a probe D7-brane in the gravity side, and turn on an appropriate $U(1)$ gauge field on the flavor brane to describe the electric field. Studying the embedding of the D7-brane for different values of the electric field, instanton density and quark masses, we thoroughly explore the possible phases of the system. We find two critical points in our considerations. We show that beside the usual critical electric field present in deconfined theories, there exists another critical field, with smaller value, below which no quark pairs even the ones with zero mass are produced and thus the electric current is zero in this (insulator) phase. At the same point, the chiral symmetry, spontaneously broken due to the gluon condensate, is restored which shows a first order phase transition. Finally, we obtain the full decay rate calculating the imaginary part of the DBI action of the probe brane and find that it becomes nonzero only when the critical value of the electric field is reached

Casimir Energy for a Coupled Fermion-Kink System and its stability

We compute the Casimir energy for a system consisting of a fermion and a pseudoscalar field in the form of a prescribed kink. This model is not exactly solvable and we use the phase shift method to compute the Casimir energy. We use the relaxation method to find the bound states and the Runge-Kutta-Fehlberg method to obtain the scattering wavefunctions of the fermion in the whole interval of $x$. The resulting phase shifts are consistent with the weak and strong forms of the Levinson theorem. Then, we compute and plot the Casimir energy as a function of the parameters of the pseudoscalar field, i.e. the slope of $\phi(x)$ at x=0 ($\mu$) and the value of $\phi(x)$ at infinity ($\theta_0$). In the graph of the Casimir energy as a function of $\mu$ there is a sharp maximum occurring when the fermion bound state energy crosses the line of E=0. Furthermore, this graph shows that the Casimir energy goes to zero for $\mu\rightarrow 0$, and also for $\mu\rightarrow \infty$ when $\theta_0$ is an integer multiple of $\pi$. Moreover, the graph of the Casimir energy as a function of $\theta_0$ shows that this energy is on the average an increasing function of $\theta_0$ and has a cusp whenever there is a zero fermionic mode. We finally compute the total energy of a system consisting of a valence fermion in the ground state. Most importantly, we show that this energy (the sum of the Casimir energy and the energy of the fermion) is minimum when the background field has winding number one, independent of the details of the background profile. Throughout the paper we compare our results with those of a simple exactly solvable model, where a piece-wise linear profile approximates the kink. We find that the kink is an almost reflectionless barrier for the fermions, within the context of our model.Comment: revtex4, 10 pages, 9 figure

Vacuum Polarization and Casimir Energy of a Dirac Field Induced by a Scalar Potential in One Spatial Dimension

We investigate the vacuum polarization and the Casimir energy of a Dirac field coupled to a scalar potential in one spatial dimension. Both of these effects have a common cause which is the distortion of the spectrum due to the coupling with the background field. Choosing the potential to be a symmetrical square-well, the problem becomes exactly solvable and we can find the whole spectrum of the system, analytically. We show that the total number of states and the total density remain unchanged as compared with the free case, as one expects. Furthermore, since the positive- and negative-energy eigenstates of the fermion are fermion-number conjugates of each other and there is no zero-energy bound state, the total density and the total number of negative and positive states remain unchanged, separately. Therefore, the vacuum polarization in this model is zero for any choice of the parameters of the potential. It is important to note that although the vacuum polarization is zero due to the symmetries of the model, the Casimir energy of the system is not zero in general. In the graph of the Casimir energy as a function of the depth of the well there is a maximum approximately when the bound energy levels change direction and move back towards their continuum of origin. The Casimir energy for a fixed value of the depth is a linear function of the width and is always positive. Moreover, the Casimir energy density (the energy density of all the negative-energy states) and the energy density of all the positive-energy states are exactly the mirror images of each other. Finally, computing the total energy of a valence fermion present in the lowest fermionic bound state, taking into account the Casimir energy, we find that the lowest bound state is almost always unstable for the scalar potential.Comment: 16 pages, 7 figure

An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition

We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs reveal some properties of the system which cannot be seen from the graph of the total Casimir energy. Finally we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately.Comment: 13 pages, 8 figure

Far-from-equilibrium initial conditions probed by a nonlocal observable

Using the gauge/gravity duality, we investigate the evolution of an out-of-equilibrium strongly-coupled plasma from the viewpoint of the two-point function of scalar gauge-invariant operators with large conformal dimension. This system is out of equilibrium due to the presence of anisotropy and/or a massive scalar field. Considering various functions for the initial anisotropy and scalar field, we conclude that the effect of the anisotropy on the evolution of the two-point function is considerably more than the effect of the scalar field. We also show that the ordering of the equilibration time of the one-point function for the non-probe scalar field and the correlation function between two points with a fixed separation can be reversed by changing the initial configuration of the plasma, when the system is out of the equilibrium due to the presence of at least two different sources like our problem. In addition, we find the equilibration time of the two-point function to be linearly increasing with respect to the separation of the two points with a fixed slope, regardless of the initial configuration that we start with. Finally we observe that, for larger separations the geodesic connecting two points on the boundary crosses the event horizon after it has reached its final equilibrium value, meaning that the two-point function can probe behind the event horizon