arXiv subjects
Publications and source records attributed to M. Khorrami.
We generalize the Maldacena correspondence to the logarithmic conformal field theories. We study the correspondence between field theories in (d+1)-dimensional AdS space and the d-dimensional logarithmic conformal field theories in the boundary of $AdS_{d+1}$. Using this correspondence, we get the n-point functions of the corresponding logarithmic conformal field theory in d-dimensions.
The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translation in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory, the object playing the role of flux of field strength per plaquette, as well as the action, are constructed. It is observed that the theory, in comparison with ordinary U(1) gauge theory, has an extra gauge field component. This phenomena is reminiscent of similar ones in formulation of SU(N) gauge theory in space with canonical noncommutativity, and also appearance of gauge field component in discrete direction of Connes' construction of the Standard Model.
A photon source is located in a rotating waveguide. An absorber with a sharp absorbing frequency absorbs some of the emitted photons. This decreases the number of photons which are detected by a detector. The frequency (energy) spectrum measured in the absorber depends on the setup (the positions of the source and the detector), and this spectrum determines the amount of absorption. The shifts are calculated for different configurations. Among other things, it is seen that even if the source and the absorber are at rest (while the waveguide is rotating), there is a nonzero frequency shift.
In the current work, a number of algorithms are developed and compared for the numerical solution of periodic (quasi-static) linear elastic mechanical boundary-value problems (BVPs) based on two different discretizations of Fourier series. The first is standard and based on the trapezoidal approximation of the Fourier mode integral, resulting in trapezoidal discretization (TD) of the truncated Fourier series. Less standard is the second discretization based on piecewise-constant approximation of the Fourier mode integrand, yielding a piecewise-constant discretization (PCD) of this series. Employing these, fixed-point algorithms are formulated via Green-function preconditioning (GFP) and finite-difference discretization (of differential operators; FDD). In particular, in the context of PCD, this includes an algorithm based on the so-called "discrete Green operator" (DGO) recently introduced by Eloh et al. (2019), which employs GFP, but not FDD. For computational comparisons, the (classic) benchmark case of a cubic inclusion embedded in a matrix (e.g., Suquet, 1997; Willot, 2015) is employed. Both discontinuous and smooth transitions in elastic stiffness at the matrix-inclusion (MI) interface are considered. In the context of both TD and PCD, a number of GFP- and FDD-based algorithms are developed. Among these, one based on so-called averaged-forward-backward-differencing (AFB) is shown to result in the greatest improvement in convergence rate. As it turns out, AFB is equivalent to the "rotated scheme" (R) of Willot (2015) in the context of TD. In the context of PCD, comparison of the performance and convergence behavior of AFB/R- and DGO-based algorithms shows that the former is more efficient than the latter for larger phase contrasts.
A spinor theory on a space with linear Lie type noncommutativity among spatial coordinates is presented. The model is based on the Fourier space corresponding to spatial coordinates, as this Fourier space is commutative. When the group is compact, the real space exhibits lattice characteristics (as the eigenvalues of space operators are discrete), and the similarity of such a \emph{lattice} with ordinary lattices is manifested, among other things, in a phenomenon resembling the famous \emph{fermion doubling} problem. A projection is introduced to make the dynamical number of spinors equal to that corresponding to the ordinary space. The actions for free and interacting spinors (with Fermi-like interactions) are presented. The Feynman rules are extracted and 1-loop corrections are investigated.
The large-N behavior of the quartic-cubic generalized two dimensional Yang Mills U(N) on the sphere is investigated, for small cubic couplings. It is shown that single transition at the critical area which is present for the quartic model, is split into two transitions, both of them are third order. the phase diagram of the system for small cubic couplings is obtained.
The structure of loop corrections is examined in a scalar field theory on a three dimensional space whose spatial coordinates are noncommutative and satisfy SU(2) Lie algebra. In particular, the 2- and 4-point functions in $ϕ^4$ scalar theory are calculated at the 1-loop order. The theory is UV-finite as the momentum space is compact. It is shown that the non-planar corrections are proportional to a one dimensional $δ$-function, rather than a three dimensional one, so that in transition rates only the planar corrections contribute.
The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined. In particular, the basic notions for constructing the observables of the theory as well as subtleties related to the proper treatment of $δ$ distributions (corresponding to conservation laws) are introduced. Explicit examples are given for scalar field theory amplitudes in the lowest order of perturbation.
A noncommutative space is considered the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper measure for integration are derived. Some general aspects of perturbative field theory calculations on this space are also discussed. Among the features of such models is that they are free from ultraviolet divergences (and hence free from UV/IR mixing as well), if the group is compact. The example of the group SO(3) or SU(2) is investigated in more detail.
In two-dimensional Yang-Mills and generalized Yang-Mills theories for large gauge groups, there is a dominant representation determining the thermodynamic limit of the system. This representation is characterized by a density the value of which should everywhere be between zero and one. This density itself is determined through a saddle-point analysis. For some values of the parameter space, this density exceeds one in some places. So one should modify it to obtain an acceptable density. This leads to the well-known Douglas-Kazakov phase transition. In generalized Yang-Mills theories, there are also regions in the parameter space where somewhere this density becomes negative. Here too, one should modify the density so that it remains nonnegative. This leads to another phase transition, different from the Douglas-Kazakov one. Here the general structure of this phase transition is studied, and it is shown that the order of this transition is typically three. Using carefully-chosen parameters, however, it is possible to construct models with phase-transition orders not equal to three. A class of these non-typical models are also studied.
The large-N behavior of Yang-Mills and generalized Yang-Mills theories in the double-scaling limit is investigated. By the double-scaling limit, it is meant that the area of the manifold on which the theory is defined, is itself a function of N. It is shown that phase transitions of different orders occur, depending on the functional dependence of the area on N. The finite-size scalings of the system are also investigated. Specifically, the dependence of the dominant representation on A, for large but finite N is determined.
The large-N limit of the expectation values of the Wilson loops corresponding to two-dimensional U(N) Yang-Mills and generalized Yang-Mills theories on a sphere are studied. The behavior of the expectation values of the Wilson loops both near the critical area and for large areas are investigated. It is shown that the expectation values of the Wilson loops at large areas behave exponentially with respect to the area of the smaller region the boundary of which is the loop; and for the so called typical theories, the expectation values of the Wilson loops exhibit a discontinuity in their second derivative (with respect to the area) at the critical area.
A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle. The reactions of the system are such that two adjacent sites, one empty the other occupied, may evolve to a state where both of these sites are either empty or occupied. The continuum version of this model in a Ddimensional region with boundary is studied, and two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the relaxation of the system toward its stationary state. Based on the first behavior, the static phase transition (discontinuous changes in the stationary profiles of the system) is studied. Based on the second behavior, the dynamical phase transition (discontinuous changes in the relaxation-times of the system) is studied. It is shown that the static phase transition is induced by the bulk reactions only, while the dynamical phase transition is a result of both bulk reactions and boundary conditions.
The large-N limit of the two-dimensional U$(N)$ Yang-Mills theory on an arbitrary orientable compact surface with boundaries is studied. It is shown that if the holonomies of the gauge field on boundaries are near the identity, then the critical behavior of the system is the same as that of an orientable surface without boundaries with the same genus but with a modified area. The diffenece between this effective area and the real area of the surface is obtained and shown to be a function of the boundary conditions (holonomies) only. A similar result is shown to hold for the group SU$(N)$ and other simple groups.
The Klein-Gordon and Dirac equations in a semi-infinite lab ($x > 0$), in the background metric $\ds^2 = u^2(x) (-\dt^2 + \dx^2) + \dy^2 + \dz^2$, are investigated. The resulting equations are studied for the special case $ u(x) = 1 + g x$. It is shown that in the case of zero transverse-momentum, the square of the energy eigenvalues of the spin-1/2 particles are less than the squares of the corresponding eigenvalues of spin-0 particles with same masses, by an amount of $mg\hbar c$. Finally, for nonzero transverse-momentum, the energy eigenvalues corresponding to large quantum numbers are obtained, and the results for spin-0 and spin-1/2 particles are compared to each other.
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and inversion, and find general forms for correlation functions.
Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for $E_n(t)$'s, the probability that $n$ consecutive sites are empty at time $t$. The general method of solving the time evolution equation is discussed. As an example, a system with next-nearest-neighbor interaction is studied.
The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the probability that $n$ consecutive sites are empty ($E_n$), has been exactly obtained. In the thermodynamic limit, the large-time behavior of the system has also been investigated. Releasing the translational invariance of the initial conditions, the evolution equation for the probability that $n$ consecutive sites, starting from the site $k$, are empty ($E_{k,n}$) is obtained. In the thermodynamic limit, the large time behavior of the system is also considered. Finally, the continuum limit of the model is considered, and the empty-interval probability function is obtained.