Minimal standard heterotic string models

Three generation heterotic string vacua in the free fermionic formulation gave rise to models with solely the MSSM states in the observable standard model charged sector. The relation of these models to Z₂×Z₂ orbifold compactifications dictates that they produce three pairs of untwisted Higgs multiplets. The reduction to one pair relies on the analysis of supersymmetric flat directions, which give a superheavy mass to the dispensable Higgs states. We explore the removal of the extra Higgs representations by using the free fermion boundary conditions, and hence we work directly at the string level, rather than in the effective low energy field theory. We present a general mechanism that achieves this reduction by using asymmetric boundary conditions between the left- and right-moving internal fermions. We incorporate this mechanism in explicit string models containing three twisted generations and a single untwisted Higgs doublet pair. We further demonstrate that an additional effect of the asymmetric boundary conditions is to substantially reduce the supersymmetric moduli space.     

Constraining f(G) Gravity Models Using Energy Conditions

Recently, energy condition inequalities in the context of modified Gauss-Bonnet gravity have been derived in Garcia et al. (Phys. Rev. D, 83:104032, 2011). Using these general inequalities, we examine the viability of specific forms of f(G) models proposed in De Felice and Tsujikawa (Phys. Lett. B, 675:1, 2009) that can be responsible for the late-time cosmic acceleration following the matter era. In doing so we also use the recent estimated values of the deceleration, jerk and snap parameters to obtain the bounds from the weak and strong energy conditions on the parameters of the above mentioned forms of f(G) gravity theories.     

Flat directions in flipped SU(5). I: All-order analysis

We present a systematic classification of field directions for the string-derived flipped SU(5) model that are D- and F-flat to all orders. Properties of the flipped SU(5) model with field values in these directions are compared to those associated with other flat directions that have been shown to be F-flat to specific finite orders in the superpotential. We discuss the phenomenological Higgs spectrum, and quark and charged-lepton mass textures.     

A Generalization of Scaling Models of Turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot (Phys. Rev. E 57(2):1737, 1998). In particular we focus on the expression for the scaling exponents ζ _n . We show that Yakhot’s result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L’vov and I. Procaccia (Phys. Rev. E 62(6):8037, 2000). The model furthermore yields a theoretical justification for the method of extended self-similarity (ESS).     

Observational Constraints on the Modified Gravity Model (MOG) Proposed by Moffat: Using the Magellanic System

A simple model for the dynamics of the Magellanic Stream (MS), in the framework of modified gravity models is investigated. We assume that the galaxy is made up of baryonic matter out of context of dark matter scenario. The model we used here is named Modified Gravity (MOG) proposed by Moffat (J. Cosmol. Astropart. Phys. 003, 2005). In order to examine the compatibility of the overall properties of the MS under the MOG theory, the observational radial velocity profile of the MS is compared with the numerical results using the χ ² fit method. In order to obtain the best model parameters, a maximum likelihood analysis is performed. We also compare the results of this model with the Cold Dark Matter (CDM) halo model and the other alternative gravity model that proposed by Bekenstein (Phys. Rev. D 70:083509, 2004), so called TeVeS. We show that by selecting the appropriate values for the free parameters, the MOG theory seems to be plausible to explain the dynamics of the MS as well as the CDM and the TeVeS models.     

Evaluating Quasilocal Energy and Solving Optimal Embedding Equation at Null Infinity

We study the limit of quasilocal energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi–Sachs energy-momentum at a retarded time. The quasilocal mass in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat spacetime.     

Activity Phase Transition for Constrained Dynamics

We consider two cases of kinetically constrained models, namely East and FA-1f models. The object of interest of our work is the activity A(t){\mathcal {A}(t)} defined as the total number of configuration changes in the interval [0, t] for the dynamics on a finite domain. It has been shown in Garrahan et al. (J Phys A 42:075007, 2009; Phys Rev Lett 98:195702, 2007) that the large deviations of the activity exhibit a non-equilibrium phase transition in the thermodynamic limit and that reducing the activity is more likely than increasing it due to a blocking mechanism induced by the constraints. In this paper, we study the finite size effects around this first order phase transition and analyze the phase coexistence between the active and inactive dynamical phases in dimension 1. In higher dimensions, we show that the finite size effects are determined by the dimension and the choice of the boundary conditions.     

Axially Symmetric Universe in Creation-Field Cosmology

Axially symmetric space-time is considered in the Hoyle-Narlikar C-field cosmology. Using methods of Narlikar and Padmanabhan (Phys. Rev. D 32:1928, 1985), the solutions have been studied when the creation field C is a function of time t only. The geometrical and physical aspects for models are also studied.     

Nahm Transform for Periodic Monopoles¶and ?=2 Super Yang–Mills Theory

We study Bogomolny equations on ℝ²×?¹. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk?hler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of ?=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius. Received: 20 July 2000 / Accepted: 29 November 2000     

An investigation of equivalence between the bulk-based and the brane-based approaches for anisotropic models

We investigate the relation between the brane-based and the bulk-based approaches for anisotropic case in brane-world models. In the brane-based approach, the brane is chosen to be fixed on a coordinate system, whereas in the bulk-based approach it is no longer static as it moves along the extra dimension. It was shown that these two approaches are equivalent for specific models in Mukohyama et al. (Phys Rev D 62:024028, 2000), Bowcock et al. (Class Quant Gravit 17:4745–4764, 2000). In this paper, it is aimed to get general formalism of the equivalence obtained in Mukohyama et al. (Phys Rev D 62:024028, 2000). We found that calculations driven by a general anisotropic bulk-based metric yield a brane-based metric in Gaussian Normal Coordinates by conserving spatial anisotropy. We also derive solutions for an anisotropic bulk-based model and get the corresponding brane-based metric of the model.     

Drude Weight in Non Solvable Quantum Spin Chains

For a quantum spin chain or 1D fermionic system, we prove that the Drude weight D verifies the universal Luttinger liquid relation v_s²=D/kv_{s}^{2}=D/\kappa, where κ is the susceptibility and v _s is the Fermi velocity. This result is proved by rigorous Renormalization Group methods and is true for any weakly interacting system, regardless its integrability. This paper, combined with Benfatto and Mastropietro (in J. Stat. Phys. 138, 1084–1108, 2010), completes the proof of the Luttinger liquid conjecture for such systems.     

Probability of inflation in loop quantum cosmology

Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically or does it require a careful fine tuning of initial parameters? In recent years there has been considerable controversy on this issue (Hollands and Wald in Gen Relativ Gravit, 34:2043, 2002; Kofman et al. in J High Energy Phys 10:057, 2002); (Gibbons and Turok in Phys Rev D 77:063516, 2008). In particular, for a quadratic potential, Kofman et al. (J High Energy Phys 10:057, 2002) have argued that the probability of inflation with at least 65 e-foldings is close to one, while Gibbons and Turok (Phys Rev D 77:063516, 2008) have argued that this probability is suppressed by a factor of ~10⁻⁸⁵. We first clarify that such dramatically different predictions can arise because the required measure on the space of solutions is intrinsically ambiguous in general relativity. We then show that this ambiguity can be naturally resolved in loop quantum cosmology (LQC) because the big bang is replaced by a big bounce and the bounce surface can be used to introduce the structure necessary to specify a satisfactory measure. The second goal of the paper is to present a detailed analysis of the inflationary dynamics of LQC using analytical and numerical methods. By combining this information with the measure on the space of solutions, we address a sharper question than those investigated in Kofman et al. (J High Energy Phys 10:057, 2002), Gibbons and Turok (Phys Rev D 77:063516, 2008), Ashtekar and Sloan (Phys Lett B 694:108, 2010): What is the probability of a sufficiently long slow roll inflation which is compatible with the seven year WMAP data? We show that the probability is very close to 1. The material is so organized that cosmologists who may be more interested in the inflationary dynamics in LQC than in the subtleties associated with measures can skip that material without loss of continuity.     

On ‘light’ fermions and proton stability in ‘big divisor’ D3/D7 large volume compactifications

Building on our earlier work (Misra and Shukla, Nucl. Phys. B 827:112, 2010; Phys. Lett. B 685:347–352, 2010), we show the possibility of generating “light” fermion mass scales of MeV–GeV range (possibly related to the first two generations of quarks/leptons) as well as eV (possibly related to first two generations of neutrinos) in type IIB string theory compactified on Swiss-Cheese orientifolds in the presence of a mobile space-time filling D3-brane restricted to (in principle) stacks of fluxed D7-branes wrapping the “big” divisor Σ _B . This part of the paper is an expanded version of the latter half of Sect. 3 of a published short invited review (Misra, Mod. Phys. Lett. A 26:1, 2011) written by one of the authors [AM]. Further, we also show that there are no SUSY GUT-type dimension-five operators corresponding to proton decay, and we estimate the proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be 10⁶¹ years. Based on GLSM calculations in (Misra and Shukla, Nucl. Phys. B 827:112, 2010) for obtaining the geometric K?hler potential for the “big divisor,” using further the Donaldson’s algorithm, we also briefly discuss in the first of the two appendices the metric for the Swiss-Cheese Calabi–Yau used, which we obtain and which becomes Ricci flat in the large-volume limit.     

Higher Dimensional Bianchi Type I Universe in Creation-field Cosmology

We have studied the Hoyle-Narlikar C-field cosmology with Bianchi type-I space-time in higher dimensions. Using methods of Narlikar and Padmanabhan (Phys. Rev. D 32:1928, 1985), the solutions have been studied when the creation field C is a function of time t only. The geometrical and physical aspects for model are also studied.     

Proton decay in four dimensional superstring models

In this paper, we discuss the contraints that emerge from baryon nonconserving processes in theSU(4)×O(4) andSU(5)×U(1) models derived in the fermionic formulation of the four dimensional superstring. We examine dimension five baryon violating operators arising a) from Higgs exchange diagrams, and b) from non-renormalisable terms which arise from the exchange of massive string states. Both kinds of the above operators put non-trivial constraints on the matter field assignments and on the vevs of various singlet fields of the string models under consideration.     

Glauber Dynamics for the Quantum Ising Model in a Transverse Field on a Regular Tree

Motivated by a recent use of Glauber dynamics for Monte Carlo simulations of path integral representation of quantum spin models (Krzakala et al. in Phys. Rev. B 78(13):134428, 2008), we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph G. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality of Peres and Winkler to the quantum setting. Then we consider the case when G is a regular b-ary tree and prove the same fast mixing results established in Martinelli et al. (Commun. Math. Phys. 250(2):301–334, 2004) for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the “cavity equation”) together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space.     

Self-gravitating darkon fluid with anisotropic scaling

The fluid model for the dark sector of the universe (darkon fluid), introduced previously in Phys. Rev. D 80, 083513, 2009, is reformulated as a modified model involving only variables from the physical phase space. The Lagrangian of the model does not possess a free particle limit and hence the particles it describes, darkons, exist only as a self-gravitating fluid. This darkon fluid presents a dynamical realization of the zero-mass Galilean algebra extended by anisotropic dilational symmetry with dynamical exponent z=\frac53z=\frac{5}{3}. The model possesses cosmologically relevant solutions which are identical to those in the previous paper. We derive also the equations for the cosmological perturbations at early times and determine their solutions. In addition, we discuss also some implications of adding higher spatial-derivative terms.     

Semi-local cosmic strings and the cosmological constant problem

We study the cosmological constant problem in a three-dimensional N = 2 supergravity theory with gauge groupSU (2)_global × U(1)_local. The model we consider is known to admit string-like configurations, the so-called semi-local cosmic strings. We show that the stability of these solitonic solutions is provided by supersymmetry through the existence of a lower bound for the energy, even though the manifold of the Higgs vacuum does not contain non-contractible loops. Charged Killing spinors do exist over configurations that saturate the Bogomol'nyi bound, as a consequence of an Aharonov-Bohm-like effect. Nevertheless, there are no physical fermionic zero modes on these backgrounds. The exact vanishing of the cosmological constant does not imply, then, Bose-Fermi degeneracy. This provides a non-trivial example of the recent claim made by Witten on the vanishing of the cosmological constant in three dimensions without unphysical degeneracies.     

Black Hole Entropy: From Shannon to Bekenstein

In this note we have applied directly the Shannon formula for information theory entropy to derive the Black Hole (Bekenstein-Hawking) entropy. Our analysis is semi-classical in nature since we use the (recently proposed Banerjee in Int. J. Mod. Phys. D 19:2365–2369, 2010 and Banerjee and Majhi in Phys. Rev. D 81:124006, 2010; Phys. Rev. D 79:064024, 2009; Phys. Lett. B 675:243, 2009) quantum mechanical near horizon mode functions to compute the tunneling probability that goes in to the Shannon formula, following the general idea of Brillouin (Science and Information Theory, Dover, New York, 2004). Our framework conforms to the information theoretic origin of Black Hole entropy, as originally proposed by Bekenstein.     

Holographic Dark Energy in Brans-Dicke Cosmology with Granda-Oliveros Cut-off

Motivated by the recent works of one of us (Karami and Fehri, Int. J. Theor. Phys. 49:1118, 2010; Phys. Lett. B 684:61, 2010), we study the holographic dark energy in Brans-Dicke gravity with the Granda-Oliveros cut-off proposed recently in literature. We find out that when the present model is combined with Brans-Dicke field the transition from normal state where w _D >−1 to the phantom regime where w _D <−1 for the equation of state of dark energy can be more easily achieved for than when resort to the Einstein field equations is made. Furthermore, the phantom crossing is more easily achieved when the matter and the holographic dark energy undergo an exotic interaction. We also calculate some relevant cosmological parameters and their evolution.