15306576
On the UV renormalizability of noncommutative field theories
UV/IR mixing is one of the most important features of noncommutative field theories. As a consequence of this coupling of the UV and IR sectors, the configuration of fields at the zero momentum limit in these theories is a very singular configuration. We show that the renormalization conditions set at a particular momentum configuration with a fixed number of zero momenta, renormalizes the Green's functions for any general momenta only when this configuration has same set of zero momenta. Therefore only when renormalization conditions are set at a point where all the external momenta are nonzero, the quantum theory is renormalizable for all values of nonzero momentum. This arises as a result of different scaling behaviors of Green's functions with respect to the UV cutoff (Λ) for configurations containing different set of zero momenta. We study this in the noncommutative 4 theory and analyse similar results for the Gross-Neveu model at one loop level. We next show this general feature using Wilsonian RG of Polchinski in the globally O(N) symmetric scalar theory and prove the renormalizability of the theory to all orders with an infrared cutoff. In the context of spontaneous symmetry breaking (SSB) in noncommutative scalar theory, it is essential to note the different scaling behaviors of Green's functions with respect to Λ for different set of zero momenta configurations. We show that in the broken phase of the theory the Ward identities are satisfied to all orders only when one keeps an infrared regulator by shifting to a nonconstant vacuum.
624279
Phase Transitions in Higher Derivative Gravity
This paper deals with black holes, bubbles and orbifolds in Gauss–Bonnet theory in five dimensional anti de Sitter space. In particular, we study stable, unstable and metastable phases of black holes from thermodynamical perspective. By comparing bubble and orbifold geometries, we analyse associated instabilities. Assuming AdS/CFT correspondence, we discuss the effects of this higher derivative bulk coupling on a specific matrix model near the critical points of the boundary gauge theory at finite temperature. Finally, we propose another phenomenological model on the boundary which mimics various phases of the bulk space-time.
118143564
The Dependence of Muon-Size on Shower Size and the Composition of Cosmic Ray Primaries
118722812
Quantum phase diagram of a spin-1/2 antiferromagnetic chain with magnetic impurity
Abstract We present the renormalization group (RG) flow diagram of a spin-half antiferromagnetic chain with magnetic impurity and one altered link. In this two parameters (competing interactions) model, one can find the complex phase diagram with many interesting fixed points. There is no evidence of intermediate stable fixed point in weak coupling phase. It may arise at the strong coupling phase. Depending on the strength of couplings the phases correspond either to a decoupled spin with Curie law behavior or a logarithmically diverging impurity susceptibility as in the two channel Kondo problem.
118315517
Thermodynamic Route to Field Equations in Gravity
Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate notions of temperature and entropy with them. Such notions provide us a possible alternative approach to understand the dynamics of gravity as an emergent phenomenon resulted out of thermodynamics of spacetime by interpreting the field equations as a thermodynamic identity TdS = dE+PdV. Interestingly, such equilibrium thermodynamic interpretation works only for Lanczos‐Lovelock theories. All these prelimany results point towards a deep connection among gravity, thermodynamics and quantum theory and also offer a new outlook regarding the nature of gravitational interaction.
119541770
Local currents for a deformed algebra of quantum mechanics with a fundamental length scale
We explore some explicit representations of a certain stable deformed algebra of quantum mechanics, considered by R Vilela Mendes, having a fundamental length scale. The relation of the irreducible representations of the deformed algebra to those of the (limiting) Heisenberg algebra is discussed, and we construct the generalized harmonic oscillator Hamiltonian in this framework. To obtain local currents for this algebra, we extend the usual nonrelativistic local current algebra of vector fields and the corresponding group of diffeomorphisms, modelling the quantum configuration space as a commutative spatial manifold with one additional dimension.
121582631
Dark energy, cosmic coincidence and future singularity of the universe
Dark energy model with the equation of state $$p_{DE} =-\rho _{DE} -A\rho _{DE}^\alpha $$, is characterised by four finite life time future singularity of the universe for different values of the parameter $$A$$ and $$\alpha $$ [Nojiri et al. in Phys Rev D 71:063004, 2005]. Since from the matter dominated era to the dark energy dominated era the ratio of the dark energy density to the matter energy density increases as the universe expand for these future singularities, the universe passes through a significant time when the dark energy density and the matter energy density are nearly comparable. Considering $$\frac{1}{r_0 }<r=\frac{\rho _{DE} }{\rho _M }<r_0 $$, where $$r_0$$ is any fixed ratio, we calculate the fraction of total life time of the universe when the universe passes through the coincidental stage for these singularities. It has been found that the fractional time varies as $$\alpha $$ varies within the range for which these finite life time future singularities occur and the fraction is smaller for smaller values of $$r_0 $$. Importance of the fractional time and observational limits onto the values of the parameter $$A$$ and $$\alpha $$ has also been discussed.