815 research outputs found

### Singularities of the Casimir Energy for Quantum Field Theories with Lifshitz Dimensions

We study the singularities that the Casimir energy of a scalar field in
spacetimes with Lifshitz dimensions exhibits, and provide expressions of the
energy in terms of multidimensional zeta functions for the massless case. Using
the zeta-regularization method, we found that when the 4-dimensional spacetime
has Lifshitz dimensions, then for specific values of the critical exponents,
the Casimir energy is singular, in contrast to the non-Lifshitz case.
Particularly we found that when the value of the critical exponent is $z=2$,
the Casimir energy is singular, while for $z\geq 3$ the Casimir energy is
regular. In addition, when flat extra dimensions are considered, the critical
exponents of the Lifshitz dimensions affect drastically the Casimir energy,
introducing singularities that are absent in the non-Lifshitz case. We also
discuss the Casimir energy in the context of braneworld models and the
perspective of Lifshitz dimensions in such framework.Comment: Major Revision, Similar to Journal Versio

### Low Dimensional Supersymmetries in SUSY Chern-Simons Systems and Geometrical Implications

We study in detail the underlying graded geometric structure of abelian N=2
supersymmetric Chern-Simons theory in $(2+1)$-dimensions. This structure is an
attribute of the hidden unbroken one dimensional N=2 supersymmetries that the
system also possesses. We establish the result that the geometric structures
corresponding to the bosonic and to the fermionic sectors are equivalent fibre
bundles over the $(2+1)$-dimensional manifold. Moreover, we find a geometrical
answer to the question why some and not all of the fermionic sections are
related to a N=2 supersymmetric algebra. Our findings are useful for the
quantum theory of Chern-Simons vortices.Comment: Revised Version. arXiv admin note: text overlap with arXiv:1308.046

### Newton's Law Modifications due to a Sol Manifold Extra Dimensional Space

The corrections to the gravitational potential due to a Sol extra dimensional
compact manifold, denoted as $M_A^3$, are studied. The total spacetime is
$M^4\times M_A^3$. We compare the range of the corrections to the range of the
$T^3$ corrections. It is found that for small values of the radius of the extra
dimensions ($R<10^{-6}$) the the Sol manifold corrections are large compared to
the 3-torus corrections. Also, Sol manifolds corrections can be larger,
comparable or smaller compared to the 3-torus case, for larger $R$.Comment: Based on talk given in Recent Developments in Gravity, June 8-11,
Ioannina, Greec

### Localized Fermions on Domain Walls and Extended Supersymmetric Quantum Mechanics

We study fermionic fields localized on topologically unstable domain walls
bounded by strings in a grand unified theory theoretical framework.
Particularly, we found that the localized fermionic degrees of freedom, which
are up and down quarks as long as charged leptons, are connected to three
independent N=2, $d=1$ supersymmetric quantum mechanics algebras. As we
demonstrate, these algebras can be combined to form higher order
representations of N=2, $d=1$ supersymmetry. Due to the uniform coupling of the
domain wall solutions to the down-quarks and leptons, we also show that a
higher order N=2, $d=1$ representation of the down-quark--lepton system is
invariant under a duality transformation between the couplings. In addition,
the two N=2, $d=1$ supersymmetries of the down-quark--lepton system, combine at
the coupling unification scale to an N=4, $d=1$ supersymmetry. Furthermore, we
present the various extra geometric and algebraic attributes that the fermionic
systems acquire, owing to the underlying N=2, $d=1$ algebras.Comment: Revised versio

### A Note on Gravitational Memory in F(R)-theories and their Equivalent Scalar-Tensor Theories

In this paper we consider the implications that the effect gravitational
memory would have on primordial black holes, within the theoretical context of
$F(R)$ related scalar-tensor theories. As we will demonstrate, under the
assumption that the initial mass of the primordial black hole is such so that
it evaporates today, this can potentially constrain the $F(R)$ related theories
of gravity. We study two scalar-tensor models and discuss the evolution of
primordial black holes created at some initial time $t_f$ in the early
universe. The results between the two models vary significantly which shows us
that, if the effect of gravitational memory is considered valid, some of the
scalar-tensor models and their corresponding $F(R)$ theories must be further
constrained.Comment: Revised version, updated ref list, similar to journal versio

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