arXiv subjects
Publications and source records attributed to V. K. Oikonomou.
We connect the fermionic fields, localized on the intersection curve $Σ$ of two D7-branes with zero background flux, to a N=2 supersymmetric quantum mechanics algebra, within the theoretical framework of F-theory.
We study the Casimir energy of a scalar field for a regular polygon with N sides. The scalar field obeys Dirichlet boundary conditions at the perimeter of the polygon. The polygon eigenvalues $λ_N$ are expressed in terms of the Dirichlet circle eigenvalues $λ_C$ as an expansion in $\frac{1}{N}$ of the form, $λ_N = λ_C (1 + \frac{4ζ(2)}{N^2} + \frac{4ζ(3)}{N^3} + \frac{28ζ(4)}{N^4}+...)$. A comparison follows between the Casimir energy on the polygon with N=4 found with our method and the Casimir energy of the scalar field on a square. We generalize the result to spaces of the form $R^d\times P_N$, with $P_N$ a N-polygon. By the same token, we find the electric field energy for a "cylinder" of infinite length with polygonal section. With the method we use and in view of the results, it stands to reason to assume that the Casimir energy of $D$-balls has the same sign with the Casimir energy of regular shapes homeomorphic to the $D$-ball. We sum up and discuss our results at the end of the article.
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 $R$.
The Yukawa interaction sector of superstring inspired models that give superconducting strings, can be described in terms of a supersymmetric quantum mechanics algebra. We relate the Witten index of susy quantum mechanics with an index characteristic to superconducting string models.
In this article we consider the Casimir energy and force of massless Majorana fermions and vector bosons between parallel plates. The vector bosons satisfy perfect electric conductor boundary conditions while the Majorana fermions satisfy bag and chiral boundary conditions. We consider various piston configurations containing one vector boson and one fermion. We present a new regularization mechanism the piston offers. In our case regularization occurs explicitly at the Casimir energy density and not at the Casimir force level, as in usual pistons. We make use of boundary broken supersymmetry to explain the number of fields that appear in all the studied cases. The effect of chiral boundary conditions in a fermion boson system is investigated. Concerning the supersymmetry issue and the vanishing Casimir energy, we study a massive Dirac fermion-scalar boson system with bag and specific Robin type boundary conditions for which the Casimir energy vanishes. Finally a two scalar bosons system between parallel plates is presented in which the singularities vanish in the total Casimir energy. A discussion on boundary broken supersymmetry follows.
In this paper we review the calculations that are needed to obtain the bosonic and fermionic effective potential at finite temperature and volume (at one loop). The calculations at finite volume correspond to $S^1\times R^d$ topology. These calculations appear in the calculation of the Casimir energy and of the effective potential of extra dimensional theories. In the case of finite volume corrections we impose twisted boundary conditions and obtain semi-analytic results. We mainly focus in the details and validity of the results. The zeta function regularization method is used to regularize the infinite summations. Also the dimensional regularization method is used in order to renormalize the UV singularities of the integrations over momentum space. The approximations and expansions are carried out within the perturbative limits. After the end of each section we briefly present applications associated to the calculations. Particularly the calculation of the effective potential at finite temperature for the Standard Model fields, the effective potential for warped and large extra dimensions and the topological mass creation. In the end we discuss on the convergence and validity of one of the obtained semi-analytic results.
In this paper we study the Casimir force for a piston configuration in $R^3$ with one dimension being slightly curved and the other two infinite. We work for two different cases with this setup. In the first, the piston is "free to move" along a transverse dimension to the curved one and in the other case the piston "moves" along the curved one. We find that the Casimir force has opposite signs in the two cases. We also use a semi-analytic method to study the Casimir energy and force. In addition we discuss some topics for the aforementioned piston configuration in $R^3$ and for possible modifications from extra dimensional manifolds.
We study the influence of the shape of compact dimensions to the Casimir energy and Casimir force of a scalar field. We examine both the massive and the massless scalar field. The total spacetime topology is $M^D\times T^2_θ$, where $M^D$ is the $D$ dimensional Minkowski spacetime and $T^2_θ$ the twisted torus described by $R_1$, $R_2$ and $θ$. For the case $R_1=R_2$ we found that the massive bulk scalar field Casimir energy is singular for $D$=even and this singularity is $R$-dependent and remains even when the force is calculated. Also the massless Casimir energy and force is regular only for D=4 (!). This is very interesting phenomenologically. We examine the energy and force as a function of $θ$. Also we address the stabilization problem of the compact space. We also briefly discuss some phenomenological implications.
We calculate the scalar Casimir energy and Casimir force for a $R^3\times N$ Kaluza-Klein piston setup in which the extra dimensional space $N$ contains a non-commutative 2-sphere, $S_{FZ}$. The cases to be studied are $T^d\times S_{FZ}$ and $S_{FZ}$ respectively as extra dimensional spaces, with $T^d$ the $d$ dimensional commutative torus. The validity of the results and the regularization that the piston setup offers are examined in both cases. Finally we examine the 1-loop corrected Casimir energy for one piston chamber, due to the self interacting scalar field in the non-commutative geometry. The computation is done within some approximations. We compare this case for the same calculation done in Minkowski spacetime $M^D$. A discussion on the stabilization of the extra dimensional space within the piston setup follows at the end of the article.
In this paper we study the influence of hard supersymmetry breaking terms in a N=1, $d=4$ supersymmetric model, in $S^1\times R^3$ spacetime topology. It is found that for some interaction terms and for certain values of the couplings, supersymmetry is unbroken for small lengths of the compact radius, and breaks dynamically as the radius increases. Also for another class of interaction terms, when the radius is large supersymmetry is unbroken and breaks dynamically as the radius decreases. It is pointed out that the two phenomena have similarities with the theory of metastable vacua at finite temperature and with the inverse symmetry breaking of continuous symmetries at finite temperature (where the role of the temperature is played by the compact dimension's radius).
The temperature inversion symmetry $R\to \frac{1}{T}$ is studied for the finite temperature effective potential of the N=1, $d=5$, supersymmetric $SU(3)_{c}{\times}SU(3)_{w}$ model, on the orbifold $S^{1}/Z_{2}$. For the value of the Wilson line parameter $α=1$ ($SU(2)_{L}$ breaks to a $U'(1)$), it is found that the effective potential contains a symmetric part and an anti-symmetric part under $ξ\to \frac{1}ξ$, with, $ξ=RT$. When $α=0$ (for which, $SU(2)_{L}$ remains unbroken) it is found that the only contribution to the effective potential that spoils the temperature inversion symmetry comes from the fermions in the fundamental representation of the gauge group, with $(+,+)$ or $(-,-)$, $Z_{2}$ parities. This is interesting since it implies that the bulk effective potential corresponding to models with orbifold fixed point localized fundamental fermions (and with no bulk fundamental fermions) has the temperature inversion symmetry.
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 of the form $M^4\times M_A^3$. The range of the Sol corrections is investigated and compared to the range of the $T^3$ corrections.
The event rates for the direct detection of a dark matter candidate, which is a Kaluza-Klein gauge boson, are evaluated for a number of nuclear targets. Realistic form factors as well as spin ME and response functions are employed.
The temperature inversion symmetry, for a non interacting supersymmetric ensemble, at finite volume, is studied. It is found that, the scaled free energy, $f(ξ)$, is antisymmetric under temperature inversion transformation, i.e. $f(ξ)=-ξ^{d}f(\frac{1}ξ)$. This occurs for antiperiodic bosons and periodic fermions, in the compact dimension. On the contrary, for periodic bosons and antiperiodic fermions, $f(ξ)=ξ^{d}f(\frac{1}ξ)$.
We study a ${N=1}$ supersymmetric model in a ${S}^{1}{\times R}^{3}$ spacetime. We find that by choosing appropriate boundary conditions for the contributing fields supersymmetry can be preserved. However if we add a hard supersymmetry breaking term, we observe that for small values of the length of the ${S}^{1}$ dimension, supersymmetry remains unbroken and breaks spontaneously when the length exceeds a critical value. The final picture resembles the first order phase transition picture.