Modeling a network of brane worlds

We study junctions of supersymmetric domain walls in N=1 supergravity theories in four dimensions, coupled to a chiral superfield with quartic superpotential having $Z_3$ symmetry. After deriving a BPS equation of the domain wall junction, we consider a stable hexagonal configuration of network of brane junctions, which are only approximately locally BPS. We propose a model for a mechanism of supersymmetry breaking without loss of stability, where a messenger for the SUSY breaking comes from the neighboring anti-BPS junction world, propagating along the domain walls connection them.Comment: 10 pages, TeX, (harvmac, big), corrected typos and added reference

Casimir Force in Compact Noncommutative Extra Dimensions and Radius Stabilization

We compute the one loop Casimir energy of an interacting scalar field in a compact noncommutative space of $R^{1,d}\times T^2_\theta$, where we have ordinary flat $1+d$ dimensional Minkowski space and two dimensional noncommuative torus. We find that next order correction due to the noncommutativity still contributes an attractive force and thus will have a quantum instability. However, the case of vector field in a periodic boundary condition gives repulsive force for $d>5$ and we expect a stabilized radius. This suggests a stabilization mechanism for a senario in Kaluza-Klein theory, where some of the extra dimensions are noncommutative.Comment: 10 pages, TeX, harvma

Compactifications of F-Theory on Calabi-Yau Threefolds at Constant Coupli ng

Generalizing the work of Sen, we analyze special points in the moduli space of the compactification of the F-theory on elliptically fibered Calabi-Yau threefolds where the coupling remains constant. These contain points where they can be realized as orbifolds of six torus $T^6$ by $Z_m \times Z_n (m, n=2, 3, 4, 6)$. At various types of intersection points of singularities, we find that the enhancement of gauge symmetries arises from the intersection of two kinds of singularities. We also argue that when we take the Hirzebruch surface as a base for the Calabi- Yau threefold, the condition for constant coupling corresponds to the case where the point like instantons coalesce, giving rise to enhanced gauge group of $Sp(k)$.Comment: 13 pages, Latex, no figures, 1 table, some error in the original version correcte

Domain Wall Junctions in Supersymmetric Field Theories in D=4

We study the possible BPS domain wall junction configurations for general polynomial superpotentials of N=1 supersymmetric Wess-Zumino models in D=4. We scan the parameter space of the superpotential and find different possible BPS states for different values of the deformation parameters and present our results graphically. We comment on the domain walls in F/M/IIA theories obtained from the Calabi-Yau fourfolds with isolated singularities and a background flux.Comment: 26 pages, 4 figure

Mass and angular momentum of black holes in 3D gravity theories with first order formalism

We apply the Wald formalism to obtain masses and angular momenta of black holes in three dimensional gravity theories using the first order formalism. Wald formalism suggests that the entropy of a black hole can be defined by an integration of a conserved charge on the bifurcation horizon, and mass and angular momentum of a black hole as an integration of some charge variation form at spatial infinity. The action of three dimensional gravity theories can be represented by a form including some auxiliary fields. As well-known examples we have calculated masses and angular momenta of some black holes in topologically massive gravity and new massive gravity theories using the first order formalism. We have also calculated mass and angular momentum of BTZ black hole and new type black hole in minimal massive gravity theory with the action represented by the first order formalism. We have also calculated the entropy and central charges of new type black hole. According to $AdS/CFT$ correspondence we suggest that the left and right moving temperatures should be equal to the Hawking temperature in the case of new type black hole in minimal massive gravity.Comment: 35 pages, title changed back to original one, some contents are added and correcte