Narrow Results

We introduce a new definition of rank 2 Gieseker-bundles with fixed determinant on a nodal curve, and show that their moduli stack is normal crossing.

Using software under development at Baylor University, we explicitly construct all layer 1 gauge, weakly coupled free fermionic heterotic string models up to order 22 in four large spacetime dimensions. The gauge models consist primarily of gauge content making a systematic construction process efficient. We present an overview of the model building procedure, redundancies in the process, methods used to reduce such redundancies and statistics regarding the occurrence of various combinations of gauge group factors and GUT groups. Statistics for both and models are presented.

We consider wormhole solutions in five-dimensional Kaluza–Klein gravity in the presence of a massless ghost four-dimensional scalar field. The system possesses two types of topological nontriviality connected with the presence of the scalar field and of a magnetic charge. Mathematically, the presence of the charge appears in the fact that the S³ part of a spacetime metric is the Hopf bundle S³ →S² with fiber S¹. We show that the fifth dimension spanned on the sphere S¹ is compactified in the sense that asymptotically, at large distances from the throat, the size of S¹ is equal to some constant, the value of which can be chosen to lie, say, in the Planck region. Then, from the four-dimensional point of view, such a wormhole contains a radial magnetic (monopole) field, and an asymptotic four-dimensional observer sees a wormhole with the compactified fifth dimension.

We discuss the effect of the dynamics of D-branes on moduli stabilization in type IIB string theory compactifications, with reference to a concrete toy model of $T^6/Z_3$ orientifold compactification with fractional D3-branes and anti-D3-branes at orbifold fixed points. The resulting attractive forces between anti-D3-branes and D3-branes, together with the repulsive forces between anti-D3-branes and O3-planes, can affect the stability of the compact space. There are no complex structure moduli in $T^6/Z_3$ orientifold, which should thus capture some generic features of more general settings where all complex structure moduli are stabilized by three-form fluxes. The simultaneous presence of branes and anti-branes brings along the breaking of supersymmetry. Non-BPS combinations of this type are typical of “brane supersymmetry breaking” and are a necessary ingredient in the KKLT scenario for stabilizing the remaining Kähler moduli. The conclusion of our analysis is that, while mutual D-brane interactions sometimes help Kähler moduli stabilization, this is not always the case.

Motivated by particle physics results, we investigate certain dyonic solutions in arbitrary dimensions. Concretely, we study the stringy constructions of such objects from concrete compactifications. Then, we elaborate their tensor network realizations using multistate particle formalism.

We search for a bosonic (nonsupersymmetric) string/gauge theory correspondence by using the ten-dimensional IIB and 0B strings as a guide. Our construction is based on the low-energy bosonic string effective action modified by an extra form flux. We prove that the closed string tachyon can be stabilized in this context, when the AdS scalem L does not exceed a certain critical value, L<L_c. The extra form may be nonperturbatively generated as a soliton from 3-string junctions, similarly to the known nonperturbative (Jackiw–Rebbi–'t Hooft–Hasenfratz) mechanism in gauge theories, as was recently argued by David, Minwalla and Núñez. We find a stable AdS₁₃×S¹³ solution that implies the existence of a 12-dimensional AdS-boundary conformal field theory with the SO(14) global symmetry in the large N't Hooft limit, which is similar to the recently proposed bosonic M-theory of Horowitz and Susskind. Taking the proposed bosonic AdS/CFT correspondence for granted, we generalize it to finite temperature. The corresponding "glueball" masses in higher space–time dimensions are calculated from the dilaton wave equation in the AdS black hole background.

An arithmetic framework for string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at c = 3. It is shown that the conformal field theoretic characters can be derived from the geometry of space–time, and that the geometry is uniquely determined by the two-dimensional field theory on the worldsheet. The modular forms that appear in these constructions admit complex multiplication, and allow an interpretation as generalized McKay–Thompson series associated to the Mathieu and Conway groups. This leads to a string motivated notion of arithmetic moonshine.

We explain the orbifold compactification in string models and present a Z_12−I orbifold compactification toward supersymmetric standard models. We also point out an effective R-parity from this string construction. The VEVs of gauge singlets are chosen such that phenomenological constraints are satisfied.

We construct two distinct brane solutions in six dimensional effective field theory models. The CP¹ sigma model and the baby skyrmion realize warped compactification of the extra dimensions for negative bulk cosmological constant. Higher winding number solutions of the baby skyrmion are also presented.

The finite-sized effect caused by compactified space–time is scrutinized by means of the linear sigma model with constituent quarks at finite temperature T and chemical potential μ, where the compactified spatial dimension with length L is taken along the Oz direction. We find several finite-size effects associated with compactified length L: (a) There are two types of Casimir energy corresponding to two types of quarks, untwisted and twisted quarks. (b) For untwisted quarks, a first-order phase transition emerges at intermediate values of L when the Casimir effect is not taken into account and is enhanced by Casimir energy at small L. (c) For twisted quarks, the phase transition is cross-over everywhere when μ≤200 MeV. When μ> 200 MeV there occurs a first-order phase transition at large L and becomes cross-over at smaller L.

We consider the partition function of super-Yang–Mills theories defined on ${𝕋}^2\times {\mathrm{\Sigma }}_g$. This path integral can be computed by the localization. The one-loop determinant is evaluated by the elliptic genus. This elliptic genus gives trivial result in our calculation. As a result, we obtain a theory defined on the Riemann surface.

The Composition Algebra-based Methodology (CAM) [B. Wolk, Pap. Phys.9, 090002 (2017); Phys. Scr.94, 025301 (2019); Adv. Appl. Clifford Algebras27, 3225 (2017); J. Appl. Math. Phys.6, 1537 (2018); Phys. Scr.94, 105301 (2019), Adv. Appl. Clifford Algebras30, 4 (2020)], which provides a new model for generating the interactions of the Standard Model, is geometrically modeled for the electromagnetic and weak interactions on the parallelizable sphere operator fiber bundle$B_n=(T𝕄,S^n\to {\mathcal{𝒮}}^n,SO(n+1),\pi )$ consisting of base space, the tangent bundle $T𝕄$ of space–time $𝕄$, projection operator $\pi$, the parallelizable spheres $S^n=\{S^1,S^3\}$ conceived as operator fibers $S^n\to {\mathcal{𝒮}}^n$ attaching to and operating on $T_p𝕄$$\forall p\in 𝕄$ as $p$ varies over $𝕄$, and as structure group, the norm-preserving symmetry group $SO(n+1)$ for each of the division algebras which is simultaneously the isometry group of the associated unit sphere. The massless electroweak $SU{(2)}_L\otimes U{(1)}_Y$ Lagrangian is shown to arise from $B_{3\otimes 1}$’s generation of a local coupling operation on sections of Dirac spinor and Clifford algebra bundles over $𝕄$. Importantly, CAM is shown to be a new genre of gauge theory which subsumes Yang–Mills Standard Model gauge theory. Local gauge symmetry is shown to be at its core a geometric phenomenon inherent to CAM gauge theory. Lastly, the higher-dimensional, topological architecture which generates CAM from within a unified eleven $(1,10)$-dimensional geometro-topological structure is introduced.

We know from a result due to Noether–Lefschetz that a very general surface of degree at least 4 in ${\mathbb{P}}^3$ contains only curves which are complete intersections with other surfaces. The main goal of this paper is to construct an explicit and smooth compactification of a parameter space for surfaces in ${\mathbb{P}}^3$ of degree $d,$ for all sufficiently large $d$, containing one conic and one line. The construction also applies to surfaces in ${\mathbb{P}}^3$ containing one plane curve and one line. As an application, we compute the degree of the locus of surfaces of degree $d,$ containing one conic and one line.

Two different topics are shown to be related. Some group presentations generalizing certain symmetric presentations found by Coxeter, and the ideal compactification of the sets obtained by lifting knots in 3-manifolds to their universal covering spaces.

We investigate the particle production in a toroidally compactified space–time due to the expansion of a Friedmann cosmological model in ℝ³ × S¹ outside a U(1) local cosmic string. The case of a Friedmann space–time is also investigated where torsion is incorporated in the connection. We present a generalization to toroidal compactification of p extra dimensions, where the topology is given by ℝ³ × T^p. Some implications are presented and discussed. Besides the dynamics of space–time, we investigate in detail the physical consequences of the topological transformations.

In this paper, we analyze the bosonic current densities induced by a magnetic flux running along an idealized cosmic string in a high-dimensional spacetime, admitting that the coordinate along the string's axis is compactified. Additionally we admit the presence of a magnetic flux enclosed by the compactification axis. In order to develop this analysis we calculate the complete set of normalized bosonic wave functions obeying a quasiperiodicity condition, with arbitrary phase β, along the compactified dimension. In this context, only azimuthal and axial currents densities take place. As to the azimuthal current, two contributions appear. The first contribution corresponds to the standard azimuthal current in a cosmic string spacetime without compactification, while the second contribution is a new one, induced by the compactification itself. The latter is an even function of the magnetic flux enclosed by the string axis and is an odd function of the magnetic flux along its core with period equal to quantum flux, Φ₀ = 2π/e. On the other hand, the nonzero axial current density is an even function of the magnetic flux along the core of the string and an odd function of the magnetic flux enclosed by it. We also find that the axial current density vanishes for untwisted and twisted bosonic fields in the absence of the magnetic flux enclosed by the string axis. Some asymptotic expressions for the current density are provided for specific limiting cases of the physical parameter of the model.

The purpose of this study is to examine the effect of topology change in the initial universe. In this study, the concept of G-cobordism is introduced to argue about the topology change of the manifold on which a transformation group acts. This G-manifold has a fiber bundle structure if the group action is free and is related to the spacetime in Kaluza–Klein theory or Einstein–Yang–Mills system. Our results revealed the fundamental processes of compactification in G-manifolds. In these processes, the initial high symmetry and multidimensional universe changes to present universe by the mechanism which lowers the dimensions and symmetries.

In this paper, connections between the path integrals for four-dimensional quantum gravity and string theory are emphasized. It is shown that there is a natural relation between these two path integrals based on the theorems on embeddings of two-dimensional surfaces in four dimensions and four-dimensional manifolds in ten dimensions. The isometry groups of the three-geometries that are spatial hypersurfaces confomally embedded in the four-manifolds are required to be subgroups of $G_2$, which is the invariance group of the Pfaffian differential system satisfied by one form in the cotangent bundles on the four-manifolds. Based on this and other physical conditions, the three-geometries are restricted to be $S^3$, $S^2\times S^1$ and ${𝔼}^3$ with a boundary, which may be included in the quantum gravitational path integral over four-manifolds which are closed at initial times followed by an exponential expansion compatible with supersymmetry.

This paper considers the relationship between geometry, symmetry and fundamental interactions — gravity and those mediated by gauge fields. We explore product spacetimes which (a) have the necessary symmetries for gauge interactions and four-dimensional gravity and (b) reduce to an $N$-dimensional isotropic universe in their flat space limit. The key technique is looking at orbits of the operator form of symmetric rank-two tensors under changes of coordinate system. Orbits containing diagonal matrices are seen to correspond to product manifolds. The $GL(N,ℝ)$ symmetry of the decompactified universe acts nonlinearly on such a product spacetime. We explore the resulting Kaluza–Klein theories, in which the internal symmetries act indirectly on space of the extra dimensions, and give two examples: a six-dimensional model in which the gauge symmetry is $U(1)$ and a seven-dimensional model in which it is $SU(2)$. We identify constraints that can be placed on any rank-two symmetric tensor to obtain such spacetimes: relationships between polynomial invariants. The multiplicities of its eigenvalues determine the dimensionalities of the factor spaces and hence the gauge symmetries. If the tensor in question is the Ricci tensor, other than two-dimensional factor spaces all the factor spaces are Einstein manifolds. This situation represents the classical vacuum of the Kaluza–Klein theory.

It is well known that the celebrated Lorenz system has an attractor such that every orbit ends inside a certain ellipsoid in forward time. We complement this result by a new phenomenon and by a new interpretation. We show that "infinity" is a global repeller for a set of parameters wider than that usually treated. We construct in a compacted space, a unit sphere that serves as the image of an ideal set at infinity. This sphere is shown to be the union of a family of periodic solutions. Each periodic solution is viewed as a limit cycle, or an isolated periodic orbit when restricted to a certain plane. The unconventional compactification is used.