M-Theory on (K3 X S^1)/Z_2

We analyze $M$-theory compactified on $(K3\times S^1)/Z_2$ where the $Z_2$ changes the sign of the three form gauge field, acts on $S^1$ as a parity transformation and on K3 as an involution with eight fixed points preserving SU(2) holonomy. At a generic point in the moduli space the resulting theory has as its low energy limit N=1 supergravity theory in six dimensions with eight vector, nine tensor and twenty hypermultiplets. The gauge symmetry can be enhanced (e.g. to $E_8$) at special points in the moduli space. At other special points in the moduli space tensionless strings appear in the theory.Comment: LaTeX file, 11 page

Torus-Fibered Calabi-Yau Threefolds with Non-Trivial Fundamental Group

We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP_9 base, with fundamental group Z_2 X Z_2. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces admit at least a Z_2 X Z_2 group of automorphisms. One then constructs Calabi-Yau threefolds X as the fiber product of two such dP_9 surfaces, demonstrating that the involutions on the surfaces lift to a freely acting Z_2 X Z_2 group of automorphisms on X. The threefolds Z are then obtained as the quotient Z=X/(Z_2 X Z_2). These Calabi-Yau spaces Z admit stable, holomorphic SU(4) vector bundles which, in conjunction with Z_2 X Z_2 Wilson lines, lead to standard-like models of particle physics with naturally suppressed nucleon decay.Comment: 60 pages, 13 figures, Typos correcte

An investigation of development appraisal methods employed by valuers and appraisers in small and medium sized practices in Brazil

Purpose – Whilst the real estate development appraisal practices of large national and international real estate companies are well understood, relatively little is known about how development appraisals are conducted by indigenous appraisers and valuers in developing countries. The purpose of this paper is to investigate how development appraisal is conducted in Brazil, compared to the UK, focusing primarily on the methods employed by small- and medium-sized real estate practices and their appraisers to appraise the viability of commercial real estate developments in the State of Sao Paulo. Design/methodology/approach – The study employs a two phase Delphi Method to capture and analyse empirical data from small- and medium-sized real estate appraisers in Brazil. Using the long established and relatively transparent UK Residual Method of development appraisal as a template against which to compare Brazilian appraisal methods, guidance and practice. To understand how indigenous development appraisers operate the Brazilian development appraisal methods, the research was conducted in Portuguese by a bi-lingual real estate expert who was familiar with both UK and Brazilian practice. Findings – The research establishes that appraisers working for small- and medium -sized real estate practices in Brazil rarely use the Residual Method. Instead, they employ a range of methods, the choice of which is heavily influenced by the availability of comparable market data, with Direct Comparison of market data and the Capitalisation of Income being the methods of choice when sufficient comparable evidence is available. Appraisers rarely employ the Residual Method as the principal development appraisal technique, using instead the Comparative Method and Discounted Cash Flow (DCF) analysis. Land prices are usually agreed or already known and developer’s profit is usually determined using DCF analysis and is highly sensitive to fluctuations in construction costs. Research limitations/implications – The research engaged with a small number of appraisers and valuers in small- and medium-sized practices in the State of Sao Paulo using a two-phase Delphi Method. The long established UK Residual Method of development appraisal was used as a template against which to compare practice in Sao Paulo State. There is potential therefore to replicate the research in other Brazilian States and transfer the methodology to other developing countries. Practical implications – In Brazil, when development land in urban areas is acquired on the basis of plot exchange, land is often sold at less than market value and the original landowner retains an equity stake in the development and shares in the development overage. The practice of “permuta física”, giving landowners the freehold of part of the development, or “permuta financeira”, whereby the landowner receives an enhanced land price, indexed against development value, is of potential relevance to the UK and other developed countries that need help in urban unlocking land markets

F-Theory on Spin(7) Manifolds: Weak-Coupling Limit

F-theory on appropriately fibered Spin(7) holonomy manifolds is defined to arise as the dual of M-theory on the same space in the limit of a shrinking fiber. A class of Spin(7) orbifolds can be constructed as quotients of elliptically fibered Calabi-Yau fourfolds by an anti-holomorphic involution. The F-theory dual then exhibits one macroscopic dimension that has the topology of an interval. In this work we study the weak-coupling limit of a subclass of such constructions and identify the objects that arise in this limit. On the Type IIB side we find space-time filling O7-planes as well as O5-planes and orbifold five-planes with a (-1)^{F_L} factor localised on the interval boundaries. These orbifold planes are referred to as X5-planes and are S-dual to a D5-O5 system. For other involutions exotic O3-planes and X3-planes on top of a six-dimensional orbifold singularity can appear. We show that the objects present preserve a mutual supersymmetry of four supercharges in the bulk of the interval and two supercharges on the boundary. It follows that in the infinite-interval and weak-coupling limit full four-dimensional N=1 supersymmetry is restored, which on the Type IIA side corresponds to an enhancement of supersymmetry by winding modes in the vanishing interval limit.Comment: 23 page

Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds

We propose a novel approach to obtain non-supersymmetric four-dimensional effective actions by considering F-theory on manifolds with special holonomy Spin(7). To perform such studies we suggest that a duality relating M-theory on a certain class of Spin(7) manifolds with F-theory on the same manifolds times an interval exists. The Spin(7) geometries under consideration are constructed as quotients of elliptically fibered Calabi-Yau fourfolds by an anti-holomorphic and isometric involution. The three-dimensional minimally supersymmetric effective action of M-theory on a general Spin(7) manifold with fluxes is determined and specialized to the aforementioned geometries. This effective theory is compared with an interval Kaluza-Klein reduction of a non-supersymmetric four-dimensional theory with definite boundary conditions for all fields. Using this strategy a minimal set of couplings of the four-dimensional low-energy effective actions is obtained in terms of the Spin(7) geometric data. We also discuss briefly the string interpretation in the Type IIB weak coupling limit.Comment: 39 pages, 4 figures, v2: improvements and clarifications on the 4d interpretation and weak coupling limit; typos correcte

Modular Invariants for Lattice Polarized K3 Surfaces

We study the class of complex algebraic K3 surfaces admitting an embedding of H+E8+E8 inside the Neron-Severi lattice. These special K3 surfaces are classified by a pair of modular invariants, in the same manner that elliptic curves over the field of complex numbers are classified by the J-invariant. Via the canonical Shioda-Inose structure we construct a geometric correspondence relating K3 surfaces of the above type with abelian surfaces realized as cartesian products of two elliptic curves. We then use this correspondence to determine explicit formulas for the modular invariants.Comment: 29 pages, LaTe

A symplectic refinement of shifted Hecke insertion

Buch, Kresch, Shimozono, Tamvakis, and Yong defined Hecke insertion to formulate a combinatorial rule for the expansion of the stable Grothendieck polynomials $G_\pi$ indexed by permutations in the basis of stable Grothendieck polynomials $G_\lambda$ indexed by partitions. Patrias and Pylyavskyy introduced a shifted analogue of Hecke insertion whose natural domain is the set of maximal chains in a weak order on orbit closures of the orthogonal group acting on the complete flag variety. We construct a generalization of shifted Hecke insertion for maximal chains in an analogous weak order on orbit closures of the symplectic group. As an application, we identify a combinatorial rule for the expansion of "orthogonal" and "symplectic" shifted analogues of $G_\pi$ in Ikeda and Naruse's basis of $K$-theoretic Schur $P$-functions.Comment: 40 pages; v2: fixed several errors, minor reorganization; v3: further corrections, condensed expositio