Structural results on convexity relative to cost functions

Mass transportation problems appear in various areas of mathematics, their solutions involving cost convex potentials. Fenchel duality also represents an important concept for a wide variety of optimization problems, both from the theoretical and the computational viewpoints. We drew a parallel to the classical theory of convex functions by investigating the cost convexity and its connections with the usual convexity. We give a generalization of Jensen's inequality for cost convex functions.Comment: 10 page

On D3-brane Potentials in Compactifications with Fluxes and Wrapped D-branes

We study the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes. If the Kahler moduli of the compact space are stabilized by nonperturbative effects, a D3-brane experiences a force due to its interaction with D-branes wrapping certain four-cycles. We compute this interaction, as a correction to the warped four-cycle volume, using explicit throat backgrounds in supergravity. This amounts to a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume. We demonstrate for warped conical spaces that the superpotential correction is given by the embedding equation specifying the wrapped four-cycle, in agreement with the general form proposed by Ganor. Our approach automatically provides a solution to the problem of defining a holomorphic gauge coupling on wrapped D7-branes in a background with D3-branes. Finally, our results have applications to cosmological inflation models in which the inflaton is modeled by a D3-brane moving in a warped throat.Comment: 45 pages, 1 figure; v2: added reference, clarified notatio

Warped Tachyonic Inflation in Type IIB Flux Compactifications and the Open-String Completeness Conjecture

We consider a cosmological scenario within the KKLT framework for moduli stabilization in string theory. The universal open string tachyon of decaying non-BPS D-brane configurations is proposed to drive eternal topological inflation. Flux-induced `warping' can provide the small slow-roll parameters needed for successful inflation. Constraints on the parameter space leading to sufficient number of e-folds, exit from inflation, density perturbations and stabilization of the Kahler modulus are investigated. The conditions are difficult to satisfy in Klebanov-Strassler throats but can be satisfied in T^3 fibrations and other generic Calabi-Yau manifolds. This requires large volume and magnetic fluxes on the D-brane. The end of inflation may or may not lead to cosmic strings depending on the original non-BPS configuration. A careful investigation of initial conditions leading to a phenomenologically viable model for inflation is carried out. The initial conditions are chosen on the basis of Sen's open string completeness conjecture. We find time symmetrical bounce solutions without initial singularities for k=1 FRW models which are correlated with an inflationary period. Singular big-bang/big-crunch solutions also exist but do not lead to inflation. There is an intriguing correlation between having an inflationary universe in 4 dimensions and 6 compact dimensions or a big-crunch singularity and decompactification.Comment: 43 pages, 9 figures. v3: Typos correcte

A Neglected Design Style: Colonial Era Hybrid Architecture, Furniture and Interior Decoration in Aotearoa New Zealand

Colonial hybrid design has been a neglected style in Aotearoa New Zealand’s and design history. However, an overview of the corpus, its quantity and plurality, with both Māori and Pākehā makers working into the early twentieth century, indicates that a reappraisal is required. The case study of one Pākehā maker, J.H. Menzies, shows a combination of respect and ignorance of toi Māori (Māori art).[i] Despite the negative connotations of cultural appropriation, a kernel of genuine creative exchange is at the heart of this colonial phenomenon, as exemplified in his work.   [i] I use this term generically to include all forms of art customarily practised by Māori, including (but not limited to) hoahoanga (architecture), toi whakairo (the art of carving) and kōwhaiwahi (painted patterns)

Supersymmetric probes on the conifold

We study the supersymmetric embeddings of different D-brane probes in the AdS_5 x T^{1,1} geometry. The main tool employed is kappa symmetry and the cases studied include D3-, D5- and D7-branes. We find a family of three-cycles of the T^{1,1} space over which a D3-brane can be wrapped supersymmetrically and we determine the field content of the corresponding gauge theory duals. Supersymmetric configurations of D5-branes wrapping a two-cycle and of spacetime filling D7-branes are also found. The configurations in which the entire T^{1,1} space is wrapped by a D5-brane (baryon vertex) and a D7-brane are also studied. Some other embeddings which break supersymmetry but are nevertheless stable are also determined.Comment: 44 pages, LaTeX; v2: typos corrected, references added, discussion of D5-brane embeddings improve

Chern-Simons Theory as the Large Mass Limit of Topologically Massive Yang-Mills Theory

We study quantum Chern-Simons theory as the large mass limit of the limit $D\to 3$ of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift $k\rightarrow k+ c_{\scriptscriptstyle V},\,\,k$ being the bare Chern-Simons parameter. In passing we also prove by explicit computation that topologically massive Yang-Mills theory is UV finite.Comment: 64 pages without figures (10 figures), DAMTP 91-34, LPTHE 91-61, NBI-HE 91-55, UGMS 91-2

Numerical Solutions of ideal two-fluid equations very closed to the event horizon of Schwarzschild black hole

The 3+1 formalism of Thorne, Price and Macdonald has been used to derive the linear two-fluid equations describing transverse and longitudinal waves propagating in the two-fluid ideal collisionless plasmas surrounding a Schwarzschild black hole. The plasma is assumed to be falling in radial direction toward the event horizon. The relativistic two-fluid equations have been reformulate, in analogy with the special relativistic formulation as explained in an earlier paper, to take account of relativistic effects due to the event horizon. Here a WKB approximation is used to derive the local dispersion relation for these waves and solved numerically for the wave number k.Comment: 16 pages, 15 figures. arXiv admin note: text overlap with arXiv:0902.3766, arXiv:0807.459

On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory

We investigate the spectrum of the gauge theory with Chern-Simons term on the noncommutative plane, a modification of the description of the Quantum Hall fluid recently proposed by Susskind. We find a series of the noncommutative massive ``plane wave'' solutions with polarization dependent on the magnitude of the wave-vector. The mass of each branch is fixed by the quantization condition imposed on the coefficient of the noncommutative Chern-Simons term. For the radially symmetric ansatz a vortex-like solution is found and investigated. We derive a nonlinear difference equation describing these solutions and we find their asymptotic form. These excitations should be relevant in describing the Quantum Hall transitions between plateaus and the end transition to the Hall Insulator.Comment: 17 pages, LaTeX (JHEP), 1 figure, added references, version accepted to JHE

Oxidised cosmic acceleration

We give detailed proofs of several new no-go theorems for constructing flat four-dimensional accelerating universes from warped dimensional reduction. These new theorems improve upon previous ones by weakening the energy conditions, by including time-dependent compactifications, and by treating accelerated expansion that is not precisely de Sitter. We show that de Sitter expansion violates the higher-dimensional null energy condition (NEC) if the compactification manifold M is one-dimensional, if its intrinsic Ricci scalar R vanishes everywhere, or if R and the warp function satisfy a simple limit condition. If expansion is not de Sitter, we establish threshold equation-of-state parameters w below which accelerated expansion must be transient. Below the threshold w there are bounds on the number of e-foldings of expansion. If M is one-dimensional or R everywhere vanishing, exceeding the bound implies the NEC is violated. If R does not vanish everywhere on M, exceeding the bound implies the strong energy condition (SEC) is violated. Observationally, the w thresholds indicate that experiments with finite resolution in w can cleanly discriminate between different models which satisfy or violate the relevant energy conditions.Comment: v2: corrections, references adde

Transverse Wave Propagation in Relativistic Two-fluid Plasmas in de Sitter Space

We investigate transverse electromagnetic waves propagating in a plasma in the de Sitter space. Using the 3+1 formalism we derive the relativistic two-fluid equations to take account of the effects due to the horizon and describe the set of simultaneous linear equations for the perturbations. We use a local approximation to investigate the one-dimensional radial propagation of Alfv\'en and high frequency electromagnetic waves and solve the dispersion relation for these waves numerically.Comment: 19 pages, 12 figure