Half‐Maximal Supersymmetry from Exceptional Field Theory

We study ‐dimensional half‐maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half‐maximal Minkowski_D and AdS_D vacua. We then show how to obtain consistent truncations of type II / 11‐dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised structures, where , and N is the number of vector multiplets obtained in the lower‐dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half‐maximal gauged SUGRA. We use this to prove that all half‐maximal warped AdS_D and Minkowski_D vacua of type II / 11‐dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M‐theory / heterotic duality. In five dimensions, we find a new SO(5, N ) double field theory with a ‐dimensional extended space. Its section condition has one solution corresponding to 10‐dimensional supergravity and another yielding six‐dimensional SUGRA.     

Noncommutative differential geometry, and the matrix representations of generalised algebras

The underly ing algebra I or a noncummutative geometry is taken to be a matrix algebra, and the set of derivatives the ad joint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of 1-firms is at free module over the algebra of matrices. The concept of a generalised algebra is delined and it is shown that this is required in order for the space of 2-forms to exist, The exterior derivative is generalised for higher-order forms and these are also shown to he free modules over the matrix algebra. Examples of mappings that preserve the differential Structure are peen, Also giken are four examples of matrix generalised algebras, and the corresponding noncommutntive geometries, including the cases where the generalised algebra corresponds to a representation of a Lie algebra or a q-deformed algebra.     

A coupled KdV system: Consistent tanh expansion,soliton-cnoidal wave solutions and nonlocal symmetries

In this paper, a coupled KdV system is shown to be solvable, having a consistent tanh expansion solution. From the consistent tanh expansion solution, a kind of soliton-cnoidal interaction solution is obtained explicitly. Moreover, the nonlocal symmetries related to the truncated Painlevé expansion and the corresponding transformation groups are also given.     

Generalised BRST symmetry and gaugeon formalism for perturbative quantum gravity: Novel observation

In this paper the novel features of Yokoyama gaugeon formalism are stressed out for the theory of perturbative quantum gravity in the Einstein curved spacetime. The quantum gauge transformations for the theory of perturbative gravity are demonstrated in the framework of gaugeon formalism. These quantum gauge transformations lead to renormalised gauge parameter. Further, we analyse the BRST symmetric gaugeon formalism which embeds more acceptable Kugo–Ojima subsidiary condition. Further, the BRST symmetry is made finite and field-dependent. Remarkably, the Jacobian of path integral under finite and field-dependent BRST symmetry amounts to the exact gaugeon action in the effective theory of perturbative quantum gravity.     

Freudenthal duality and generalized special geometry

Freudenthal duality, introduced in Borsten et al. (2009) [1] and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential.Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.     

Intersecting D-branes, Chern-kernels and the inflow mechanism

We analyse a system of arbitrarily intersecting D-branes in ten-dimensional supergravity. Chiral anomalies are supported on the intersection branes, called I-branes. For non-transversal intersections anomaly cancellation has been realized until now only cohomologically but not locally, due to short-distance singularities. In this paper we present a consistent local cancellation mechanism, writing the δ-like brane currents as differentials of the recently introduced Chern-kernels, J=dK. In particular, for the first time we achieve anomaly cancellation for dual pairs of D-branes. The Chern-kernel approach allows to construct an effective action for the RR-fields which is free from singularities and cancels the quantum anomalies on all D-branes and I-branes.     

Consistent Riccati expansion solvable classification and soliton-cnoidal wave interaction solutions for an extended Korteweg-de Vries equation

In this paper, we consider an extended Korteweg-de Vries (KdV) equation. Using the consistent Riccati expansion (CRE) method of Lou, the extended KdV equation is proved to be CRE solvable in only two distinct cases. These two CRE solvable models are the KdV-Lax and KdV-Sawada-Kotera (KdV-SK) equations. In addition, applying the nonauto-Bäcklund transformations which are provided by the CRE method, we present the explicit construction for soliton-cnoidal wave interaction solutions which represent a soliton propagating on a cnoidal periodic wave background in the KdV-Lax and KdV-SK equations, respectively.     

New Gaugings and Non‐Geometry

We discuss the possible realisation in string/M theory of the recently discovered family of four‐dimensional maximal gauged supergravities, and of an analogous family of seven‐dimensional half‐maximal gauged supergravities. We first prove a no‐go theorem that neither class of gaugings can be realised via a compactification that is locally described by ten‐ or eleven‐dimensional supergravity. In the language of Double Field Theory and its M theory analogue, this implies that the section condition must be violated. Introducing the minimal number of additional coordinates possible, we then show that the standard S ³ and S ⁷ compactifications of ten‐ and eleven‐dimensional supergravity admit a new class of section‐violating generalised frames with a generalised Lie derivative algebra that reproduces the embedding tensor of the and gaugings respectively. The physical meaning, if any, of these constructions is unclear. They highlight a number of the issues that arise when attempting to apply the formalism of Double Field Theory to non‐toroidal backgrounds. Using a naive brane charge quantisation to determine the periodicities of the additional coordinates restricts the gaugings to an infinite discrete set and excludes all the gaugings other than the standard one.     

Consistent,Covariant and Multiplicative Anomalies

It is shown that the multiplicative anomaly in the vector-axial-vector model, which apparently has nothing to do with the breaking of classical current symmetries, nevertheless is strictly related to the well known consistent and covariant anomalies.     

Noncommutativity, Generalized Uncertainty Principle and FRW Cosmology

We consider the effects of noncommutativity and the generalized uncertainty principle on the FRW cosmology with a scalar field. We show that, the cosmological constant problem and removability of initial curvature singularity find natural solutions in this scenarios.     

Generalised phase contrast: microscopy,manipulation and more

Generalised phase contrast (GPC) not only leads to more accurate phase imaging beyond thin biological samples, but serves as an enabling framework in developing tools over a wide spectrum of contemporary applications in optics and photonics, including optical trapping and micromanipulation, optical phase cryptography, light-efficient image projection and parallel laser beam shaping for optical landscapes. In this review, we discuss the fundamental ideas behind generalised phase contrast and present a survey of its exciting applications.     

Consistent histories,robust histories,and verifiable histories

A distinction is made among consistent histories in general, and those that are robustly consistent, and finally those that are classically verifiable. In the case of an individual system, the Copenhagen view would regard only its verifiable history to have actually taken place. We analyze the consequences if instead one associates reality with a finer and yet robust history. There are distinct disadvantages. In general one should probabilistically sum over the fine-grained consistent histories, even when the events have already happened.     

Magnetic avalanches: Josephson, Bean, and Bak

Josephson junction arrays provide an ideal physical realization for studying the complex dynamics of the sort found in sandpile models. They provide a means of separately investigating the dual physical effects of nonlinearity and disorder, and hold promise as an example for establishing a rigorous connection between the governing differential equations and the corresponding cellular automaton.     

0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

Structures and Spectral Characteristics of Silylborane,Silylaluminum Hydride,Silylphosphine, and Silyl Mercaptan

The vibrational frequencies of several silanes H₃SiX (X=BH₂, AlH₂, PH₂ and SH) are determined. The infrared and Raman spectra are plotted. Several scale procedures were use to improve the theoretical spectra. The geometric parameters in the planar, staggered and eclipsed structures of these species are fully optimized and compared with ab initio calculations. Basis set effects on the calculated structures are discussed. A few thermodynamic parameters, net atomic charges, dipole moment and energy are also computed.     

Gravity, non-commutative geometry and the Wodzicki residue

We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator D on an n dimensional compact Riemannian manifold with n ≥ 4, n even, the Wodzicki residue Res(D⁻ⁿ⁺²) is the integral of the second coefficient of the heat kernel expansion of D². We use this result to derive a gravity action for commutative geometry which is the usual Einstein-Hilbert action and we also apply our results to a non-commutative extension which is given by the tensor product of the algebra of smooth functions on a manifold and a finite dimensional matrix algebra. In this case we obtain gravity with a cosmological constant.     

Pontrjagin forms, Chern Simons classes, Codazzi transformations, and affine hypersurfaces

We show that the primary and secondary characteristic classes vanish in the context of affine differential geometry. This gives rise to obstructions to realizing a conformal class of metrics on a manifold either as the first or as the second fundamental form of an affine immersion.