Torsion Manifolds Research Articles

Fourier transform synchrotron spectroscopy of the COD-bending fundamental of CD3OD

The high-resolution Fourier transform spectrum of the CD3OD isotopologue of methanol in the region of the COD-bending fundamental band at 775 cm−1 has been recorded at the Far Infrared Beamline of the Canadian Light Source synchrotron. The torsion-rotation structure has been analyzed for sub-bands from K = 0 to 16 for both A and E torsional symmetries in the vt = 0 torsional state of the COD-bending mode. Energy term values for the excited COD-bending levels have been determined, and fitted to J(J + 1) power-series expansions to provide substate J = 0 origins. These have in turn been fitted to a basic Fourier model in order to map the torsional energy structure. The K-reduced COD-bending torsional origins follow a regular oscillatory pattern as a function of K with a significantly reduced amplitude relative to that of the vibrational ground state. With use of a simple formula for the change in the torsional constant F, the torsional barrier height V3 is found to be 440.25 cm−1, an increase of 22% relative to the ground state. The COD bend does not show evidence of anharmonic Fermi resonances with the ground torsional manifold, but J-localized level-crossing resonances coupling the 5A and 8A substates with vt = 4 ground level partners have been observed and characterized.

The C0 estimate for the quaternionic Calabi conjecture

We prove the C0 estimate for the quaternionic Monge-Ampère equation on compact hyperKähler with torsion manifolds. Our goal is to provide a simpler proof than the one presented in [3].

Unraveling torsional bath interactions with the CO stretching state in methanol

Quantum mechanical models describing the effects of a C3 internal rotor have been successful in modeling all the torsional manifolds of isolated vibrational states. However, modeling the coupling between nearly degenerate small amplitude vibrations in the C3 internal rotation case remains far from satisfactory and a variety of practical and fundamental questions persist on basis sets, the relative importance of effects and how the problem should be approached. The ν8 C–O stretching state of methanol has been well studied with infrared techniques and has the potential to serve as an experimental reference data set for the development of models for the coupled large and small amplitude motion case. A combined infrared-microwave study of the lowest K A-states of vt=3, vt=4 and ν8 has been performed to understand the nature of the interactions between ν8 the excited torsional states. The interaction between vt=4 and ν8 at K=0+ has been confirmed to be Fermi type with magnitude of 2.5cm−1. Additionally, the fundamental a-symmetry and b-symmetry Coriolis interactions between vt=3 and ν8 have been estimated to be 8900MHz and −360MHz, respectively. The magnitude of these interactions suggests that modeling the ν8 state, the vt=3 state, and the vt=4 states will have to carefully account for these interactions.

Instantons on sine-cones over Sasakian manifolds

We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K\"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric torsion. Furthermore, a deformation of the metric on the sine-cone over 3-Sasakian manifolds allows one to introduce a hyper-K\"ahler with torsion (HKT) structure. In the large-volume limit these KT and HKT spaces become Calabi-Yau and hyper-K\"ahler conifolds, respectively. We construct gauge connections on complex vector bundles over conical KT and HKT manifolds which solve the instanton equations for Yang-Mills fields in higher dimensions.

Gauge/gravity duality in heterotic string theory

Gravity duals for little string theories --- which give rise to four-dimensional theories that undergo permanent confinement in the infrared --- have not been studied in great detail. We address this question in the framework of heterotic SO(32) and E_8 x E_8 string theory, constructing these backgrounds by wrapping heterotic five-branes on calibrated two-cycles of non-Kahler resolved conifolds. Related to deformations of the underlying little string theories, we find numerous analytic solutions preserving N = 1 supersymmetry in four-dimensions. These theories all have non-abelian global symmetries that generally arise from both the heterotic vector bundle and from certain orbifold states. In the decoupling limit, we argue that the gravity duals are given by non-Kahler manifolds that have both blown-up two-cycles and three-cycles at the origin. We argue this following certain duality sequences that include M-theory torsional manifolds at an intermediate step, which help us to construct new type I' gauge/gravity duality pairs. In the M-theory duality frame, we also elucidate new sequences of flips and flops.

Supercharges in the hyper-Kähler with torsion supersymmetric sigma models

We construct explicitly classical and quantum supercharges satisfying the standard ${\cal N} = 4$N=4 supersymmetry algebra in the supersymmetric sigma models describing the motion over hyper-Kähler with torsion manifolds. One member of the family of superalgebras thus obtained is equivalent to the superalgebra derived and formulated earlier in purely mathematical framework.

Local metrics admitting a principal Killing–Yano tensor with torsion

In this paper we initiate a classification of local metrics admitting the principal Killing–Yano tensor with a skew-symmetric torsion. It is demonstrated that in such spacetimes rank-2 Killing tensors occur naturally and mutually commute. We reduce the classification problem to that of solving a set of partial differential equations, and we present some solutions to these PDEs. In even dimensions, three types of local metrics are obtained: one of them naturally generalizes the torsion-less case while the others occur only when the torsion is present. In odd dimensions, we obtain more varieties of local metrics. The explicit metrics constructed in this paper are not the most general possible admitting the required symmetry; nevertheless, it is demonstrated that they cover a wide variety of solutions of various supergravities, such as the Kerr–Sen black holes of (un-)gauged Abelian heterotic supergravity, the Chong–Cvetic–Lü–Pope black hole solution of five-dimensional minimal supergravity or the Kähler with torsion manifolds. The relation between generalized Killing–Yano tensors and various torsion Killing spinors is also discussed.

Electric Field Induced Phase Transitions in Polymers: A Novel Mechanism for High Speed Energy Storage

Using first-principles simulations, we identify the microscopic origin of the nonlinear dielectric response and high energy density of polyvinylidene-fluoride-based polymers as a cooperative transition path that connects nonpolar and polar phases of the system. This path explores a complex torsional and rotational manifold and is thermodynamically and kinetically accessible at relatively low temperatures. Furthermore, the introduction of suitable copolymers significantly alters the energy barriers between phases providing tunability of both the energy density and the critical fields.

Yang-Mills fields in flux compactifications on homogeneous manifolds with SU(4)-structure

The SU(4)-instanton equations are natural BPS equations for instantons on 8-manifolds. We study these equations on nearly Kaehler and Calabi-Yau torsion manifolds of the form M x G/H, with G/H a coset space and M a product of a torus with Euclidean space. By imposing G-invariance the instanton equations reduce to interesting equations on M; for example, equations used by Kapustin and Witten in the geometric Langlands program arise in this way. We carry out reductions in a number of examples, and where possible present simple solutions.

High-resolution spectrum of the ν9 band and reinvestigation of the ν8 band of cis-CH3ONO

The infrared spectrum of methyl nitrite CH3ONO has been recorded at a spectral resolution of 0.003cm−1 using a Fourier-transform spectrometer Bruker IFS125HR. The ν8 band of the cis isomer has been reinvestigated in the 780–880cm−1 spectral range to complete the study made by Goss et al. (2004) [3] and to fit the internal rotor splittings. The BELGI-IR program, which enables us to treat an isolated infrared band for asymmetric molecules containing one internal methyl rotor has been used for the analysis and predictions of spectra. Finally 1036 lines (913 A-type and 123 E-type lines for J≤50 and Ka≤28) have been assigned for the cis isomer and fitted with a standard deviation of 0.00047cm−1.Furthermore, for the first time, the ν9 band of cis-CH3ONO was investigated in the 540–660cm−1 spectral range and rather large internal rotation splittings were also observed at higher J values. For the ν9 band, the effective approach performed with the BELGI-IR program allowed us to analyze and reproduce 682 lines up to J=50 and Ka=18 with a standard deviation of 0.00051cm−1. The multiple vibration–rotation–torsion interactions, which are likely to occur between the excited v9=1 and v8=1 states and the torsional manifolds are discussed.

Rotationally and torsionally inelastic scattering of methanol on helium

Cross-sections and rate coefficients have been computed for rotationally and torsionally inelastic transitions between levels of the torsional manifolds ν= 0, 1 and 2 of methanol; the collision partner was the helium atom. We find the torsional inelasticity to be most pronounced for transitions between the excited states, ν= 1 and 2. The torsionally inelastic cross-sections are smaller, on average, than the cross-sections for pure rotationally inelastic transitions, by typically an order of magnitude. We compared cross-sections calculated using the full CH3OH–He interaction potential, which is a function of the torsion angle, with the cross-sections computed for the staggered conformation, i.e. for a fixed value of the torsion angle. The agreement between these two sets of results improves with increasing magnitude of the cross-section. Accordingly, the use of previous results, for the rotational excitation of methanol by He and by H2, obtained for the staggered conformation, should not compromise the analysis of observations of methanol in the interstellar medium.

Symmetries of the Dirac operator with skew-symmetric torsion

In this paper, we consider the symmetries of the Dirac operator derived from a connection with skew-symmetric torsion, ∇T. We find that the generalized conformal Killing–Yano tensors give rise to symmetry operators of the massless Dirac equation, provided an explicitly given anomaly vanishes. We show that this gives rise to symmetries of the Dirac operator in the case of strong Kähler with torsion (KT) and strong hyper-Kähler with torsion (HKT) manifolds.

Index theorems on torsional geometries

We study various topological invariants on a torsional geometry in the presence of a totally anti-symmetric torsion H under the closed condition dH = 0, which appears in string theory compactification scenarios. By using the identification between the Clifford algebra on the geometry and the canonical quantization condition of fermions in quantum mechanics, we construct N=1 quantum mechanical sigma model in the Hamiltonian formalism. We extend this model to N=2 system, equipped with the totally anti-symmetric tensor associated with the torsion on the target space geometry. Next we construct transition elements in the Lagrangian path integral formalism and apply them to the analyses of the Witten indices in supersymmetric systems. We explicitly show the formulation of the Dirac index on the torsional manifold which has already been studied. We also formulate the Euler characteristic and the Hirzebruch signature on the torsional manifold.

Moduli space of torsional manifolds

We characterize the geometric moduli of non-Kähler manifolds with torsion. Heterotic supersymmetric flux compactifications require that the six-dimensional internal manifold be balanced, the gauge bundle be Hermitian Yang–Mills, and also the anomaly cancellation be satisfied. We perform the linearized variation of these constraints to derive the defining equations for the local moduli. We explicitly determine the metric deformations of the smooth flux solution corresponding to a torus bundle over K3.

In the realm of the geometric transitions

We complete the duality cycle by constructing the geometric transition duals in the type IIB, type I and heterotic theories. We show that in the type IIB theory the background on the closed string side is a Kähler deformed conifold, as expected, even though the mirror type IIA backgrounds are non-Kähler (both before and after the transition). On the other hand, the type I and heterotic backgrounds are non-Kähler. Therefore, on the heterotic side these backgrounds give rise to new torsional manifolds that have not been studied before. We show the consistency of these backgrounds by verifying the torsional equation.

Geometric transitions, flops and non-Kähler manifolds: I

We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in M-theory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G 2 manifolds that are circle fibrations over non-Kähler manifolds is presented.

Bifurcation tunneling dynamics in the water trimer

Recent far-infrared vibration–rotation–tunneling experiments have probed intricate details of the hydrogen bond tunneling dynamics in the water trimer through excitation of intermolecular vibrational transitions to states of sequentially increasing energy. The experimentally observed bifurcation splitting in the water trimer evolves from an equally spaced quartet in the vibrational ground state to a slightly asymmetrical quartet for intermediate torsional vibrational states lying below 100 cm−1. Even more asymmetric bifurcation splittings have been observed in the out-of-plane librational band of (H2O)3 near 520 cm−1. These patterns may be caused by the bifurcation and flip rearrangements becoming comparable in magnitude. Alternatively, some of the data can be fitted by introducing tunneling matrix elements corresponding to multiple elementary rearrangements. Analysis of the observed bifurcation tunneling splittings of (D2O)3 confirms that the dominant bifurcation pathway includes the torsional flipping motion of the neighboring water molecules. Quantification of the bifurcation matrix elements of (D2O)3 furthermore reveals that these vary within each torsional manifold.

Reduced-dimensionality quantum bound state treatment of hydrogen-bonded clusters: torsional vibrational manifold of the water trimer

A review of our reduced-dimensionality quantum dynamical treatments of the coupled low-frequency large-amplitude torsional vibrations of the water trimer is presented. It covers three-dimensional bound state calculations of the intermolecular torsional energy levels of (H 2O) 3, (D 2O) 3, and other isotopomers, and quantum (3+1)-dimensional torsional-stretching calculations of torsional-state dependent vibrationally averaged rotational constants of isotopically pure and mixed water trimers.

Ribonucleic acid folder: The earliest moves of a good structure seeker

We identify the earliest folding events of a classical soft-mode ribonucleic acid chain under renaturation conditions. Due to hard-mode elimination, when this problem is cast in terms of intrinsic (dihedral torsional) coordinates, the weight of the differential volume, resulting merely from the transformation from Cartesian onto intrinsic coordinates, is not constant. This inherent geometry resulting from the embedding of the infinite Cartesian space onto the compact torsional manifold has physical consequences, especially in the earliest folding times, when the intramolecular potential has not yet had a chance to outweigh it. Thus, the early folding events are induced by a coupling between the inherent geometry and the hydrodynamic drag, and they predate the occurrence of nonbonded intrachain interactions. Thus, by contrasting the early geometrically determined probability distribution in torsional conformation space with the energetically favorable regions, we elucidate how the interplay between hydrodynamic control and potential energy surface during the early stages of folding (10 ps–1 μs) determines the expediency of the process. In this way we are able to decide in simple cases whether geometry and Watson–Crick complementarities represent reinforcing or conflicting propensities, defining a good seeker or a bad folder.

Torsional Splitting in the Degenerate Vibrational States of 70Ge2H6: Rotation–Torsion Analysis of the ν7 and ν9 Fundamentals

The rotational and torsional structure of the ν7 and ν9 degenerate fundamentals of 70Ge2H6 has been analyzed under high resolution. The torsional structure of both v7 = 1 and v9 = 1 states can be fitted by a simple one-parameter formula. The x,y-Coriolis interaction with the parallel ν5 fundamental was accounted for in the analysis of ν7. A strong perturbation of the J structure of the E3s torsional component of the KΔK = −2 subbranches of ν9 can be explained by the resonance with an E3s excited level of the pure torsional manifold. The perturber is centered at 361.58 cm−1, very close to the value estimated with a barrier height of 285 cm−1. This confirms that the fundamental torsional wavenumber is close to 103 cm−1, in good agreement with the “ab initio” prediction. The torsional splittings of all the infrared active degenerate fundamentals, ν7, ν8, and ν9, follow the trend predicted by theory, and have been fitted by exploratory calculations accounting only for the torsional Coriolis-coupling mechanism of all degenerate vibrational fundamentals in several torsional states. This confirms that torsional Coriolis coupling is the dominant mechanism responsible for the decrease of the torsional splitting in the degenerate vibrational states. A higher value of the barrier had to be used for the ν9 mode.