IIA Solutions Research Articles

Linearly-realised worldsheet supersymmetry in pp-wave backgrounds

We study the linearly-realised worldsheet supersymmetries in the “massive” type II light-cone actions for pp-wave backgrounds. The pp-waves have 16+ N sup Killing spinors, comprising 16 “standard” Killing spinors that occur in any wave background, plus N sup “supernumerary” Killing spinors (0⩽ N sup⩽16) that occur only for special backgrounds. We show that only the supernumerary Killing spinors give rise to linearly-realised worldsheet supersymmetries after light-cone gauge fixing, while the 16 standard Killing spinors describe only non-linearly realised inhomogeneous symmetries. We also study the type II actions in the physical gauge, and we show that although in this case the actions are not free, there are now linearly-realised supersymmetries coming both from the standard and the supernumerary Killing spinors. In the physical gauge, there are no mass terms for any worldsheet degrees of freedom, so the masses appearing in the light-cone gauge may be viewed as gauge artefacts. We obtain type IIA and IIB supergravity solutions describing solitonic strings in pp-wave backgrounds, and show how these are related to the physical-gauge fundamental string actions. We study the supersymmetries of these solutions, and find examples with various numbers of Killing spinors, including total numbers that are odd.

A construction of G2 holonomy spaces with torus symmetry

In the present work the Calderbank–Pedersen description of four-dimensional manifolds with self-dual Weyl tensor is used to obtain examples of quaternionic-Kahler metrics with two commuting isometries. The eigenfunctions of the hyperbolic Laplacian are found by use of Backglund transformations acting over solutions of the Ward monopole equation. The Bryant–Salamon construction of G 2 holonomy metrics arising as R 3 bundles over quaternionic-Kahler base spaces is applied to this examples to find internal spaces of the M-theory that leads to an N=1 supersymmetry in four dimensions. Type IIA solutions will be obtained too by reduction along one of the isometries. The torus symmetry of the base spaces is extended to the total ones.

(Twisted) toroidal compactification ofppwaves

The maximally supersymmetric type IIB $\mathrm{pp}$ wave is compactified on spatial circles, with and without an auxiliary rotational twist. All spatial circles of constant radius are identified. Without the twist, an ${S}^{1}$ compactification can preserve 24, 20 or 16 supercharges. ${T}^{2}$ compactifications can preserve 20, 18 or 16 supercharges; ${T}^{3}$ compactifications can preserve 18 or 16 supercharges and higher compactifications preserve 16 supercharges. The world sheet theory of this background is discussed. The T dual and decompactified type IIA and M-theoretic solutions which preserve 24 supercharges are given. Some comments are made regarding the AdS parent and the CFT description.

A note on half-supersymmetric bound states in M-theory and type IIA string theory

By using O(7,7) transformations, to deform D6-branes, we obtain half-supersymmetric bound state solutions of type IIA supergravity, containing D6, D4, D2, D0, F1-branes and waves. We lift the solutions to M-theory which gives half-supersymmetric M-theory bound states, e.g. KK6–M5–M5–M5– M2–M2–M2–MW. We also take near-horizon limits for the type IIA solutions, which give supergravity duals of seven-dimensional non-commutative open string theory (with spacetime and space–space non-commutativity), non-commutative Yang–Mills theory (with space–space and light-like non-commutativity) and an open D4-brane theory.

Supersymmetric fluxbrane intersections and closed string tachyons

We consider NS-NS superstring model with several ``magnetic'' parameters $b_s$ (s=1, ...,N) associated with twists mixing a compact $S^1$ direction with angles in $N$ spatial 2-planes of flat 10-dimensional space. It generalizes the Kaluza-Klein Melvin model which has single parameter $b$. The corresponding U-dual background is a R-R type IIA solution describing an orthogonal intersection of $N$ flux 7-branes. Like the Melvin model, the NS-NS string model with $N$ continuous parameters is explicitly solvable; we present its perturbative spectrum and torus partition function explicitly for the N=2 case. For generic $b_s$ (above some critical values) there are tachyons in the $S^1$ winding sector. A remarkable feature of this model is that while in the Melvin N=1 case all supersymmetry is broken, a fraction of it may be preserved for $N >1$ by making a special choice of the parameters $b_s$. Such solvable NS-NS models may be viewed as continuous-parameter analogs of non-compact orbifold models. They and their U-dual R-R fluxbrane counterparts may have some ``phenomenological'' applications. In particular, in N=3 case one finds a special 1/4 supersymmetric R-R 3-brane background. Putting Dp-branes in flat twisted NS-NS backgrounds leads to world-volume gauge theories with reduced amount of supersymmetry. We also discuss possible ways of evolution of unstable backgrounds towards stable ones.

The Kaluza Klein Melvin solution in M-theory

We study some aspects of the Kaluza-Klein Melvin solution in M-theory. The associated magnetic field has a maximal critical value $B=\pm 1/R$ where $R$ is the radius of the compactification circle. It is argued that the Melvin background of type IIA with magnetic field $B$ and of type 0A with magnetic field $B'=B-1/R$ are equivalent. Evidence for this conjecture is provided using a further circle compactification and a `9-11' flip. We show that partition functions of nine-dimensional type IIA strings and of a $(-1)^F\sigma_{1/2}$ type IIA orbifold both with NS-NS Melvin fluxtubes are related by such shift of the magnetic field. Then the instabilities of both IIA and 0A Melvin solutions are analyzed. For each theory there is an instanton associated to the decay of spacetime. In the IIA case the decay mode is associated to the nucleation of $D6/D\bar{6}$-brane pairs, while in the 0A case spacetime decays through Witten's bubble production.

Einstein spaces in five and seven dimensions and non-supersymmetric gauge theories

A one-parameter family of new solutions representing Einstein spaces in d=5,7 is presented, and used to construct non-supersymmetric backgrounds in type IIB and M-theory that asymptotically approach AdS 5× S 5 and AdS 7× S 4. Upon dimensional reduction, the latter gives a type IIA solution representing a 4-brane with Ramond-Ramond charge, which interpolates between the “near-horizon" non-extremal D4 brane and a geometry connected by T-duality to a new constant dilaton solution in type IIB. We discuss the possibility that M-theory on this space may be related to a (0,2) six-dimensional field theory on S 1× S 1, with fermions obeying antiperiodic boundary conditions in both circles.

More on probing branes with branes

We generalize the Gibbons-Wiltshire solution of four dimensional Kaluza-Klein black holes in order to describe Type IIA solutions of bound states of D6 and D0-branes. We probe the solutions with a D6-brane and a D0-brane. We also probe a system of D2+D0-branes and of a D2-brane bound to a F1-string with a D2-brane. A precise agreement between the SYM and the SUGRA calculations is found for the static force as well as for the v 2 force in all cases.

Superstring dualities and p-brane bound states

We show that the M-theory/IIA and IIA/IIB superstring dualities together with the diffeomorphism invariance of the underlying theories require the presence of certain p-brane bound states in IIA and IIB superstring theories preserving 1 2 of the space-time supersymmetry. We then confirm the existence of IIA and IIB supergravity solutions having the appropriate p-brane bound states interpretation.

Chiral supersymmetric pp-wave solutions of IIA supergravity

We describe solutions of type IIA (N=2, D=10) supergravity built under the assumption of the existence of at least one residual chiral supersymmetry. Their geometry is of pp-wave type. Explicit parametrization of the metric and matter field components, in terms of Killing spinors and arbitrary functions, is provided.

Superstring dualities and p-brane bound states

We show that the M-theory/IIA and IIA/IIB superstring dualities together with the diffeomorphism invariance of the underlying theories require the presence of certain p-brane bound states in IIA and IIB superstring theories preserving 1/2 of the spacetime supersymmetry. We then confirm the existence of IIA and IIB supergravity solutions having the appropriate p-brane bound states interpretation.

Overlapping branes in M-theory

We construct new supersymmetric solutions of D = 11 supergravity describing n orthogonally “overlapping” membranes and fivebranes for n = 2,…,8. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve at least 2 − n of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a fivebrane in a string. After reducing n overlapping membranes to obtain n overlapping D-2-branes in D = 10, T-duality generates new overlapping D-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions leads to the D = 11 solutions. Some of the new solutions reduce to dilaton black holes in D = 4. Additionally, we present a D = 10 solution that describes two D-5-branes overlapping in a string. T-duality then generates further D = 10 solutions and uplifting one of the type IIA solutions gives a new D = 11 solution describing two fivebranes overlapping in a string.

The chemical behaviour of the azido group bonded to copper(I): Synthesis and reactivity of thiothiatriazolato and alkynyl complexes

The copper(I) azido-derivatives, (PPh 3)(phen)CuN 3 (Ia) and (PPh 3)(TMP)CuN 3 (Ib) (phen = 1,10-phenanthroline; TMP = 3,4,7,8-tetramethyl-1,10-phenanthroline), obtained from [(PPh 3) 2CuN 3] 2 and the bidentate ligand (biL), react with CS 2 to give the thiothiatriazolato-copper(I) complexes, (PPh 3)(phen)Cu NC(S)SNN (IIa) and (PPh 3)(TMP)Cu NC(S)SNN (IIb). The preparation of IIa and IIb occurs only when free triphenylphosphine is present in the reaction medium. The isothiocyanate complexes, (PPh 3)(biL)Cu(NCS) (biL = phen, IIIa; biL = TMP, IIIb) are formed, instead of IIa and IIb, when free PPh 3 is not added to the reaction medium. The complexes IIIa and IIIb are also obtained when CH 2Cl 2 solutions of IIa and IIb are stirred for 15 h in the absence of light; if longer reaction times are used, the dimeric isothiocyanato complexes [(biL)Cu(NCS)] 2 are formed. Compounds IIa and IIb react with PhCOCl to give (PPh 3)(biL)CuCl and 4-benzoyl-1,2,3,4-thiatriazole-5-thione, PhCO NC(S)SNN . Treatment of Ia and Ib, or [(PPh 3) 2CuN 3] 2, with COS did not lead to isolation of characterizable products. An unsaturated molecule such as ethyl propriolate, EtO 2CCCH, does not behave as a 1,3-dipolarophile in its reactions with Ia and Ib, the alkynyl derivatives [(biL)Cu 2(CCCO 2Et) 2] n ( n is probably 2; biL = phen, IVa; biL = TMP, IVb), being obtained. Similarly the azido-complex [(PPh 3) 2CuN 3] 2 reacts with ethyl propiolate to give the asymmetric binuclear alkynyl derivative, (PPh 3) 3Cu 2(CCCO 2Et) 2 (V). The reaction of V with hydrogen chloride gives EtO 2CCCH and the known complex (PPh 3) 3Cu 2Cl 2, confirming the above formulation. The reactions of V with neutral ligands such as TMP, phen and CyNC have also been studied, leading to the isolation of new copper(I) alkynyl-derivatives.

INTERACTION BETWEEN WATER-SOLUBLE PROTEINS AND ACID DYES

The interaction between water-soluble proteins and acid dyes was investigated spectrophotometrically, where the crystalline bovine serum albumin (Ia) and egg albumin (Ib) were used. The acid dyes used were C. I. Acid Orange 7 (IIa), C. I. Mordant Violet 5 (IIb), C. I. Acid Red 178 (IIc), Acid Complex Violet 4R (IId) and C. I. Acid Blue 158 (IIe). The absorption spectra were measured with aqueous solutions of different concentrations of Ia and Ib. The absorption intensities of IIaand IIb at λmax, respectively, decreased in low concentration of albumin, reached the minimumat certain amount of I, and they began to increase with increase in I. In the case of IIc, however, the absorption intensity at the concentration of 4.3×10-5mol/l did not decrease until the added Ia reached 2.0×10-3g/l, and increased markedly from this point. The higher pH, the more quantity of I was required to reach the minimum absorption intensity of II. More quantity of Ib was required than Ia, since the charge Ib is lower than that of Ia. No significant change was observed in the spectrum of the aqueous solutions of IId and IIe upon addition of various amounts of I. The association equilibrium exists between monomer and dimer in the aqueous solutions of IIa, IIb and IIc. But IId and IIe could not be measured owing to little change.In view of the observations on basic vinyl copolymer, it may be concluded that the bonding between I and II is ionic in character and changes in absorption intensity are attributable to the changes in aggregation of II on I.