Narrow Results

In this paper, we introduce a new ‘Thom class’ formulation of topological T-duality for principal torus bundles. This definition is equivalent to the established one of Bunke, Rumpf, and Schick but has the virtue of removing the global assumptions on the H-flux required in the old definition. With the new definition, we provide easier and more transparent proofs of the classification of T-duals and generalize the local formulation of T-duality for circle bundles by Bunke, Schick, and Spitzweck to the torus case.

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green–Schwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.

We demonstrate that twisted equivariant differential K-theory of transverse complex curves accommodates exotic charges of the form expected of codimension$=$2 defect branes, such as of $\mathrm{\text{D7}}$-branes in IIB/F-theory on $𝔸$-type orbifold singularities, but also of their dual 3-brane defects of class-S theories on M5-branes. These branes have been argued, within F-theory and the AGT correspondence, to carry special $\mathrm{\text{SL}}(2)$-monodromy charges not seen for other branes, at least partially reflected in conformal blocks of the ${𝔰𝔲}_2$-WZW model over their transverse punctured complex curve. Indeed, it has been argued that all “exotic” branes of string theory are defect branes carrying such U-duality monodromy charges — but none of these had previously been identified in the expected brane charge quantization law given by K-theory.

Here we observe that it is the subtle (and previously somewhat neglected) twisting of equivariant K-theory by flat complex line bundles appearing inside orbi-singularities (“inner local systems”) that makes the secondary Chern character on a punctured plane inside an $𝔸$-type singularity evaluate to the twisted holomorphic de Rham cohomology which Feigin, Schechtman and Varchenko showed realizes $\widehat{{{𝔰𝔩}_2}^k}$-conformal blocks, here in degree 1 — in fact it gives the direct sum of these over all admissible fractional levels $k=-2+\kappa /r$. The remaining higher-degree $\widehat{{{𝔰𝔩}_2}^k}$-conformal blocks appear similarly if we assume our previously discussed “Hypothesis H” about brane charge quantization in M-theory. Since conformal blocks — and hence these twisted equivariant secondary Chern characters — solve the Knizhnik–Zamolodchikov equation and thus constitute representations of the braid group of motions of defect branes inside their transverse space, this provides a concrete first-principles realization of anyon statistics of — and hence of topological quantum computation on — defect branes in string/M-theory.

Recent progress on the calculation of the – potential is reviewed. Scaling is discussed from the perspective of critical phenomenon. Methods for fitting the correlations of Polyakov operators and the Wilson loops are reviewed and two new methods, the iterative method and the improved ratio method, are discussed in detail. These new methods are used to analyze/re-analyze the previously published data on Polyakov loops and new data on large Wilson loops. Convincing numerical evidences together with several analytical arguments strongly support the conclusion that the asymptotic scaling sets in at β~6 with and α=0.43±0.03. These results agree well with the potential model analysis of experimental data on and systems, and favors the Neveu-Schwarz strings as the underlying string theory. Finally, key issues on the use of the parallel computers are explored, with the conclusion that parallel computers are highly suitable for these floating-point intensive computations.

We develop a systematic DLCQ perturbation theory and show that DLCQ S-matrix does not have a covariant continuum limit for processes with p⁺=0 exchange. This implies that the role of the zero mode is more subtle than ever considered in DLCQ and hence must also be treated with great care in nonperturbative approach. We also make a brief comment on DLCQ in string theory.

The possibility of parity violation through space–time torsion has been explored in a scenario containing fields with different spins. Taking the Kalb–Ramond (KR) field as the source of torsion, an explicitly parity violating U(1) _EM gauge-invariant theory has been constructed by extending the KR field with a Chern–Simons term.

In this paper we study the noncommutative description of the DBI Lagrangian and its T-dual counterpart. We restrict the freedoms of the noncommutativity parameters of these Lagrangians. Therefore the noncommutativity parameter, the effective metric, the effective coupling constant of the string and the extra modulus of the effective T-dual theory, can be expressed in terms of the closed string variables g, B, g_s and the noncommutativity parameter of the effective theory of open string.

Four-dimensional Manin triples and Drinfeld doubles are classified and the corresponding two-dimensional Poisson–Lie T-dual sigma models on them are constructed. The simplest example of a Drinfeld double allowing decomposition into two nontrivially different Manin triples is presented.

We study string-loop corrections to magnetic black hole. Four-dimensional theory is obtained by compactification of the heterotic string theory on the manifold K3×T² or on a suitable orbifold yielding N=1 supersymmetry in 6D. The resulting 4D theory has N=2 local supersymmetry. Prepotential of this theory receives only one-string-loop correction. The tree-level gauge couplings are proportional to the inverse effective string coupling and decrease at small distances from the center of magnetic black hole, so that loop corrections to the gauge couplings are important in this region. We solve the system of Killing spinor equations (conditions for the supersymmetry variations of the fermions to vanish) and Maxwell equations. At the string-tree level, we reproduce the magnetic black hole solution which can also be obtained by solving the system of the Einstein–Maxwell equations and the equations of motion for the moduli. String-loop corrections to the tree-level solution are calculated in the first order in string coupling. The resulting corrections to the metric and dilaton are large at small distances from the center of the black hole. Possible smearing of the singularity at the origin by quantum corrections is discussed.

We give a simplified and more complete description of the loop variable approach for writing down gauge-invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite worldsheet cutoff and that in the ir limit, equivalence with the Callan–Symanzik β-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon–photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite worldsheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into the standard form.

We argue that a system of interacting D-branes, generalizing a recent proposal, can be modeled as a quantum Hall fluid. We show that tachyon condensation in such a system is equivalent to one-particle tunneling. In a conformal field theory effective description, that induces a transition from a theory with central charge c = 2 to a theory with c = 3/2, with a corresponding symmetry enhancement.

In this paper we study the effects of noncommutativity on a closed superstring propagating in the space–time that is compactified on tori. The effects of compactification and noncommutativity appear in the momentum, quantization, supercurrent, super-conformal generators and in the boundary state of the closed superstring emitted from a D_p-brane with the NS ⊗ NS background B-field.

The explicit form of the fermionic zero-modes in the five-brane backgrounds of type IIA and IIB supergravity theories is investigated. In type IIA five-brane background there are four zero-modes of gravitinos and dilatinos. In type IIB five-brane background four zero-modes of dilatinos and no zero-modes of gravitinos are found. These zero-modes indicate the four-fermion condensates which have been suggested in a calculation of the tension of the D-brane in five-brane backgrounds.

We proceed with the investigation of a method of quantization of the observable sector of closed bosonic strings. For the presentation of the quantum algebra of observables the construction cycle concerning elements of order ℏ⁶ has been carried out. We have computed the quantum corrections to the only generating relation of order ℏ⁶. This relation is of spin-parity J^P = 0⁺. We found that the quantum corrections to this relation break the semidirect splitting of the classical algebra into an Abelian, infinitely generated subalgebra and a non-Abelian, finitely generated subalgebra . We have established that there are no ("truly independent") generating relations of order ℏ⁷.

We discuss the Penrose limit of the classical string geometry obtained from a truly marginal deformation of SL(2) ⊗ SU(2) WZNW model.

We review the attempts to construct black hole/string solutions in asymptotically plane wave spacetimes. First, we demonstrate that geometries admitting a covariantly constant null Killing vector cannot admit event horizons, which implies that pp-waves cannot describe black holes. However, relaxing the symmetry requirements allows us to generate solutions which do possess regular event horizons while retaining the requisite asymptotic properties. In particular, we present two solution generating techniques and use them to construct asymptotically plane wave black string/brane geometries.

We improve the study of the lack of perturbative unitarity of noncommutative space-time quantum field theories derived from open string theory in electric backgrounds, enforcing the universality of the mechanism by which a tachyonic branch cut appears when the Seiberg-Witten limit freezes the string in an unstable vacuum. The main example is realized in the context of the on-shell four-tachyon amplitude of the bosonic string, and the dependence of the phenomenon on the brane-worldvolume dimension is analysed. We discuss the possibility of a proof in superstring theory, and finally mention the NCOS limit in this framework.

In this paper some properties of the superstring with noncommutative worldsheet are studied. We study the noncommutativity of the spacetime, generalization of the Poincaré symmetry of the superstring, the changes of the metric, antisymmetric tensor and dilaton.

The gaugino propagator is calculated by explicitly considering the propagation of a heterotic string between two different points in spacetime using the nontrivial worldsheet conformal field theory for the five-brane background. We find that there are no propagations of gaugino which is in the spinor representation of the nontrivial four-dimensional space of the five-brane background. This result is consistent with the arguments on the fermion zero-modes of the five-brane background in the low-energy heterotic supergravity theory. Furthermore, assuming the continuous limit to the flat spacetime background at the place far away from the five-brane, we suggest an effective propagator which is effective only at the place far away from the five-brane in the flat spacetime limit. From the effective propagator we evaluate a possible gaugino pair condensation. The result is consistent with the suggested scenario of the gaugino condensation in the five-brane background in the low-energy heterotic supergravity theory.

We discuss several possibilities of probing string theory through cosmology, e.g., the imprints of short distance physics on CMB anisotropies, the signatures of brane inflationary models, and the cosmological constraints on D-matter.