arXiv subjects

Matthias Blau

Publications and source records attributed to Matthias Blau.

At least 55 records · Page 3Linked to original sources

arXiv2003

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.

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arXiv2003

Solvable models of strings in homogeneous plane wave backgrounds

We solve closed string theory in all regular homogeneous plane-wave backgrounds with homogeneous NS three-form field strength and a dilaton. The parameters of the model are constant symmetric and anti-symmetric matrices k_{ij} and f_{ij} associated with the metric, and a constant anti-symmetric matrix h_{ij} associated with the NS field strength. In the light-cone gauge the rotation parameters f_{ij} have a natural interpretation as a constant magnetic field. This is a generalisation of the standard Landau problem with oscillator energies now being non-trivial functions of the parameters f_{ij} and k_{ij}. We develop a general procedure for solving linear but non-diagonal equations for string coordinates, and determine the corresponding oscillator frequencies, the light-cone Hamiltonian and level matching condition. We investigate the resulting string spectrum in detail in the four-dimensional case and compare the results with previously studied examples. Throughout we will find that the presence of the rotation parameter f_{ij} can lead to certain unusual and unexpected features of the string spectrum like new massless states at non-zero string levels, stabilisation of otherwise unstable (tachyonic) modes, and discrete but not positive definite string oscillator spectra.

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arXiv2002

Homogeneous Plane Waves

Motivated by the search for potentially exactly solvable time-dependent string backgrounds, we determine all homogeneous plane wave (HPW) metrics in any dimension and find one family of HPWs with geodesically complete metrics and another with metrics containing null singularities. The former generalises both the Cahen-Wallach (constant $A_{ij}$) metrics to time-dependent HPWs, $A_{ij}(t)$, and the Ozsvath-Schücking anti-Mach metric to arbitrary dimensions. The latter is a generalisation of the known homogeneous metrics with $A_{ij}\sim 1/t^2$ to a more complicated time-dependence. We display these metrics in various coordinate systems, show how to embed them into string theory, and determine the isometry algebra of a general HPW and the associated conserved charges. We review the Lewis-Riesenfeld theory of invariants of time-dependent harmonic oscillators and show how it can be deduced from the geometry of plane waves. We advocate the use of the invariant associated with the extra (timelike) isometry of HPWs for lightcone quantisation, and illustrate the procedure in some examples.

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arXiv2002

On the Boundary Dynamics of Chern-Simons Gravity

We study Chern-Simons theory with a complex G_C or a real G x G gauge group on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a G_C/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, for (E/A)dS gravity, the boundary action is a WZW model with target space (E/A)dS_3, reminiscent of a worldsheet for worldsheet mechanism. We discuss in some detail the properties of the boundary theories that arise and we confront our results with various related constructions in the literature.

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arXiv2002

Penrose limits, supergravity and brane dynamics

We investigate the Penrose limits of classical string and M-theory backgrounds. We prove that the number of (super)symmetries of a supergravity background never decreases in the limit. We classify all the possible Penrose limits of AdS x S spacetimes and of supergravity brane solutions. We also present the Penrose limits of various other solutions: intersecting branes, supersymmetric black holes and strings in diverse dimensions, and cosmological models. We explore the Penrose limit of an isometrically embedded spacetime and find a generalisation to spaces with more than one time. Finally, we show that the Penrose limit is a large tension limit for all branes including those with fields of Born--Infeld type.

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arXiv2002

Penrose limits and maximal supersymmetry

We show that the maximally supersymmetric pp-waves of IIB superstring and M-theories can be obtained as a Penrose limit of the supersymmetric AdS x S solutions. In addition we find that in a certain large tension limit, the geometry seen by a brane probe in an AdS x S background is either Minkowski space or a maximally supersymmetric pp-wave.

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arXiv2001

A new maximally supersymmetric background of IIB superstring theory

We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then discuss T-duality and the relation to M-theory.

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arXiv2001

Instantons, the Information Metric, and the AdS/CFT Correspondence

We describe some remarkable properties of the so-called Information Metric on instanton moduli space. This Metric is manifestly gauge and conformally invariant and coincides with the Euclidean AdS_5 metric on the one-instanton SU(2) moduli space for the standard metric on R^4. We propose that for an arbitrary boundary metric the AdS/CFT bulk space-time is the instanton moduli space equipped with the Information Metric. To test this proposal, we examine the variation of the instanton moduli and the Information Metric for first-order perturbations of the boundary metric and obtain three non-trivial and somewhat surprising results: (1) The perturbed Information Metric is Einstein. (2) The perturbed instanton density is the corresponding massless boundary-to-bulk scalar propagator. (3) The regularized boundary-to-bulk geodesic distance is proportional to the logarithm of the perturbed instanton density. The Hamilton-Jacobi equation implied by (3) equips the moduli space with a rich geometrical structure which we explore. These results tentatively suggest a picture in which the one-instanton sector of SU(2) Yang-Mills theory (rather than some large-N limit) is in some sense holographically dual to bulk gravity.

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arXiv2000

Killing Spinors and SYM on Curved Spaces

We construct two families of globally supersymmetric counterparts of standard Poincaré supersymmetric SYM theories on curved space-times admitting Killing spinors, in all dimensions less than six and eight respectively. The former differs from the standard theory only by mass terms for the fermions and scalars and modified supersymmetry transformation rules, the latter in addition has cubic Chern-Simons like couplings for the scalar fields. We partially calculate the supersymmetry algebra of these models, finding R-symmetry extensions proportional to the curvature. We also show that generically these theories have no continuous Coulomb branch of maximally supersymmetric vacua, but that there exists a half-BPS Coulomb branch approaching the standard Coulomb branch in the Ricciflat limit.

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arXiv2000

On the Relationship between the Rozansky-Witten and the 3-Dimensional Seiberg-Witten Invariants

The Seiberg-Witten analysis of the low-energy effective action of d=4 N=2 SYM theories reveals the relation between the Donaldson and Seiberg-Witten (SW) monopole invariants. Here we apply analogous reasoning to d=3 N=4 theories and propose a general relationship between Rozansky-Witten (RW) and 3-dimensional Abelian monopole invariants. In particular, we deduce the equality of the SU(2) Casson invariant and the 3-dimensional SW invariant (this includes a special case of the Meng-Taubes theorem relating the SW invariant to Milnor torsion). Since there are only a finite number of basic RW invariants of a given degree, many different topological field theories can be used to represent essentially the same topological invariant. This leads us to advocate using higher rank Abelian gauge theories to shed light on the higher (non-Abelian) RW invariants and we write down candidate higher rank SW equations.

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arXiv1999

On Subleading Contributions to the AdS/CFT Trace Anomaly

In the context of the AdS/CFT correspondence, we perform a direct computation in AdS_5 supergravity of the trace anomaly of a d=4, N=2 SCFT. We find agreement with the field theory result up to next to leading order in the 1/N expansion. In particular, the order N gravitational contribution to the anomaly is obtained from a Riemann tensor squared term in the 7-brane effective action deduced from heterotic - type I duality. We also discuss, in the AdS/CFT context, the order N corrections to the trace anomaly in d=4, N=4 SCFTs involving SO or Sp gauge groups.

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arXiv1997

Aspects of U-Duality in Matrix Theory

We explore various aspects of implementing the full M-theory U-duality group E_{d+1}, and thus Lorentz invariance, in the finite N matrix theory (DLCQ of M-theory) on d-tori: (1) We generalize the analysis of U-duality orbits of BPS states by Elitzur et al. (hep-th/9707217) from E_{d} to E_{d+1}. (2) We identify the new E_{d+1}-symmetries with Nahm-duality-like symmetries (N-duality) exchanging the rank N of the matrix theory gauge group with other quantum numbers. (3) We describe the action of N-duality on BPS bound states, thus making testable predictions for the Lorentz invariance of matrix theory. (4) We discuss the problems that arise in the matrix theory limit for BPS states with no top-dimensional branes, i.e. configurations with N=0. (5) We show that N-duality maps the matrix theory SYM picture to the matrix string picture and argue that, for d even, the latter should be thought of as an M-theory membrane description (which appears to be well defined even for d>5). (6) We find a compact and unified expression for a U-duality invariant of E_{d+1} for all d and show that in d=5,6 it reduces to the black hole entropy cubic E_{6}- and quartic E_{7}-invariants respectively. (7) We describe some of the solitonic states in d=6,7 and give an example (a `rolled-up' Taub-NUT 6-brane) of a configuration exhibiting the unusual 1/g_{s}^{3}-behaviour.

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arXiv1997

Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds

Euclidean supersymmetric theories are obtained from Minkowskian theories by performing a reduction in the time direction. This procedure elucidates certain mysterious features of Zumino's N=2 model in four dimensions, provides manifestly hermitian Euclidean counterparts of all non-mimimal SYM theories, and is also applicable to supergravity theories. We reanalyse the twists of the 4d N=2 and N=4 models from this point of view. Other applications include SYM theories on special holonomy manifolds. In particular, we construct a twisted SYM theory on Kaehler 3-folds and clarify the structure of SYM theory on hyper-Kaehler 4-folds.

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arXiv1996

Some General Aspects of Coset Models and Topological Kazama-Suzuki Models

We study global aspects of N=2 Kazama-Suzuki coset models by investigating topological G/H Kazama-Suzuki models in a Lagrangian framework based on gauged Wess-Zumino-Witten models. We first generalize Witten's analysis of the holomorphic factorization of bosonic G/H models to models with N=1 and N=2 supersymmetry. We also find some new anomaly-free and supersymmetric models based on non-diagonal embeddings of the gauge group. We then explain the basic properties (action, symmetries, metric independence, ...) of the topologically twisted G/H Kazama-Suzuki models. We explain how all of the above generalizes to non-trivial gauge bundles. We employ the path integral methods of localization and abelianization (shown to be valid also for non-trivial bundles) to establish that the twisted G/H models can be localized to bosonic H/H models (with certain quantum corrections), and can hence be reduced to an Abelian bosonic T/T model, T a maximal torus of H. We also present the action and the symmetries of the coupling of these models to topological gravity. We determine the bosonic observables for all the models based on classical flag manifolds and the bosonic observables and their fermionic descendants for models based on complex Grassmannians.

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arXiv1996

Grassmannian Topological Kazama-Suzuki Models and Cohomology

We investigate in detail the topological gauged Wess-Zumino-Witten models describing topological Kazama-Suzuki models based on complex Grassmannians. We show that there is a topological sector in which the ring of observables (constructed from the Grassmann odd scalars of the theory) coincides with the classical cohomology ring of the Grassmannian for all values of the level k. We perform a detailed analysis of the non-trivial topological sectors arising from the adjoint gauging, and investigate the general ring structure of bosonic correlation functions, uncovering a whole hierarchy of level-rank relations (including the standard level-rank duality) among models based on different Grassmannians. Using the previously established localization of the topological Kazama-Suzuki model to an Abelian topological field theory, we reduce the correlators to finite-dimensional purely algebraic expressions. As an application, these are evaluated explicitly for the CP{2} model at level k and shown for all k to coincide with the cohomological intersection numbers of the two-plane Grassmannian G(2,k+2), thus realizing the level-rank duality between this model and the G(2,k+2) model at level one.

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arXiv1996

Aspects of N_{T}\geq 2 Topological Gauge Theories and D-Branes

We comment on various aspects of topological gauge theories possessing N_{T}\geq 2 topological symmetry: (1) We show that the construction of Vafa-Witten and Dijkgraaf-Moore of `balanced' topological field theories is equivalent to an earlier construction in terms of N_{T}=2 superfields inspired by Susy QM. (2) We explain the relation between topological field theories calculating signed and unsigned sums of Euler numbers of moduli spaces. (3) We show that the topological twist of N=4 d=4 Yang-Mills theory recently constructed by Marcus is formally a deformation of four-dimensional super-BF theory. (4) We construct a novel N_{T}=2 topological twist of N=4 d=3 Yang-Mills theory, a `mirror' of the Casson invariant model, with some unusual features. (5) We give a complete classification of the topological twists of N=8 d=3 Yang-Mills theory and show that they are realised as world-volume theories of Dirichlet two-brane instantons wrapping supersymmetric three-cycles of Calabi-Yau three-folds and G_{2}-holonomy Joyce manifolds. (6) We describe the topological gauge theories associated to D-string instantons on holomorphic curves in K3s and Calabi-Yau 3-folds.

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arXiv1996

Solving Topological Field Theories on Mapping Tori

Using gauge theory and functional integral methods, we derive concrete expressions for the partition functions of BF theory and the U(1|1) model of Rozansky and Saleur on $Σx S^{1}$, both directly and using equivalent two-dimensional theories. We also derive the partition function of a certain non-abelian generalization of the U(1|1) model on mapping tori and hence obtain explicit expressions for the Ray-Singer torsion on these manifolds. Extensions of these results to BF and Chern-Simons theories on mapping tori are also discussed. The topological field theory actions of the equivalent two-dimensional theories we find have the interesting property of depending explicitly on the diffeomorphism defining the mapping torus while the quantum field theory is sensitive only to its isomorphism class defining the mapping torus as a smooth manifold.

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arXiv1995

Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories

We review localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories. These are the functional integral counterparts of the Mathai-Quillen formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula respectively. In each case, we first introduce the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups), and describe the finite dimensional integration formulae. We then discuss some applications to path integrals and give an overview of the relevant literature. The applications we deal with include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang-Mills theory.

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