2,871 research outputs found

    Boston University School of Medicine Alumni News

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    Newsletter for Boston University School of Medicine alumni

    Bundle gerbes and moduli spaces

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    In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are generators of the third de Rham cohomology groups of these moduli spaces.Comment: 19 pages. Latex2e, typos corrected, a reference adde

    Type I D-branes in an H-flux and twisted KO-theory

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    Witten has argued that charges of Type I D-branes in the presence of an H-flux, take values in twisted KO-theory. We begin with the study of real bundle gerbes and their holonomy. We then introduce the notion of real bundle gerbe KO-theory which we establish is a geometric realization of twisted KO-theory. We examine the relation with twisted K-theory, the Chern character and provide some examples. We conclude with some open problems.Comment: 23 pages, Latex2e, 2 new references adde

    Non-Geometric Magnetic Flux and Crossed Modules

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    It is shown that the BRST operator of twisted N=4 Yang-Mills theory in four dimensions is locally the same as the BRST operator of a fully decomposed non-Abelian gerbe. Using locally defined Yang-Mills theories we describe non-perturbative backgrounds that carry a novel magnetic flux. Given by elements of the crossed module G x Aut G, these non-geometric fluxes can be classified in terms of the cohomology class of the underlying non-Abelian gerbe, and generalise the centre ZG valued magnetic flux found by 't Hooft. These results shed light also on the description of non-local dynamics of the chiral five-brane in terms of non-Abelian gerbes.Comment: 26 pages, LaTeX; v2: expanded, typos corrected; v3: typos corrected, version to apper in Nucl. Phys.

    Gerbes, M5-Brane Anomalies and E_8 Gauge Theory

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    Abelian gerbes and twisted bundles describe the topology of the NS-NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted nonabelian gerbes describe the topology of the 4-form field strength G of M-theory. We show that twisted nonabelian gerbes are relevant in the study and resolution of global anomalies of multiple coinciding M5-branes. Global anomalies for one M5-brane have been studied by Witten and by Diaconescu, Freed and Moore. The structure and the differential geometry of twisted nonabelian gerbes (i.e. modules for 2-gerbes) is defined and studied. The nonabelian 2-form gauge potential living on multiple coinciding M5-branes arises as curving (curvature) of twisted nonabelian gerbes. The nonabelian group is in general Ω~E8\tilde\Omega E_8, the central extension of the E_8 loop group. The twist is in general necessary to cancel global anomalies due to the nontriviality of the 11-dimensional 4-form G field strength and due to the possible torsion present in the cycles the M5-branes wrap. Our description of M5-branes global anomalies leads to the D4-branes one upon compactification of M-theory to Type IIA theory.Comment: 19 page

    An Invitation to Higher Gauge Theory

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    In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum Gravity and Quantum Geometry at the 2009 Corfu Summer Institut

    Stress triggering in thrust and subduction earthquakes and stress interaction between the southern San Andreas and nearby thrust and strike-slip faults

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    Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 109 (2004): B02303, doi:10.1029/2003JB002607.We argue that key features of thrust earthquake triggering, inhibition, and clustering can be explained by Coulomb stress changes, which we illustrate by a suite of representative models and by detailed examples. Whereas slip on surface-cutting thrust faults drops the stress in most of the adjacent crust, slip on blind thrust faults increases the stress on some nearby zones, particularly above the source fault. Blind thrusts can thus trigger slip on secondary faults at shallow depth and typically produce broadly distributed aftershocks. Short thrust ruptures are particularly efficient at triggering earthquakes of similar size on adjacent thrust faults. We calculate that during a progressive thrust sequence in central California the 1983 Mw = 6.7 Coalinga earthquake brought the subsequent 1983 Mw = 6.0 Nuñez and 1985 Mw = 6.0 Kettleman Hills ruptures 10 bars and 1 bar closer to Coulomb failure. The idealized stress change calculations also reconcile the distribution of seismicity accompanying large subduction events, in agreement with findings of prior investigations. Subduction zone ruptures are calculated to promote normal faulting events in the outer rise and to promote thrust-faulting events on the periphery of the seismic rupture and its downdip extension. These features are evident in aftershocks of the 1957 Mw = 9.1 Aleutian and other large subduction earthquakes. We further examine stress changes on the rupture surface imparted by the 1960 Mw = 9.5 and 1995 Mw = 8.1 Chile earthquakes, for which detailed slip models are available. Calculated Coulomb stress increases of 2–20 bars correspond closely to sites of aftershocks and postseismic slip, whereas aftershocks are absent where the stress drops by more than 10 bars. We also argue that slip on major strike-slip systems modulates the stress acting on nearby thrust and strike-slip faults. We calculate that the 1857 Mw = 7.9 Fort Tejon earthquake on the San Andreas fault and subsequent interseismic slip brought the Coalinga fault ~1 bar closer to failure but inhibited failure elsewhere on the Coast Ranges thrust faults. The 1857 earthquake also promoted failure on the White Wolf reverse fault by 8 bars, which ruptured in the 1952 Mw = 7.3 Kern County shock but inhibited slip on the left-lateral Garlock fault, which has not ruptured since 1857. We thus contend that stress transfer exerts a control on the seismicity of thrust faults across a broad spectrum of spatial and temporal scales.J. L. was supported by the National Science Foundation through grant NSFEAR0003888; R. S. gratefully acknowledges funding from Swiss Re
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