802 publications from this institution
Perturbative calculations based on the operator formalism described in chapters 7 – 10 can be used when at least one of the strings at each interaction vertex is a physical on-shell state. That approach is effective for calculations of tree and one-loop amplitudes but is not applicable for multiloop amplitudes, since these necessarily involve at least one vertex coupling three internal (and therefore off-shell) strings.
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No abstract is provided for this article.
String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework for geometry that reduces to ordinary differential geometry when the curvature is asymptotically small. In the 1990's, many interesting results were obtained about the behavior of string theory in spacetimes that develop singularities. In many cases, the physics at the singularity is governed by an effective Lagrangian constructed using an interesting bit of classical geometry such as the association of A-D-E groups with certain hypersurface singularities or the ADHM construction of instantons. In other examples, the physics at the singularity cannot be described in classical terms but involves a non-Gaussian conformal field theory.
Just as D-brane charge of type-IIA and type-IIB superstrings is clas- sied, respectively, by K 1 (X)and K( X), Ramond-Ramondelds in these theories are classied, respectively, by K(X)and K 1 ( X). Byanalyzing a recent proposal for how to interpret quantum self-duality of RRelds, we show that the Dirac quanti- zation formula for the RR p-forms, when properly formulated, receives corrections thatreflectcurvature,lowerbranecharges,andananomalyofD-braneworld-volume fermions. TheK-theoryframeworkisimportanthere,becausetheterminvolvingthe fermion anomaly cannot be naturally expressed in terms of cohomology and dier- ential forms.
Simple mean field methods can be used to describe transitions between different space-time models in string theory. These include transitions between different Calabi-Yau manifolds, and more exotic things such as the Calabi-Yau/Landau-Ginzberg correspondence.
No abstract is provided for this article.
Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-poin
This paper addresses various questions involving global anomalies in particle theory and string theory. It is shown that the question of whether a manifold is a spin manifold is equivalent to a question about global anomalies in the propagation of a point particle. In the superstring case, it is shown that the measure of the heterotic theory has no global anomalies on any Riemann surface. This generalizes known one loop results. Also, a topological condition is derived which restricts the possible choices of Wilson lines for grand unified symmetry breaking. It is argued that the long-term development of global anomalies in string theory will involve eventual study of global anomalies in the determinant of the Dirac-Ramond operator.
It is conjectured that the coefficients of the Jones polynomial can be computed by counting solutions of the KW equations on a four-dimensional half-space, with certain boundary conditions that depend on a knot. The boundary conditions are defined by a away from the knot with a further singularity along the knot. In a previous paper, we gave a precise formulation of the Nahm pole boundary condition in the absence of knots, in the present paper, we do this in the more general case with knots included. We show that the KW equations with generalized Nahm pole boundary conditions are elliptic, and that the solutions are polyhomogeneous near the boundary and near the knot, with exponents determined by solutions of appropriate indicial equations. This involves the analysis of a depth two incomplete iterated edge operator. As in our previous paper, a key ingredient in the analysis is a convenient new Weitzenbock formula that is well-adapted to the specific problem.}
A bstract In recent years, a surprisingly direct and simple rigorous understanding of quantum Liouville theory has developed. We aim here to make this material more accessible to physicists working on quantum field theory.
A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r + 1/2, is inconsistent. We describe here a more subtle anomaly that can affect SU(2) gauge theory in four dimensions under the condition that fermions transform with half-integer spin under SU(2) and bosons transform with integer spin. Such a theory, formulated in a way that requires no choice of spin structure, and with an odd number of fermion multiplets in representations of spin 4r + 3/2, is inconsistent. The theory is consistent if one picks a spin or spinc structure. Under Higgsing to U(1), the new SU(2) anomaly reduces to a known anomaly of “all-fermion electrodynamics.” Like that theory, an SU(2) theory with an odd number of fermion multiplets in representations of spin 4r + 3/2 can provide a boundary state for a five-dimensional gapped theory whose partition function on a closed five-manifold Y is (−1)∫Yw2w3. All statements have analogs with SU(2) replaced by Sp(2N). There is also an analog in five dimensions.
The connection between instantons and the breaking of supersymmetry and ordinary symmetries is studied in a variety of (2+1)-dimensional gauge theories.
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The timelike tube theorem asserts that in quantum field theory without gravity, the algebra of observables in an open set $${\mathcal {U}}$$ is the same as
No abstract is provided for this article.
A relation between approaches to integrability in superconformal Yang-Mills theory
Superconducting cosmic strings are a plausible consequence of symmetry breaking in grand unified gauge theories. The luminosity in electromagnetic radiation of an oscillating current-carrying loop may substantially exceed the luminosity in gravitational radiation. In the typical case considered, the energy released electromagnetically is 1049 erg s−1, or 1066 erg in toto. Several consequences follow from this, the most interesting of which is the possibility that such loops may heat their surroundings, generating large, dense spherical shells of gas. Galaxies forming on these gravitationally unstable shells at moderate redshift will be seen at the present epoch to lie on bubbles having radii in the range 10–20h −1 Mpc if the initial ratio of luminosity in electromagnetic waves to that in gravitational wavess is > 10−3 for mass/length 1022 g cm−1. The required primordial energy density in magnetic fields is > 3 × 10−9 of the radiation energy density, if the charge carriers are bosons or superheavy fermions. Since these shells fill up space, the galaxies will have a distribution similar to that found in a recent survey of the northern sky. When the current saturates, a loop will emit particles copiously, and may be seen as an X-ray source at z ∼ 10–50. Such loops may also contribute significantly to the hard X-ray and γ-ray backgrounds and to 1020 eV cosmic rays.
