802 publications from this institution
This paper gives various methods for constructing vector bundles over elliptic curves and more generally over families of elliptic curves. We construct universal families over generalized elliptic curves via spectral cover methods and also by extensions, and then give a relative version of the construction in families. We give various examples and make Chern class computations.
No abstract is provided for this article.
A twistor-like transform of ten-dimensional supersymmetric Yang-Mills theory is described. It generalizes previous work on N = 4 supersymmetric Yang-Mills theory in four dimensions. Partial results are obtained concerning a twistorial transform of N = 1 supergravity in ten dimensions. The motivation for this work is the possibility that the twistor transform of ten-dimensional supersymmetric field theory is the proper starting point for understanding the geometrical meaning of superstring theory. Developing the twistor transform requires developing the needed tools for coupling a superstring to a background supergravity field; this coupling is described in the last section.
Choose from multiple link options via Crossref
I review the arguments that led theoretical physicistsin the 1970's to suspect that lepton number is not an exact symmetry of nature, and to guess a rough range of neutrino massess.
In these notes, I will sketch a new approach to Khovanov homology of knots and links based on counting the solutions of certain elliptic partial differential equations in four and five dimensions. The equations are formulated on four and five-dimensional manifolds with boundary, with a rather subtle boundary condition that encodes the knots and links. The construction is formally analogous to Floer and Donaldson theory in three and four dimensions. It was discovered using quantum field theory arguments but can be described and understood purely in terms of classical gauge theory. (Based on a lecture at the conference Low-Dimensional Manifolds and High-Dimensional Categories, University of California at Berkeley, June 2011).
We analyze the u-plane contribution to Donaldson invariants of a four-manifold X. For $b_2^+(X)>1$, this contribution vanishes, but for $b_2^+=1$, the Donaldson invariants must be written as the sum of a u-plane integral and an SW contribution. The u-plane integrals are quite intricate, but can be analyzed in great detail and even calculated. By analyzing the u-plane integrals, the relation of Donaldson theory to N=2 supersymmetric Yang-Mills theory can be described much more fully, the relation of Donaldson invariants to SW theory can be generalized to four-manifolds not of simple type, and interesting formulas can be obtained for the class numbers of imaginary quadratic fields. We also show how the results generalize to extensions of Donaldson theory obtained by including hypermultiplet matter fields.
In these lecture notes from Strings `91, I briefly sketch the analogy between two dimensional black holes and the s-wave sector of four dimensional black holes, and the physical interest of the latter, particularly in the magnetically charged case.
No abstract is provided for this article.
The purpose of this article is to describe some themes in theoretical physics that developed independently for many years, in some cases for decades, and then converged rather suddenly beginning around 1994–95. The convergence produced an upheaval sometimes called “the second superstring revolution.” It is as significant in its own way as “the first superstring revolution,” the period around 1984–85 when the potential of string theory to give a unified description of natural law was first widely appreciated.
In bosonic JT gravity, minimally coupled to bulk matter, there exists a single, delta-function-normalisable state in each $SL(2,R)$ representation of the matter QFT for any pair of positive energies $E_L, E_R$ at the left and right boundaries. In $\mathcal{N} = 2$ super-JT gravity coupled to matter, we show that there exists a single normalisable state in each $SU(1,1|1)$ matter representation (given appropriate R-charges) that has exactly zero energy at both boundaries. For non-BPS representations, these states have the peculiar property that they break all supersymmetry in the bulk, while preserving supersymmetry at both boundaries. Projecting the algebras of boundary observables onto these zero-energy states leads to a Type II$_1$ von Neumann factor at each boundary that contains a single operator for each supersymmetric matter boundary primary with sufficiently small R-charge. For neutral boundary primaries, the Type II$_1$ factor has a natural action on the matter QFT Hilbert space (with no additional gravitational degrees of freedom) such that the QFT vacuum is the unique tracial state. Moreover, the product of neutral matter operators can be found very explicitly and has a remarkably simple form. When primaries with nonzero matter R-charge are included, the trace can be written as a sum over matter vacuum expectation values associated to each allowed boundary R-charge $J_R$, with the terms in the sum weighted by $\mathrm{cos}(\pi J_R)$. In this way, the ground state algebras encode the ratios of the number of BPS microstates within each R-charge sector. In addition to the results on super-JT gravity described above, we provide a purely Lorentzian derivation of the algebraic structure of canonically quantised (bosonic) JT gravity plus matter, without appeal to the Euclidean gravitational path integrals used in previous work.
New instanton effects in supersymmetric QCD, Chris Beasley, Edward Witten
An exact conformal field theory describing a black hole in two-dimensional space-time is found as an SL(2,openR)/U(1) gauged Wess-Zumino-Witten model. For k=9/4, the conformal field theory can be regarded as a classical solution of the same system that is probed in the c=1 matrix model. The conformal field theory governing the space-time is regular at the Riemannian singularity, but it appears that generic perturbations blow up there. It is argued that the end point of the Hawking black-hole evaporation is the standard space-time of the c=1 matrix model, which should be regarded as an analog of the extreme Reissner-Nordstr\"om black hole of four-dimensional general relativity. The c=1 model is thus a model of the quantum mechanics of matter interacting with a black hole.
In these lecture notes from Strings `91, I briefly sketch the analogy between two dimensional black holes and the s-wave sector of four dimensional black holes, and the physical interest of the latter, particularly in the magnetically charged case.
We review what is known about boundary conditions in General Relativity on a spacetime of Euclidean signature. The obvious Dirichlet boundary condition, in which one specifies the boundary geometry, is actually not elliptic and in general does not lead to a well-defined perturbation theory. It is better-behaved if the extrinsic curvature of the boundary is suitably constrained, for instance if it is positive- or negative-definite. A different boundary condition, in which one specifies the conformal geometry of the boundary and the trace of the extrinsic curvature, is elliptic and always leads formally to a satisfactory perturbation theory. These facts might have interesting implications for semiclassical approaches to quantum gravity. April, 2018
