802 publications from this institution
String theory has the peculiar property that quantum formulas were discovered before any classical formulas and that the quantum formulas are unusually beautiful. It has always been perplexingly hard to find an underlying classical theory via whose quantization string theory could be effectively understood. Nowadays, in the light of quantum duality symmetries and the unification of the different string theories in M theory, we are beginning to suspect a relation between quantum and classical physics quite different from what we have had before. The matrix model may be pointing the way, but we have not yet grasped its implications.
No abstract is provided for this article.
It has long been known that in principle, the genus g vacuum amplitude for bosonic strings or superstrings in 26 or 10 dimensions can be entirely determined from conditions of holomorphy. Moreover, this has been done in practice for bosonic strings of low genus. Here we describe in a unified way how to determine the bosonic string and superstring vacuum amplitude in genus 1 and 2 via holomorphy. The main novelty is the superstring analysis in genus 2, where we use holomorphy to get a new understanding of some of the results that previously have been obtained by more explicit calculations.
A variant of the usual supersymmetric nonlinear sigma model is described, governing maps from a Riemann surfaceΣ to an arbitrary almost complex manifo
In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable <italic>q</italic>. The two main steps are to reinterpret three-dimensional Chern-Simons gauge theory in four dimensional terms and then to apply electric-magnetic duality. The variable <italic>q</italic> is associated to instanton number in the dual description in four dimensions. In the second lecture, I describe how Khovanov homology can emerge upon adding a fifth dimension.
Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time interpretations. For instance, three-dimensional Chern-Simons gauge theory can arise as a string theory. The world-sheet model in this case involves a topological sigma model. Instanton contributions to the sigma model give rise to Wilson line insertions in the space-time Chern-Simons theory. A certain holomorphic analog of Chern-Simons theory can also arise as a string theory.
Certain aspects of the antifield-antibracket formalism for quantization of gauge theories are clarified. In particular, we discuss the geometrical meaning of the antifields, the geometric meaning of the antibracket, and the geometric meaning of the operator Δ that appears in the quantum correction to the master equation. Finally, we point out that the antibracket formalism contains most of the ingredients that would be needed to formulate an abstract Chern-Simons Lagrangian, as in open string field theory.
Just as parallel threebranes on a smooth manifold are related to string theory on AdS 5 × S 5 , parallel threebranes near a conical singularity are related to string theory on AdS5 × X 5, for a suitable X 5. For the example of the conifold singularity, for which X 5 = (SU(2) × SU(2))/U(1), we argue that string theory on AdS5 × X 5 can be described by a certain N = 1 supersymmetric gauge theory which we describe in detail.
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.
No abstract is provided for this article.
We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions with or without supersymmetry. The matching between variants of JT gravity and matrix ensembles depends on the assumed symmetries. Time-reversal symmetry in the boundary theory means that unorientable spacetimes must be considered in the bulk. In such a case, the partition function of JT gravity is still related to the volume of the moduli space of conformal structures, but this volume has a quantum correction and has to be computed using Reidemeister-Ray-Singer torsion. Presence of fermions in the boundary theory (and thus a symmetry $(-1)^F$) means that the bulk has a spin or pin structure. Supersymmetry in the boundary means that the bulk theory is associated to JT supergravity and is related to the volume of the moduli space of super Riemann surfaces rather than of ordinary Riemann surfaces. In all cases we match JT gravity or supergravity with an appropriate random matrix ensemble. All ten standard random matrix ensembles make an appearance -- the three Dyson ensembles and the seven Altland-Zirnbauer ensembles. To facilitate the analysis, we extend to the other ensembles techniques that are most familiar in the case of the original Wigner-Dyson ensemble of hermitian matrices. We also generalize Mirzakhani's recursion for the volumes of ordinary moduli space to the case of super Riemann surfaces.
Do the elementary particles known as neutrinos have mass? Yes, according to recent experiments. But how much? A surprising — and controversial — result suggests that the answer is not what we thought.
Extending recent discussions of the Hagedorn transition in string theory, we argue that this transition is a first-order phase transition with a very large heat (corresponding to a genus-zero contribution to the free energy that appears above the critical temperature). Formally analyzing the k-loop contributions to the free energy at temperatures far above the Hagedorn temperature leads to a number of interesting speculations about the underlying degrees of freedom in string theory.
No abstract is provided for this article.
A framework for background-independent open-string field theory is proposed. The approach involves using the Batalin-Vilkovisky formalism, in a way suggested by recent developments in closed-string field theory, to implicitly define a gauge-invariant Lagrangian in a hypothetical "space of all open-string world-sheet theories." It is built into the formalism that classical solutions of the string field theory are Becchi-Rouet-Stora-Tyutin- (BRST-) invariant open-string world-sheet theories and that, when expanding around a classical solution, the infinitesimal gauge transformations are generated by the world-sheet BRST operator.
In toroidal compactification of string theory, enlarged symmetry groups arise at special radii of the compactified dimensions. Here an orbifold-like construction is considered in which the degrees of freedom describing the compact spatial dimensions are twisted by symmetries which exist only for special values of the radius. Constraints on the possible twists arising from the requirements of worldsheet supersymmetry and modular invariance are described, and some simple examples are given. One motivation for this work is that in twisting by a symmetry which exists only at a special value of the radius, one of the dilaton-like fields can acquire a mass, since the radius of the compact space is fixed.
No abstract is provided for this article.
Since superstring theories are necessarily ten-dimensional theories, any discussion of phenomenology must begin with a discussion of how apparent four-dimensional physics is related to underlying ten-dimensional physics. The present chapter is devoted to this question. We will carry out the discussion in the context of field theory, but with an emphasis on properties that depend only on qualitative assumptions, not numerical details, and so can remain valid in string theory. What we will try to accomplish in this chapter is not to develop detailed models of compactification but to set the stage and introduce some of the essential concepts.
