Publications

Two-dimensional models with (0,2) supersymmetry: perturbative aspects

Certain perturbative aspects of two-dimensional sigma models with (0, 2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of “chiral differential operators” is related to sigma models. In the process, we obtain, for example, an understanding of the one-loop beta function in terms of holomorphic data. A companion paper will study nonperturbative behavior of these theories.

An Introduction To The Web-Based Formalism

This paper summarizes our rather lengthy paper, Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions, and is meant to be an informal, yet detailed, introduction and summary of that larger work.

Super Atiyah classes and obstructions to splitting of supermoduli space

The first obstruction to splitting a supermanifold S is one of the three components of its super Atiyah class, the two other components being the ordinary Atiyah classes on the reduced space M of the even and odd tangent bundles of S. We evaluate these classes explicitly for the moduli space of super Riemann surfaces (super moduli space) and its reduced space, the moduli space of spin curves. These classes are interpreted in terms of certain extensions arising from line bundles on the square of the varying (super) Riemann surface. These results are used to give a new proof of the non-projectedness of ${\mathfrak{M}}_{g,1}$, the moduli space of super Riemann surfaces with one puncture.

Anomalies in String Theory with D-Branes

We analyze global anomalies for elementary Type II strings in the presence of D-branes. Global anomaly cancellation gives a restriction on the D-brane topology. This restriction makes possible the interpretation of D-brane charge as an element of K-theory.

APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory

These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field theory -- it is a property of the algebra of observables and not just of the states.

Vacuum configurations for superstrings

We study candidate vacuum configurations in ten-dimensional O(32) and E8 × E8 supergravity and superstring theory that have unbroken N = 1 supersymmetry in four dimensions. This condition permits only a few possibilities, all of which have vanishing cosmological constant. In the E8 × E8 case, one of these possibilities leads to a model that in four dimensions has an E6 gauge group with four standard generations of fermions.

Fermion Quantum Numbers in Kaluza-Klein Theory

No abstract is provided for this article.

Phase transitions in M-theory and F-theory

Phase transitions are studied in M-theory and F-theory. In M-theory compactification to five dimensions on a Calabi-Yau, one can find topology-changing transitions similar to those seen in conformal field theory, but the non-geometrical phases known in conformal field theory are absent. At boundaries of moduli space where such phases might have been expected, the moduli space ends, by a conventional or unconventional physical mechanism. The unconventional mechanisms, which roughly involve the appearance of tensionless strings, can sometimes be better understood in F-theory.

Eigenvalue inequalities for fermions in gauge theories

We show that QCD with a sufficient number of fermions of zero bare mass has physical massless particles. That result also follows from triangle anomalies,

More On Superstring Perturbation Theory: An Overview Of Superstring Perturbation Theory Via Super Riemann Surfaces

This article is devoted to an overview of superstring perturbation theory from the point of view of super Riemann surfaces. We aim to elucidate some of the subtleties of superstring perturbation that caused difficulty in the early literature, focusing on a concrete example -- the $SO(32)$ heterotic string compactified on a Calabi-Yau manifold, with the spin connection embedded in the gauge group. This model is known to be a significant test case for superstring perturbation theory. Supersymmetry is spontaneously broken at 1-loop order, and to treat correctly the supersymmetry-breaking effects that arise at 1- and 2-loop order requires a precise formulation of the procedure for integration over supermoduli space. In this paper, we aim as much as possible for an informal explanation, though at some points we provide more detailed explanations that can be omitted on first reading.

Superstring Theory 2 Volume Hardback Set

<i>Superstring Theory Volume 1: Introduction Volume 2: Loop Amplitudes, Anomalies and Phenomenology</i>

No abstract is provided for this article.

JT Gravity and the Ensembles of Random Matrix Theory

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.

Why Does Quantum Field Theory in Curved Spacetime Make Sense? And What Happens to the Algebra of Observables in the Thermodynamic Limit?

This article aims to explain some of the basic facts about the questions raised in the title, without the technical details that are available in the literature. We provide a gentle introduction to some rather classical results about quantum field theory in curved...

Lectures on Geometry

No abstract is provided for this article.

CURRENT ALGEBRA, BARYONS, AND QUARK CONFINEMENT

No abstract is provided for this article.

A NONPERTURBATIVE SUPERPOTENTIAL WITH E₈-SYMMETRY

We compute the non-perturbative superpotential in $F$-theory compactification to four dimensions on a complex three-fold $\P^1\times S$, where $S$ is a rational elliptic surface. In contrast to examples considered previously, the superpotential in this case has interesting modular properties; it is essentially an $E_8$ theta function.

Global Gravitational Anomalies

No abstract is provided for this article.