Jacques Distler

Aspects of (2, 0) string compactifications

This paper is devoted to the study of compactifications of the heterotic string with (2, 0) world sheet supersymmetry. This leads to a theory with N = 1 supersymmetry in spacetime. It has been claimed on general grounds that (2, 0) compactifications should not be solutions to the string equations of motion when the effect of world sheet instantons is taken into account. We find that this is not necessarily correct. We formulate a precise condition for a (2, 0) compactification to be a solution and construct the first explicit example of a nontrivial (2, 0) compactification on a Calabi-Yau manifold. We discuss general techniques for analysing the structure of the four-dimensional effective theories that result from (2, 0) compactifications.

Tinkertoys for Gaiotto duality

We describe a procedure for classifying

NILPOTENT ORBITS AND CODIMENSION-2 DEFECTS OF 6d

\mathcal{N} = 2

{\mathcal N} = (2, 0)

superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D AN−1 SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N = 5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian

THEORIES

\mathcal{N} = 2

2D quantum gravity, topological field theory and the multicritical matrix models☆

SCFTs.

(0,2) Landau-Ginzburg theory☆

We study the local properties of a class of codimension-2 defects of the 6d N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra \mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism twist around the defect. This class is a natural generalisation of the defects of the 6d theory of type SU(N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the 4d central charges a and c, and to the flavour central charge k.

A Critical matrix model at c = 1

Abstract We discuss the theory of 2D quantum gravity coupled to a c = −2 conformal field theory. We show that this theory has an interpretation as a topological field theory. The correlation functions of this theory are identical to those of the K = 1 multicritical matrix model, which is believed to be the discrete analogue of this continuum theory. We show that by perturbing the topological field theory, one can also recover the higher multicritical points, corresponding to the K > 1 matrix models. Finally, we introduce the N = 1 supersymmetric analogue of this topological field theory, 2D quantum supergravity coupled to a c = 1 superconformal field theory. The multicritical behaviour of this model will be discussed in a separate publication.

Tinkertoys for the D N series

Abstract A large class of (0,2) Calabi-Yau σ-models and Landau-Ginzburg orbifolds are shown to arise as different “phases” of supersymmetric gauge theories. We find a phenomenon in the Landau-Ginzburg phase which may enable one to understand which Calabi-Yau σ-models evade destabilization by worldsheet instantons. Examples of (0,2) Landau-Ginzburg vacua are analyzed in detail, and several novel features of (0,2) models are discussed. In particular, we find that (0,2) models can have different quantum symmetries from the (2,2) models built on the same Calabi-Yau manifold, and that a new kind of topology change can occur in (0,2) models of string theory.

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

By taking the critical limit of Penner’s matrix model we obtain a continuum theory whose free energy at genus-g is the Euler characteristic of moduli space of Riemann surfaces of genus-g. The exponents, and the appearance of logarithmic corrections suggest that we are dealing with a theory at c=1.