Related papers: $N=2$ Supersymmetric Integrable Models and Topolog…
We obtain lattice models whose continuum limits correspond to $N=2$ superconformal coset models. This is done by taking the well known vertex model whose continuum limit is the $G \times G/G$ conformal field theory, and twisting the…
It is discussed how a limiting procedure of (super)conformal field theories may result in logarithmic (super)conformal field theories. The construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field…
In these lectures we discuss the supersymmetry algebra and its irreducible representations. We construct the theories of rigid supersymmetry and gave their superspace formulations. The perturbative quantum properties of the extended…
We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal…
A superfield formulation is presented of the central charge anomaly in quantum corrections to solitons in two-dimensional theories with N=1 supersymmetry. Extensive use is made of the superfield supercurrent, that places the supercurrent…
This contribution briefly describes some developments of the use of string symmetries and anomaly cancellation mechanisms to include string loop corrections in the construction of the low-energy effective supergravity of superstrings.…
In these 4 lectures, I give a brief introduction to the principles of effective field theory and discuss their application via 3 examples: (i) the Standard Model as an effective theory; (ii) non-linear sigma models and the composite Higgs;…
A brief review of the harmonic superspace approach to the construction of $\mathcal{N}=2$ supersymmetric higher spin theories is given. We define off-shell analytic harmonic gauge potentials of $\mathcal{N}=2$ supersymmetric higher-spin…
In these notes I briefly outline SL(2) degenerate conformal field theories and their application to some related models, namely 2d gravity and N=2 discrete superconformal series.
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…
We briefly review the general structure of integrable particle theories in 1+1 dimensions having N=1 supersymmetry. Examples are specific perturbed superconformal field theories (of Yang-Lee type) and the N=1 supersymmetric sine-Gordon…
These lectures discuss some of the general issues in developing a phenomenology for Superstring Theory/M Theory. The focus is on the question: how might one obtain robust, generic predictions. For example, does the theory predict low energy…
We approach the study of non--integrable models of two--dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact $S$-matrix and Form Factors of the integrable field theories we…
The conformal field theory for the $gl(N,N)$ affine Lie superalgebra in two space-time dimensions is studied. The energy-momentum tensor of the model, with vanishing Virasoro anomaly, is constructed. This theory has a topological symmetry…
The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in…
A general two dimensional fractional supersymmetric conformal field theory is investigated. The structure of the symmetries of the theory is studied. Then, applying the generators of the closed subalgebra generated by $(L_{-1}, L_{0},…
We study the twisted $N=2$ supersymmetric Yang-Mills theory coupled with the hypermultiplets (TQCD). We suggest that the family of TQCD can be served as a powerful tool for studying the quantum field theoretic properties of the underlying…
These are lecture notes of lectures presented at the 1993 Trieste Summer School, dealing with two classes of two-dimensional field theories, (topological) Yang-Mills theory and the G/G gauged WZW model. The aim of these lectures is to…
In this paper we consider the representation theory of a non-standard quantization of sl(2). This paper contains several results which have applications in quantum topology, including the classification of projective indecomposable modules…