相关论文: Notes on index of quantum integrability
The twisted index of 3d $\mathcal{N}=2$ gauge theories on $S^1 \times \Sigma$ has an algebro-geometric interpretation as the Witten index of an effective supersymmetric quantum mechanics. In this paper, we consider the contributions to the…
We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum.…
Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of…
The symmetry algebra $P_\infty = W_\infty \oplus H \oplus I_\infty$ of integrable systems is defined. As an example the classical Sophus Lie point symmetries of all higher KP equations are obtained. It is shown that one (``positive'') half…
We study the quantum integrability of the O(N) nonlinear $\sigma$ (nls) model and the O(N) Gross-Neveu (GN) model on the half-line. We show that the \nls model is integrable with Neumann, Dirichlet and a mixed boundary condition, and that…
The goal of this note is to study the analog in unstable ${{\mathbb A}^1}$-homotopy theory of the unit map from the motivic sphere spectrum to the Hermitian K-theory spectrum, i.e., the degree map in Hermitian K-theory. We show that "Suslin…
In the theory of quantum cohomologies the WDVV equations imply integrability of the system $(I\partial_\mu - zC_\mu)\psi = 0$. However, in generic situation -- of which an example is provided by the Seiberg-Witten theory -- there is no…
The aim of this paper is to investigate the non-relativistic limit of integrable quantum field theories with fermionic fields, such as the O(N) Gross-Neveu model, the supersymmetric Sinh-Gordon and non-linear sigma models. The…
We investigate the low-energy properties of a generalized quantum sine-Gordon model in one dimension with a self-dual symmetry. This model describes a class of quantum phase transitions that stems from the competition of different orders.…
Building on insights from the theory of integrable lattices, the integrability is claimed for nonlinear replica sigma models derived in the context of real symmetric random matrices. Specifically, the fermionic and the bosonic replica…
We examine the effective field theory of the Bethe ansatz integrable Heisenberg antiferromagnetic spin chains. It shows that the quantum critical theories for the integer spin-S chains should be characterized by the SO(3)level-S…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar…
Supersymmetric quantum mechanical models are computed by the Path integral approach. In the $\beta\rightarrow0$ limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of…
I propose a method for measuring the Witten index using a lattice simulation. The index is useful to discuss spontaneous breaking of supersymmetry. As a test of the method, I also report some numerical results for the supersymmetric quantum…
We present a model of partial compositeness arising as the IR limit of a SU(4) gauge theory with only fermionic matter. This group is one of the most promising ones among a handful of possible choices allowing a symmetry breaking pattern…
A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian.…
We review applications of the sine-Gordon model, the O(3) non-linear sigma model, the U(1) Thirring model, and the O(N) Gross--Neveu model to quasi one-dimensional quantum magnets, Mott insulators, and carbon nanotubes. We focus upon the…
We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of…
Non-Abelian strings are considered in {\em non}-supersymmetric theories with fermions in various appropriate representations of the gauge group U($N$). We derive the electric charge quantization conditions and the index theorems counting…