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We show how to classify the asymptotically-free gauge theories in four spacetime dimensions, focussing here on the case of purely fermionic matter. The classification depends on the fact (which we prove) that both the dimension and Dynkin…
We extend the notion of space shifts introduced by L. D. Faddeev and A. Yu. Volkov (Phys. Lett. B 315 (1993)) for certain quantum light cone lattice equations of sine-Gordon type at root of unity. As a result we obtain a compatibility…
We find the fermionic R-operator based on Bazhanov-Stroganov three-parameter elliptic parametrization of the free fermion model, and the corresponding Yang-Baxter and decorated Yang-Baxter equations, which are of the difference type in one…
Generalized Baxter's relations on the transfer-matrices (also known as Baxter's TQ relations) are constructed and proved for an arbitrary untwisted quantum affine algebra. Moreover, we interpret them as relations in the Grothendieck ring of…
Lie algebra valued equations translating the integrability of a general two-dimensional Wess-Zumino-Witten model are given. We found simple solutions to these equations and identified three types of new integrable non-linear sigma models.…
The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, is considered. The partition function is computed using the Izergin-Korepin method,…
Superconformal indices of 3d N=2 supersymmetric field theories are investigated from the Yang-Baxter equation point of view. Solutions of the star-triangle relation, vertex and IRF Yang-Baxter equations are expressed in terms of the…
For a spatially flat Friedmann model with line element $ds^2=a^2 [ da^2/B(a)-dx^2-dy^2-dz^2 ] $, the 00-component of the Einstein field equation reads $8\pi G T_{00}=3/a^2$ containing no derivative. For a nonlinear Lagrangian ${\cal L}(R)$,…
Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the…
We show a new neutral-fermionic presentation of Ikeda-Naruse's $K$-theoretic $Q$-functions, which represent a Schubert class in the $K$-theory of coherent sheaves on the Lagrangian Grassmannian. Our presentation provides a simple…
We consider Lindblad equations for one dimensional fermionic models and quantum spin chains. By employing a (graded) super-operator formalism we identify a number of Lindblad equations than can be mapped onto non-Hermitian interacting…
In this paper, we initiate the study of the interplay between $k$-graphs and the Yang-Baxter equation. For this, we provide two very different perspectives. One one hand, we show that the set of all set-theoretic solutions of the…
We consider a model with anomaly-free Abelian gauge axial-vector symmetry, which is intended to mimic the standard electroweak gauge chiral SU(2)_L x U(1)_Y theory. Within this model we demonstrate: (1) Strong Yukawa interactions between…
In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete…
We study the ground state of the boundary Izergin-Korepin model. The boundary Izergin-Korepin model is defined by so-called $R$-matrix and $K$-matrix for $U_q(A_2^{(2)})$ which satisfy Yang-Baxter equation and boundary Yang-Baxter equation…
This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of…
It is proposed to use the pinch technique (PT) to obtain the gauge-independent thermal $\beta$ function in a hot Yang-Mills gas. Calculations of the thermal $\beta$ function are performed at one-loop level in four different gauges, (i) the…
We present an approach to a non-commutative-like phase space which allows to analyze quasi-free states on the CAR algebra in analogy to quasi-free states on the CCR algebra. The used mathematical tools are based on a new algebraic structure…
A gauge-fixing procedure for the Yang-Mills theory on an n-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not…
Let $\Gamma$ be a discrete group satisfying the approximation property (AP). Let $X$, $Y$ be $\Gamma$-spaces and $\pi \colon Y \to X$ be a proper factor map which is injective on the non-free part. We prove the one-to-one correspondence…