Related papers: Boxed Plane Partitions as an Exactly Solvable Boso…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
We study the relation between the partition function of a non--relativistic particle, that describes the equilibrium fluctuations implicitly, and the partition function of the same system, deduced from the Langevin equation, that describes…
We clarify a few conceptual problems of quantum field theory on the level of exactly solvable models with fermions. The ultimate goal of our study is to gain a deeper understanding of differences between the usual ("spacelike") and…
We present three classes of exactly solvable models for fermion and boson systems, based on the pairing interaction. These models are solvable in any dimension. As an example we show the first results for fermion interacting with repulsive…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
All ten symmetry classes of plane partitions that fit in a given box are known to be enumerated by simple product formulas, but there is still no unified proof for all of them. Progress towards this goal can be made by establishing…
Blowup equations and holomorphic anomaly equations are two universal yet completely different approaches to solve refined topological string theory on local Calabi-Yau threefolds corresponding to A- and B-model respectively. The former…
We consider the field theory of $N$ massless bosons which are free except for an interaction localized on the boundary of their 1+1 dimensional world. The boundary action is the sum of two pieces: a periodic potential and a coupling to a…
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing separation of variables in polar coordinates are particular…
We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been…
We give a general construction of correlation functions in rational conformal field theory on a possibly non-orientable surface with boundary in terms of 3-dimensional topological quantum field theory. The construction applies to any…
Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities,…
It is shown that the free energy associated to a finite dimensional Airy structure is an analytic function at each finite order of the $\hbar$ expansion. Semiclassical series itself is in general divergent. Calculations are facilitated by…
The surface partition of large clusters is studied analytically within a frame-work of the ``Hills and Dales Model''. Three formulations are solved exactly by using the Laplace-Fourier transformation method. In the limit of small amplitude…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
We study certain bijection between plane partitions and $\mathbb{N}$-matrices. As applications, we prove a Cauchy-type identity for generalized dual Grothendieck polynomials. We introduce two statistics on plane partitions, whose generating…
Classification theory and the study of projective varieties which are covered by rational curves of minimal degrees naturally leads to the study of families of singular rational curves. Since families of arbitrarily singular curves are hard…
We study the relationship between one-dimensional fermion gas-impurity models and quantum dissipative systems, via the method of constructive bosonisation and unitary transformation. Starting from an anisotropic Coqblin-Schrieffer model, a…
Using the implicit function theorem, we prove existence of solutions of the so-called conformally covariant split system on compact 3-dimensional Riemannian manifolds. They give rise to non-Constant Mean Curvature (non-CMC) vacuum initial…