Related papers: SOS model partition function and the elliptic weig…
We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering or electron-electron scattering. These…
We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged)…
We study projective completions of affine algebraic varieties induced by filtrations on their coordinate rings. In particular, we study the effect of the 'multiplicative' property of filtrations on the corresponding completions and…
In this paper we identify the problem of equivariant vortex counting in a $(2,2)$ supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov-Witten invariants of the GIT quotient target…
We compute the exact partition function, the universal ground state degeneracy and boundary state of the 2-D Ising model with boundary magnetic field at off-critical temperatures. The model has a domain that exhibits states localized near…
We derive exact formulae for the partition function and the expectation values of Wilson/'t Hooft loops, thus directly checking their S-duality transformations. We focus on a special class of N=2 gauge theories on S^4 with fundamental…
We prove that strictly elliptic operators with generalized Wentzell boundary conditions generate analytic semigroups of angle $\frac{\pi}{2}$ on the space of continuous function on a compact manifold with boundary.
We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…
We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of…
We derive the partition functions of the Schwarz-type four-dimensional topological half-flat 2-form gravity model on K3-surface or T^4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class…
We compute the algebra of left and right currents for a principal chiral model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We define primary fields for the current algebra that match the affine primaries at the…
We study the partially asymmetric exclusion process with open boundaries. We generalise the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid…
We use a Hodge decomposition and its generalization to non-abelian flat vector bundles to calculate the partition function for abelian and non- abelian BF theories in $n$ dimensions. This enables us to provide a simple proof that the…
We evaluate the partition function of three dimensional theories of gravity in the quantum regime, where the AdS radius is Planck scale and the central charge is of order one. The contribution from the AdS vacuum sector can - with certain…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
In this paper screening currents of the second kind are considered. They are constructed in any affine current algebra for directions corresponding to simple roots with multiplicity one in a decomposition of the highest root on a set of…
In this work we derive results concerning Elliptic Functions using as tools general formulas from previus work.
We introduce an elliptic algebra $U_{q,p}(\hat{sl_2})$ with $p=q^{2r} (r\in \R_{>0})$ and present its free boson representation at generic level $k$. We show that this algebra governs a structure of the space of states in the $k-$fusion…
The main result of these notes is an analytical expression for the partition function of the circular brane model for arbitrary values of the topological angle. The model has important applications in condensed matter physics. It is related…
The algebraic engineering technique is applied to a class of 3D $\mathcal{N}=2$ gauge theories on the omega-deformed background $\mathbb{R}_\epsilon^2\times S^1$. The vortex partition function and the fundamental qq-character are obtained…