相关论文: TBA type equations and tropical curves

We apply mirror symmetry to the problem of counting holomorphic rational curves in a Calabi-Yau threefold X with Z_3 x Z_3 Wilson lines. As we found in Part A [hep-th/0703182], the integral homology group H_2(X,Z)=Z^3 + Z_3 + Z_3 contains…

We use the gauged linear sigma model introduced by Witten to calculate instanton expansions for correlation functions in topological sigma models with target space a toric variety $V$ or a Calabi--Yau hypersurface $M \subset V$. In the…

We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is…

We introduce a method for computing corrections to Bethe approximation for spin models on arbitrary lattices. Unlike cluster variational methods, the new approach takes into account fluctuations on all length scales. The derivation of the…

The quantum $\tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an…

We produce a flat $\Lambda$-module of $\Lambda$-adic critical slope overconvergent modular forms, producing a Hida-type theory that interpolates such forms over $p$-adically varying integer weights. This provides a Hida-theoretic…

We prove that the number of tropical critical points of an affine matroid (M,e) is equal to the beta invariant of M. Motivated by the computation of maximum likelihood degrees, this number is defined to be the degree of the intersection of…

Using the principles of the conformal quantum field theory and the finite size corrections of the energy of the ground and various excited states, we calculate the boundary critical exponents of single- and multicomponent Bethe ansatz…

We investigate the problem of counting tropical genus g curves in g-dimensional tropical abelian varieties. For g = 2, 3, we prove that the tropical count matches the count provided by G\"ottsche, Bryan-Leung, and Lange-Sernesi in the…

In two previous papers [26, 27], the exact solutions of the spin-1/2 chains with arbitrary boundary fields were constructed via the off-diagonal Bethe ansatz (ODBA). Here we introduce a method to approach the thermodynamic limit of those…

This is a follow-up paper of arXiv:1805.00115, where rational curves in surfaces that satisfy general positioned point and cross-ratio conditions were enumerated. A suitable correspondence theorem provided in arXiv:1509.07453 allowed us to…

In this paper we compute the scaling functions of the effective central charges for various quantum integrable models in a deep ultraviolet region $R\to 0$ using two independent methods. One is based on the ``reflection amplitudes'' of the…

We evaluate the superconformal index using the Bethe Ansatz (BA) approach for 4d $\mathcal{N}=1$ toric quiver gauge theories with a small amount of gauge groups. We restrict to $\mathrm{SU}(2)$ gauge factors and compare the results with the…

Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in…

In recent times, a wide variety of combinatorics has been introduced in order to solve problems from algebraic geometry. Newton-Okounkov bodies and tropical geometry are two such combinatorial theories. As shown by Kaveh and Manon, there is…

We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to…

The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin chains, 2D statistical lattice models (vertex…

We present tools and definitions to study abstract tropical manifolds in dimension 2, which we call simply tropical surfaces. This includes explicit descriptions of intersection numbers of 1-cycles, normal bundles to some curves and…

We suggest an approach to the problem of finding integral equations for the excited states of an integrable model, starting from the Thermodynamic Bethe Ansatz equations for its ground state. The idea relies on analytic continuation through…

We study Jacobian varieties for tropical curves. These are real tori equipped with integral affine structure and symmetric bilinear form. We define tropical counterpart of the theta function and establish tropical versions of the…