Related papers: Small-tau expansion for the form factor of glued q…

The $r$-uniform expansion $F^{(r)+}$ of a graph $F$ is obtained by enlarging each edge with $r-2$ new vertices such that altogether we use $(r-2)|E(F)|$ new vertices. Two simple lower bounds on the largest number $\mathrm{ex}_r(n,F^{(r)+})$…

We derive some exact bounds on the free energy W(J) in an SU(N) gauge theory, where J_mu^b is a source for the gluon field A_mu^b in the minimal Landau gauge, and W(J) is the generating functional of connected correlators, exp W(J) =…

The purpose of this paper is to give an application of the gluing theorem for special Lagrangian submanifolds of a Calabi-Yau 3-fold. We proved a gluing theorem before to smooth a codimension-two singularity of a particular special…

The classical stability theorem of Erd\H{o}s and Simonovits states that, for any fixed graph with chromatic number $k+1 \ge 3$, the following holds: every $n$-vertex graph that is $H$-free and has within $o(n^2)$ of the maximal possible…

We present the analytical $\alpha_{s}^3$ correction to the $Z^{0}$ decay rate into hadrons. We calculate this correction up to (and including) terms of the order $(m_Z^2/m_{top}^2)^3$ in the large top quark mass expansion. We rely on the…

We present a numerical study of the gluon propagator in lattice Landau gauge for three-dimensional pure-SU(2) lattice gauge theory at couplings beta = 4.2, 5.0, 6.0 and for lattice volumes V = 40^3, 80^3, 140^3. In the limit of large V we…

Simulating lattice gauge theories on quantum computers presents unique challenges that drive the development of novel theoretical frameworks. The orbifold lattice approach offers a scalable method for simulating SU($N$) gauge theories in…

Let $G$ be a triangle-free graph on $n$ vertices with adjacency matrix eigenvalues $\mu_1(G)\geq \mu_2(G)\geq \dots \geq \mu_n(G)$. In this paper we study the quantity $$\mu_1(G)+\mu_n(G).$$ We prove that for any triangle-free graph $G$ we…

We consider boundary conditions at the vertex of a star graph which make Schroedinger operators on the graph self-adjoint, in particular, the two-parameter family of such conditions invariant with respect to permutations of graph edges. It…

We identify the scaling limits for the sizes of the largest components at criticality for inhomogeneous random graphs when the degree exponent $\tau$ satisfies $\tau>4$. We see that the sizes of the (rescaled) components converge to the…

We discuss the relationship between the fractional quantum Hall effect in the vicinity of the thin-torus, a.k.a. Tao-Thouless (TT), limit and quantum spin chains. We argue that the energetics of fractional quantum Hall states in Jain…

In the previous article "Refined Analytic Torsion on Manifolds with Boundary" we have presented a construction of refined analytic torsion in the spirit of Braverman and Kappeler, which does apply to compact manifolds with and without…

For a complete description of the physical properties of low-energy QCD, it might be advantageous to first reformulate QCD in terms of gauge-invariant dynamical variables, before applying any approximation schemes. Using a canonical…

We calculated the differential cross sections of the processes in which one of the pair created tau particles at an e^+ e^- collider decays into lepton flavor violating final states e.g. tau -> mu gamma, tau -> 3 mu, tau -> mu ee. Using the…

I review the recent progress in studying long-distance singularities in gauge-theory scattering amplitudes in terms of Wilson lines. The non-Abelian exponentiation theorem, which has been recently generalised to the case of multi-leg…

A set of edges $T$ in a graph $G$ is triangle-independent if $T$ contains at most one edge from each triangle in $G$. Let $\alpha_1(G)$ denote the maximum size of the triangle-independent set in $G$, and let $\tau_B(G)$ denote minimum size…

Perturbation theory is shown to be working in the IR limit of pure SU(3) Yang-Mills theory in Landau gauge by an unconventional setting of the perturbative expansion. A dynamical mass is predicted for the gluon and the lattice data are…

We investigate the zero-forcing number for triangle-free graphs. We improve upon the trivial bound, $\delta \le Z(G)$ where $\delta$ is the minimum degree, in the triangle-free case. In particular, we show that $2 \delta - 2 \le Z(G)$ for…

We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown…

We calculate the string tension, K, and some of the lightest glueball masses, M, in 3+1 dimensional SU(N) lattice gauge theories for N=2,3,4,5 . From the continuum extrapolation of the lattice values, we find that the mass ratios,…