QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime

An integral solution to the quantum Knizhnik-Zamolodchikov ($q$KZ) equation with $|q|=1$ is presented. Upon specialization, it leads to a conjectural formula for correlation functions of the XXZ model in the gapless regime. The validity of this conjecture is verified in special cases, including the nearest neighbor correlator with an arbitrary coupling constant, and general correlators in the XXX and XY limits

Unit circle elliptic beta integrals

We present some elliptic beta integrals with a base parameter on the unit circle, together with their basic degenerations.Comment: 15 pages; minor corrections, references updated, to appear in Ramanujan

Vibrational states and disorder in continuously compressed model glasses

We present in this paper a numerical study of the vibrational eigenvectors of a two-dimensional amorphous material, previously deeply studied from the point of view of mechanical properties and vibrational eigen-frequencies [7-10]. Attention is paid here to the connection between the mechanical properties of this material in term of elastic heterogeneities (EH), and how these inherent heterogeneous structures affect the vibrational eigenvectors and their plane waves decomposition. The systems are analysed for different hydrostatic pressures, and using results from previous studies, a deeper understanding of the boson peak scenario is obtained. The vibrational spectrum of a continuously densified silica glass is also studied, from which it appears that the pulsation associated with the boson peak follows the same pressure dependence trend than that of transverse waves with pulsation associated with the EH characteristic size.Comment: 9 pages, 12 figure

B_K with two flavors of dynamical overlap fermions

We present a two-flavor QCD calculation of $B_K$ on a $16^3 \times 32$ lattice at $a\sim 0.12$ fm (or equivalently $a^{-1}\sim$1.67 GeV). Both valence and sea quarks are described by the overlap fermion formulation. The matching factor is calculated non-perturbatively with the so-called RI/MOM scheme. We find that the lattice data are well described by the next-to-leading order (NLO) partially quenched chiral perturbation theory (PQChPT) up to around a half of the strange quark mass ($m_s^{\rm phys}/2$). The data at quark masses heavier than $m_s^{\rm phys}/2$ are fitted including a part of next-to-next-to-leading order terms. We obtain $B_K^{\bar{\rm MS}}(2 {\rm GeV})= 0.537(4)(40)$, where the first error is statistical and the second is an estimate of systematic uncertainties from finite volume, fixing topology, the matching factor, and the scale setting.Comment: 36 pages, 14 figures, comments and references added, analysis and systematic error revised, minor change in the final result. version to appear in PRD, reference correcte

Hadron Structure on the Lattice

A few chosen nucleon properties are described from a lattice QCD perspective: the nucleon sigma term and the scalar strangeness in the nucleon; the vector form factors in the nucleon, including the vector strangeness contribution, as well as parity breaking effects like the anapole and electric dipole moment; and finally the axial and tensor charges of the nucleon. The status of the lattice calculations is presented and their potential impact on phenomenology is discussed.Comment: 17 pages, 9 figures; proceedings of the Conclusive Symposium of the Collaborative Research Center 443 "Many-body structure of strongly interacting systems", Mainz, February 23-25, 201

Some remarks on D-branes and defects in Liouville and Toda field theories

In this paper we analyze the Cardy-Lewellen equation in general diagonal model. We show that in these models it takes simple form due to some general properties of conformal field theories, like pentagon equations and OPE associativity. This implies, that the Cardy-Lewellen equation has simple form also in non-rational diagonal models. We specialize our finding to the Liouville and Toda field theories. In particular we prove, that conjectured recently defects in Toda field theory indeed satisfy the cluster equation. We also derive the Cardy-Lewellen equation in all $sl(n)$ Toda field theories and prove that the forms of boundary states found recently in $sl(3)$ Toda field theory hold in all $sl(n)$ theories as well.Comment: 30 pages, some comments, explanations and references adde

Properties of generalized univariate hypergeometric functions

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E_7 (elliptic, hyperbolic) and of type E_6 (trigonometric) using the appropriate versions of the Nassrallah-Rahman beta integral, and we derive contiguous relations using fundamental addition formulas for theta and sine functions. The top level degenerations of the hyperbolic and trigonometric hypergeometric functions are identified with Ruijsenaars' relativistic hypergeometric function and the Askey-Wilson function, respectively. We show that the degeneration process yields various new and known identities for hyperbolic and trigonometric special functions. We also describe an intimate connection between the hyperbolic and trigonometric theory, which yields an expression of the hyperbolic hypergeometric function as an explicit bilinear sum in trigonometric hypergeometric functions.Comment: 46 page

On 3d extensions of AGT relation

An extension of the AGT relation from two to three dimensions begins from connecting the theory on domain wall between some two S-dual SYM models with the 3d Chern-Simons theory. The simplest kind of such a relation would presumably connect traces of the modular kernels in 2d conformal theory with knot invariants. Indeed, the both quantities are very similar, especially if represented as integrals of the products of quantum dilogarithm functions. However, there are also various differences, especially in the "conservation laws" for integration variables, which hold for the monodromy traces, but not for the knot invariants. We also discuss another possibility: interpretation of knot invariants as solutions to the Baxter equations for the relativistic Toda system. This implies another AGT like relation: between 3d Chern-Simons theory and the Nekrasov-Shatashvili limit of the 5d SYM.Comment: 23 page

Ghost-gluon coupling, power corrections and ΛMSˉ\Lambda_{\bar{\rm MS}} from lattice QCD with a dynamical charm

This paper is a first report on the determination of \Lambda_{\msbar} from lattice simulations with 2+1+1 twisted-mass dynamical flavours {\it via} the computation of the ghost-gluon coupling renormalized in the MOM Taylor scheme. We show this approach allows a very good control of the lattice artefacts and confirm the picture from previous works with quenched and ${\rm N}_f$=2 twisted-mass field configurations which prove the necessity to include non-perturbative power corrections in the description of the running. We provide with an estimate of \Lambda_{\msbar} in very good agreement with experimental results. To our knowledge it is the first calculation with a dynamical charm quark which makes the running up to $\alpha_s(M_Z)$ much safer.Comment: 11 pages, 3 figures, 3 tables (new version accepted to be published in Phys. Rev. D