We study the integral Bailey lemma associated with the A_n-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional N = 1 quiver gauge theories with the gauge groups being products of SU(n + 1), we provide evidence for various new dualities. Further con rmation is achieved by explicitly checking that the `t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.

The charm quark mass is one of the fundamental parameters of the Standard Model Lagrangian. In this work we present a determination of the MSbar charm mass from a fit to the inclusive and charm HERA deep-inelastic structure function data. The analysis is performed within the xFitter framework, with structure functions computed in the FONLL general-mass scheme as implemented in APFEL. In the case of the FONLL-C scheme, we obtain mc(mc) = 1.335 +- 0.043(exp) +0.019 -0.000(param) +0.011 -0.008(mod) +0.033 -0.008(th) GeV. We also perform an analogous determination in the fixed-flavor-number scheme at next-to-leading order, finding mc(mc) = 1.318 +- 0.054(exp) +0.011 -0.010(param) +0.015 -0.019(mod) +0.045 -0.004(th) GeV, compatible with the FONLL-C value. Our results are consistent with previous determinations from DIS data as well as with the PDG world average.

We extend the observations of our previous paper JHEP 1409, 071 (2014) [arXiv:1405.5285]. In particular, we show that the secular growth of the loop corrections to the two--point correlation functions is gauge independent: we observe the same growth in the case of the static gauge for the constant background electric field. Furthermore we solve the kinetic equation describing photon production from the background fields, which was derived in our previous paper and allows one to sum up leading secularly growing corrections from all loops. Finally, we show that in the constant electric field background the one--loop correction to the current of the produced pairs is not zero: it also grows with time and violates time translational and reversal invariance of QED on the constant electric field background.

We consider the AGT correspondence in the context of the conformal field theory M(p, p')\otimes H, where M(p,p') is the minimal model based on the Virasoro algebra labeled by two co-prime integers p,p' and H is the free boson theory based on the Heisenberg algebra. Using Nekrasov's instanton partition functions without modification to compute conformal blocks in M(p, p')\otimes H leads to ill-defined or incorrect expressions.

We propose the procedure to make this expressions are well defined and check these proposal in two cases: 1. 1-point torus, when the operator insertion is the identity, and 2. The 6-point Ising conforma block on the sphere that involves six Ising magnetic operators.

The first untagged decay-time-integrated amplitude analysis of *B**s*0 → *K*S0*K*±*π*∓ decays is performed using a sample corresponding to 3.0 fb−1 of *pp* collision data recorded with the LHCb detector during 2011 and 2012. The data are described with an amplitude model that contains contributions from the intermediate resonances *K**(892)0,+, *K*2*(1430)0,+ and *K*0*(1430)0,+, and their charge conjugates. Measurements of the branching fractions of the decay modes *B**s*0 → *K**(892)±*K*∓ and 𝐵0𝑠→𝐾∗(---)(892)0𝐾0(---)Bs0→K∗(---)(892)0K0(---) are in agreement with, and more precise than, previous results. The decays *B**s*0 → *K*0*(1430)±*K*∓ and 𝐵0𝑠→𝐾∗0(---)(1430)0𝐾0(---)Bs0→K0∗(---)(1430)0K0(---) are observed for the first time, each with significance over 10 standard deviations.

A search for the Ξ++*𝑐**𝑐* baryon through the Ξ++*𝑐**𝑐**→ D*+*pK**−**π*+ decay is performed with a data sample corresponding to an integrated luminosity of 1*.*7 fb*−*1 recorded by the LHCb experiment in *pp* collisions at a centre-of-mass energy of 13 TeV. No significant signal is observed in the mass range from the kinematic threshold of the decay to 3800 MeV/*c*2. An upper limit is set on the ratio of branching fractions =(Ξ++*𝑐**𝑐*→*𝐷*+*𝑝**𝐾*−*𝜋*+)(Ξ++*𝑐**𝑐*→Λ+*𝑐**𝐾*−*𝜋*+*𝜋*+) with ℛ *<* 1*.*7 (2*.*1) *×* 10*−*2 at the 90% (95%) confidence level at the known mass of the Ξ++*𝑐**𝑐* state.

A bstract We continue our study of the AGT correspondence between instanton counting on ${{{{{\ mathbb {C}}^ 2}}}\ left/{{{{\ mathbb {Z}} _p}}}\ right.} $ and Conformal field theories with the symmetry algebra $\ mathcal {A}\ left ({r, p}\ right) $. In the cases r= 1, p= 2 and r= 2, p= 2 this algebra specialized to: $\ mathcal {A}\ left ({1, 2}\ right)=\ mathcal {H}\ oplus\ widehat {\ mathfrak {sl}}{(2) _1} $ and $\ mathcal {A}\ left ({2, 2}\ right)=\ mathcal {H}\ oplus\ widehat {\ mathfrak {sl}}{(2) _2}\ oplus\ mathrm {NSR} $.

We developed a general non-perturbative framework for the BFKL spectrum of planar N=4 SYM, based on the Quantum Spectral Curve (QSC). It allows one to study the spectrum in the whole generality, extending previously known methods to arbitrary values of conformal spin *n*. We show how to apply our approach to reproduce all known perturbative results for the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue and get new predictions. In particular, we re-derived the Faddeev-Korchemsky Baxter equation for the Lipatov spin chain with non-zero conformal spin reproducing the corresponding BFKL kernel eigenvalue. We also get new non-perturbative analytic results for the Pomeron eigenvalue in the vicinity of |*n*| = 1*, *Δ = 0 point and we obtained an explicit formula for the BFKL intercept function for arbitrary conformal spin up to the 3-loop order in the small coupling expansion and partial result at the 4-loop order. In addition, we implemented the numerical algorithm of arXiv:1504.06640 as an auxiliary file to this arXiv submission. From the numerical result we managed to deduce an analytic formula for the strong coupling expansion of the intercept function for arbitrary conformal spin.

For an arbitrary generalized quantum integrable spin chain we introduce a “master T-operator” which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary space. We show that the functional relations for the transfer matrices are equivalent to an infinite set of model-independent bilinear equations of the Hirota form for the master T-operator, which allows one to identify it with tau-function of an integrable hierarchy of classical soliton equations. In this paper we consider spin chains with rational GL(N)-invariant R-matrices but the result is independent of a particular functional form of the transfer matrices and directly applies to quantum integrable models with more general (trigonometric and elliptic) R-matrices and to supersymmetric spin chains.

We discuss relation between the cluster integrable systems and spin chains in the context of their correspondence with 5d supersymmetric gauge theories. It is shown that gl*N* XXZ-type spin chain on *M* sites is isomorphic to a cluster integrable system with *N × M* rectangular Newton polygon and *N × M* fundamental domain of a ‘fence net’ bipartite graph. The Casimir functions of the Poisson bracket, labeled by the zig-zag paths on the graph, correspond to the inhomogeneities, on-site Casimirs and twists of the chain, supplemented by total spin. The symmetricity of cluster formulation implies natural spectral duality, relating gl*N* -chain on *M* sites with the gl*M* -chain on *N* sites. For these systems we construct explicitly a subgroup of the cluster mapping class group GQ and show that it acts by permutations of zig-zags and, as a consequence, by permutations of twists and inhomogeneities. Finally, we derive Hirota bilinear equations, describing dynamics of the tau-functions or A-cluster variables under the action of some generators of GQ.

We discuss the relation between the cluster integrable systems and *q*-difference Painlevé equations. The Newton polygons corresponding to these integrable systems are all 16 convex polygons with a single interior point. The Painlevé dynamics is interpreted as deautonomization of the discrete flows, generated by a sequence of the cluster quiver mutations, supplemented by permutations of quiver vertices.

We also define quantum *q*-Painlevé systems by quantization of the corresponding cluster variety. We present formal solution of these equations for the case of pure gauge theory using *q*-deformed conformal blocks or 5-dimensional Nekrasov functions. We propose, that quantum cluster structure of the Painlevé system provides generalization of the isomonodromy/CFT correspondence for arbitrary central charge.

We study conformal field theory with the symmetry algebra

We develop a recursive approach to computing Neveu-Schwarz conformal blocks associated with n-punctured Riemann surfaces. This work generalizes the results of [1] obtained recently for the Virasoro algebra. The method is based on the analysis of the analytic properties of the superconformal blocks considered as functions of the central charge *c*. It consists of two main ingredients: the study of the singular behavior of the conformal blocks and the analysis of their asymptotic properties when *c* tends to infinity. The proposed construction is applicable for computing multi-point blocks in different topologies. We consider some examples for genus zero and one with different numbers of punctures. As a by-product, we propose a new way to solve the recursion relations, which gives more efficient computational procedure and can be applied to SCFT case as well as to pure Virasoro blocks.

We present an approach that gives rigorous construction of a class of crossing invariant functions in *c* = 1 CFTs from the weakly invariant distributions on the moduli space \( {\mathcal{M}}_{0,4}^{\mathrm{SL}\left(s,\mathbb{C}\right)} \) of SL(2*,* ℂ) flat connections on the sphere with four punctures. By using this approach we show how to obtain correlation functions in the Ashkin-Teller and the Runkel- Watts theory. Among the possible crossing-invariant theories, we obtain also the analytic Liouville theory, whose consistence was assumed only on the basis of numerical tests.

Differential cross sections of deep inelastic scattering of charged leptons from hadrons are investigated by using the gauge/string duality. We consider vector mesons derived from different holographic dual models obtaining a general expression. We focus on the strongly coupled regime of dual gauge theories for different values of the Bjorken parameter. We find new predictions which are particularly interesting for differential scattering cross sections of polarized leptons scattered off polarized vector mesons. We also carry out a detailed comparison of the moments of the structure functions with lattice QCD results.

We study deep inelastic scattering structure functions from hadrons using different holographic dual models which describe the strongly coupled regime of gauge theories in the large N limit. Particularly, we consider scalar and vector mesons obtained from holographic descriptions with fundamental degrees of freedom, corresponding to N = 2 supersymmetric and non-supersymmetric Yang-Mills theories. We explicitly obtain analytic expressions for the full set of eight structure functions, i.e., F 1, F 2, g 1, g 2, b 1, b 2, b 3, b 4, arising from the standard decomposition of the hadronic tensor of spin-one hadrons. We obtain the relations 2F 1 = F 2 and 2b 1 = b 2. In addition, we find b 1 ∼ O(F 1) as suggested by Hoodbhoy, Jaffe and Manohar for vector mesons. Also, we find new relations among some of these structure functions.

Two-point current correlation functions of the large *N* limit of supersymmetric and non-supersymmetric Yang-Mills theories at strong coupling are investigated in terms of their string theory dual models with quenched flavors. We consider non-Abelian global symmetry currents, which allow one to investigate vector mesons with *N* *f* *>* 1. From the correlation functions we construct the deep inelastic scattering hadronic tensor of spin-one mesons, obtaining the corresponding eight structure functions for polarized vector mesons. We obtain several relations among the structure functions. Relations among some of theirmoments are also derived. Aspects of the sub-leading contributions in the 1*/N* and *N* *f* */N* expansions are discussed. At leading order we find a universal behavior of the hadronic structure functions.

We study the dual description of the eta-deformed OSP(N|2m) sigma model in the asymptotically free regime (N > 2m+2). Compared to the case of classical Lie groups, for supergroups there are inequivalent eta-deformations corresponding to different choices of simple roots. For a class of such deformations we propose the system of screening charges depending on a continuous parameter b, which defines the eta-deformed OSP(N|2m) sigma model in the limit b -> 1 and a certain Toda QFT as b -> 0. In the sigma model regime we show that the leading UV asymptotic of the eta-deformed model coincides with a perturbed Gaussian theory. In the perturbative regime b -> 0 we show that the tree-level two-particle scattering matrix matches the expansion of the trigonometric OSP(N|2m) S-matrix.

The reduction of the duality invariant approach to M-theory by a U-duality group valued Scherk-Schwarz twist is considered. We show that all gaugings of SUGRA can be obtained by dimensional reduction of the extended space.

A search for exclusive or quasi-exclusive γγ → W+W− production, via pp → p(*)W+W−p(*) →p(*)μ±e∓p(*) at s√=8s=8 TeV, is reported using data corresponding to an integrated luminosity of 19.7 fb−1. Events are selected by requiring the presence of an electron-muon pair with large transverse momentum pT(μ±e∓) > 30 GeV, and no associated charged particles detected from the same vertex. The 8 TeV results are combined with the previous 7 TeV results (obtained for 5.05 fb−1 of data). In the signal region, 13 (2) events are observed over an expected background of 3.9 ± 0.6 (0.84 ± 0.15) events for 8 (7) TeV, resulting in a combined excess of 3.4σ over the background-only hypothesis. The observed yields and kinematic distributions are compatible with the standard model prediction for exclusive and quasi-exclusive γγ → W+W− production. Upper limits on the anomalous quartic gauge coupling operators a0,CW (dimension-6) andfM0,1,2,3 (dimension-8), the most stringent to date, are derived from the measured dilepton transverse momentum spectrum.

We consider the conformal blocks in the theories with extended conformal W-symmetry for the integer Virasoro central charges. We show that these blocks for the generalized twist fields on sphere can be computed exactly in terms of the free field theory on the covering Riemann surface, even for a non-abelian monodromy group. The generalized twist fields are identified with particular primary fields of the W-algebra, and we propose a straightforward way to compute their W-charges. We demonstrate how these exact conformal blocks can be effectively computed using the technique arisen from the gauge theory/CFT correspondence. We discuss also their direct relation with the isomonodromic tau-function for the quasipermutation monodromy data, which can be an encouraging step on the way of definition of generic conformal blocks for W-algebra using the isomonodromy/CFT correspondence.