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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.

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.