Revisiting N=4 superconformal blocks

21 pages; v2: version published in JHEPWe study four-point correlation functions of four generic half-BPS supermultiplets of N=4 SCFT in four dimensions. We use the two-particle Casimir of four-dimensional superconformal algebra to derive superconformal blocks which contribute to the partial wave expansion of such correlators. The derived blocks are defined on analytic superspace and allow us in principle to find any component of the four-point correlator. The lowest component of the result agrees with the superconformal blocks found by Dolan and Osborn.Peer reviewe

Cluster Adjacency for m=2 Yangian Invariants

11 pages, 3 figuresWe classify the rational Yangian invariants of the $m=2$ toy model of $\mathcal{N}=4$ Yang-Mills theory in terms of generalised triangles inside the amplituhedron $\mathcal{A}_{n,k}^{(2)}$. We enumerate and provide an explicit formula for all invariants for any number of particles $n$ and any helicity degree $k$. Each invariant manifestly satisfies cluster adjacency with respect to the $Gr(2,n)$ cluster algebra.Peer reviewe

A Shortcut to the Q-Operator

Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2 Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independent operatorial solutions to Baxter's TQ equation may be constructed as commuting transfer matrices if a twist field is present. The latter are obtained by tracing over infinitely many oscillator states living in the auxiliary channel of an associated monodromy matrix. We furthermore compare and differentiate our approach to earlier articles addressing the problem of the construction of the Q-operator for the XXX chain. Finally we speculate on the importance of Q-operators for the physical interpretation of recent proposals for the Y-system of AdS/CFT.Comment: 41 pages, 2 figures; v2: references added; v3: version published in J. Stat. Mec

Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains

We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to generic finite-dimensional representations in quantum space. The results equally apply to non-compact representations of highest or lowest weight type. We furthermore fill an apparent gap in the literature, and provide the nearest-neighbor Hamiltonians of the spin chains in question for all cases where the gl(n) representations are described by rectangular Young diagrams, as well as for their infinite-dimensional generalizations. They take the form of digamma functions depending on operator-valued shifted weights.Comment: 26 pages, 1 figur

Archaeological Assessment of Two Sites in the Vicinity of Floodwater Retarding Structure No. 11, Salado Creek Watershed, Bexar County, Texas

In March of 1977, the Center for Archaeological Research at The University of Texas at San Antonio was contacted by Mr. George C. Marks of the United States Department of Agriculture Soil Conservation Service (Temple, Texas) regarding further archaeological research at two archaeological sites within the area of proposed Floodwater Retarding Structure No. 11 on the Salado Creek Watershed in Bexar County, Texas. These two sites had been located in an earlier reconnaissance of the region conducted by the Center for Archaeological Research (Hester et al. 1974). Recommendations made at that time for these two sites included a careful definition of the limits of the archaeological materials and an evaluation of subsurface potential

Contribution to a ranking procedure for polymeric caotings and hydrophobic agents for concrete

One of the possible ways to protect the concrete is using coatings and hydrophobic agents that act as a barrier against the environment. When selecting the material for concrete protection, importance should be given to these properties of diffusion and permeability. The coatings and the hydrophobic agents must stop the penetration of water and delay the influence of aggressive agents, allowing the structure to breathe by a water vapour diffusion mechanism. An evaluation of the surface layer transport properties gives information on the durability of a particular concrete. In order to make the selection of coatings and hydrophobic agents for concrete protection, it is important to analyse the compound’s technical and economical performances. A ranking procedure, developed by Czarnecki and Lukowski, is applied on a series of concrete protection products. The ranking procedure is applied to evaluate durability experiments, carried out on some commercially available silicone, acrylic and epoxy compounds for surface treatment of concrete. The ranking procedure transforms experimental data of properties into one numerical value, by which the products can be classified according to the way on which their properties present an optimised or even best buy combination. The paper shows the use of the ranking procedure methodology, and points at the importance of the choice of the criteria and of their relative weight factor in the evaluation. The method is a valuable tool for the ranking of similar materials, whose performance is based on the same or similar physical or chemical processes

Large spin systematics in CFT

20 pages; v2: version published in JHEPUsing conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.Peer reviewe

Six and seven loop Konishi from Luscher corrections

In the present paper we derive six and seven loop formulas for the anomalous dimension of the Konishi operator in N=4 SYM from string theory using the technique of Luscher corrections. We derive analytically the integrand using the worldsheet S-matrix and evaluate the resulting integral and infinite sum using a combination of high precision numerical integration and asymptotic expansion. We use this high precision numerical result to fit the integer coefficients of zeta values in the final analytical answer. The presented six and seven loop results can be used as a cross-check with FiNLIE on the string theory side, or with direct gauge theory computations. The seven loop level is the theoretical limit of this Luscher approach as at eight loops double-wrapping corrections will appear.Comment: 18 pages, typos correcte

Lessons from crossing symmetry at large N

20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe