Revisiting instanton corrections to the Konishi multiplet

We revisit the calculation of instanton effects in correlation functions in ${\cal N}=4$ SYM involving the Konishi operator and operators of twist two. Previous studies revealed that the scaling dimensions and the OPE coefficients of these operators do not receive instanton corrections in the semiclassical approximation. We go beyond this approximation and demonstrate that, while operators belonging to the same ${\cal N}=4$ supermultiplet ought to have the same conformal data, the evaluation of quantum instanton corrections for one operator can be mapped into a semiclassical computation for another operator in the same supermultiplet. This observation allows us to compute explicitly the leading instanton correction to the scaling dimension of operators in the Konishi supermultiplet as well as to their structure constants in the OPE of two half-BPS scalar operators. We then use these results, together with crossing symmetry, to determine instanton corrections to scaling dimensions of twist-four operators with large spin.Comment: 25 pages; v2: minor changes, typos correcte

Some analytic results for two-loop scattering amplitudes

We present analytic results for the finite diagrams contributing to the two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a recently proposed representation for the integrand of the amplitude in terms of (momentum) twistors and focus on a restricted kinematics in which the answer depends only on two independent cross-ratios. The theory of motives can be used to vastly simplify the results, which can be expressed as simple combinations of classical polylogarithms.Comment: 18 page

Contrast coding choices in a decade of mixed models

Contrast coding in regression models, including mixed-effect models, changes what the terms in the model mean. In particular, it determines whether or not model terms should be interpreted as main effects. This paper highlights how opaque descriptions of contrast coding have affected the field of psycholinguistics. We begin with a reproducible example in R using simulated data to demonstrate how incorrect conclusions can be made from mixed models; this also serves as a primer on contrast coding for statistical novices. We then present an analysis of 3384 papers from the field of psycholinguistics that we coded based upon whether a clear description of contrast coding was present. This analysis demonstrates that the majority of the psycholinguistic literature does not transparently describe contrast coding choices, posing an important challenge to reproducibility and replicability in our field

More on the duality correlators/amplitudes

We continue the study of n-point correlation functions of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the l-loop corrections by making l Lagrangian insertions. We argue that there exists a simple relation between the (n+l)-point tree-level correlator with l Lagrangian insertions and the integrand of the n-particle l-loop MHV scattering amplitude, as obtained by the recent momentum twistor construction of Arkani-Hamed et al. We present several examples of this new duality, at one and two loops.Comment: 14 pages Latex, 1 figur

Supersymmetric Wilson loops in diverse dimensions

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Wilson Loops @ 3-Loops in Special Kinematics

We obtain a compact expression for the octagon MHV amplitude / Wilson loop at 3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed coefficients. We do this by making use of the cyclic and parity symmetry of the amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as in the leading term in the expansion away from this limit. We also make a natural and quite general assumption about the functional form of the result, namely that it should consist of weight 6 polylogarithms whose symbol consists of basic cross-ratios only (and not functions thereof). We also describe the uplift of this result to 10 points.Comment: 26 pages. Typos correcte

Differential equations for multi-loop integrals and two-dimensional kinematics

In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar N=4 SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop eight-point finite diagrams which relate them to massive hexagons. After the reduction to two-dimensional kinematics, we solve them using symbol technology. The terms invisible to the symbols are found through boundary conditions coming from double soft limits. These equations are valid at all-loop order for double pentaladders and allow to solve iteratively loop integrals given lower-loop information. Comments are made about multi-leg and multi-loop integrals which can appear in this special kinematics. The main motivation of this investigation is to get a deeper understanding of these tools in this configuration, as well as for their application in general four-dimensional kinematics and to less supersymmetric theories.Comment: 25 pages, 7 figure

Towards a Computational Model of Actor-Based Language Comprehension

Neurophysiological data from a range of typologically diverse languages provide evidence for a cross-linguistically valid, actor-based strategy of understanding sentence-level meaning. This strategy seeks to identify the participant primarily responsible for the state of affairs (the actor) as quickly and unambiguously as possible, thus resulting in competition for the actor role when there are multiple candidates. Due to its applicability across languages with vastly different characteristics, we have proposed that the actor strategy may derive from more basic cognitive or neurobiological organizational principles, though it is also shaped by distributional properties of the linguistic input (e.g. the morphosyntactic coding strategies for actors in a given language). Here, we describe an initial computational model of the actor strategy and how it interacts with language-specific properties. Specifically, we contrast two distance metrics derived from the output of the computational model (one weighted and one unweighted) as potential measures of the degree of competition for actorhood by testing how well they predict modulations of electrophysiological activity engendered by language processing. To this end, we present an EEG study on word order processing in German and use linear mixed-effects models to assess the effect of the various distance metrics. Our results show that a weighted metric, which takes into account the weighting of an actor-identifying feature in the language under consideration outperforms an unweighted distance measure. We conclude that actor competition effects cannot be reduced to feature overlap between multiple sentence participants and thereby to the notion of similarity-based interference, which is prominent in current memory-based models of language processing. Finally, we argue that, in addition to illuminating the underlying neurocognitive mechanisms of actor competition, the present model can form the basis for a more comprehensive, neurobiologically plausible computational model of constructing sentence-level meaning

A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces

Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain structures on the (equivariant) intersection cohomology of the Uhlenbeck partial compactification of the moduli space of framed G-bundles on P^2. More precisely, it predicts the existence of an action of the corresponding W-algebra on the above cohomology, satisfying certain properties. We propose a "finite analog" of the (above corollary of the) AGT conjecture. Namely, we replace the Uhlenbeck space with the space of based quasi-maps from P^1 to any partial flag variety G/P of G and conjecture that its equivariant intersection cohomology carries an action of the finite W-algebra U(g,e) associated with the principal nilpotent element in the Lie algebra of the Levi subgroup of P; this action is expected to satisfy some list of natural properties. This conjecture generalizes the main result of arXiv:math/0401409 when P is the Borel subgroup. We prove our conjecture for G=GL(N), using the works of Brundan and Kleshchev interpreting the algebra U(g,e) in terms of certain shifted Yangians.Comment: minor change

On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture

In this paper we study the nonperturbative corrections to the generalized Konishi anomaly that come from the strong coupling dynamics of the gauge theory. We consider U(N) gauge theory with adjoint and Sp(N) or SO(N) gauge theory with symmetric or antisymmetric tensor. We study the algebra of chiral rotations of the matter field and show that it does not receive nonperturbative corrections. The algebra implies Wess-Zumino consistency conditions for the generalized Konishi anomaly which are used to show that the anomaly does not receive nonperturbative corrections for superpotentials of degree less than 2l+1 where 2l=3c(Adj)-c(R) is the one-loop beta function coefficient. The superpotentials of higher degree can be nonperturbatively renormalized because of the ambiguities in the UV completion of the gauge theory. We discuss the implications for the Dijkgraaf-Vafa conjecture.Comment: 23 page