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Pedro Vieira

Publications and source records attributed to Pedro Vieira.

At least 73 records · Page 4Linked to original sources
arXiv2012

Multichannel Conformal Blocks for Polygon Wilson Loops

We introduce the notion of Multichannel Conformal Blocks relevant for the Operator Product Expansion for Null Polygon Wilson loops with more than six edges. As an application of these, we decompose the one loop heptagon Wilson loop and predict the value of its two loop OPE discontinuities. At the functional level, the OPE discontinuities are roughly half of the full result. Using symbols they suffice to predict the full two loop result. We also present several new predictions for the heptagon result at any loop order.

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arXiv2012

From Polygon Wilson Loops to Spin Chains and Back

Null Polygon Wilson Loops (WL) in N=4 SYM can be computed using the Operator Product Expansion in terms of a transition amplitude on top of a color flux tube (FT). That picture is valid at any value of the 't Hooft coupling. So far it has been efficiently used at weak coupling (WC) in cases where only a single particle is flowing. At any finite value of the coupling however, an infinite number of particles are flowing on top of the color FT. A major open problem in this approach was how to deal with generic multi-particle states at WC. In this paper we study the propagation of any number of FT excitations at WC. We do this by first mapping the WL into a sum of two point functions of local operators. This map allows us to translate the integrability techniques developed for the spectrum problem back to the WL. E.g., the FT Hamiltonian can be represented as a simple kernel acting on the loop. Having an explicit representation for the FT Hamiltonian allows us to treat any number of particles on an equal footing. We use it to bootstrap some simple cases where two particles are flowing, dual to N2MHV amplitudes. The FT is integrable and therefore has other (infinite set of) conserved charges. The generating function of conserved charges is constructed from the monodromy (M) matrix between sides of the polygon. We compute it for some simple examples at leading order at WC. At strong coupling (SC), these Ms were the main ingredients of the Y-system solution. To connect the WC and SC computations, we study a case where an infinite number of particles are propagating already at leading order at WC. We obtain a precise match between the WC and SC Ms. That match is the WL analogue of the well known Frolov-Tseytlin limit where the WC and SC descriptions become identical. Hopefully, putting the WC and SC descriptions on the same footing is the first step in understanding the all loop structure.

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arXiv2012

Tailoring Three-Point Functions and Integrability IV. Theta-morphism

We compute structure constants in N=4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic description called the Theta-morphism. In this approach we introduce impurities at each spin chain site, act with particular differential operators on the standard algebraic Bethe ansatz vectors and generate in this way higher loop eigenvectors. The final results for the structure constants take a surprisingly simple form. For some quantities we conjecture all loop generalizations. These are based on the tree level and one loop patterns together and also on some higher loop experiments involving simple operators.

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arXiv2012

Quantum Integrability for Three-Point Functions

Quantum corrections to three-point functions of scalar single trace operators in planar N=4 Super-Yang-Mills theory are studied using integrability. At one loop, we find new algebraic structures that not only govern all two loop corrections to the mixing of the operators but also automatically incorporate all one loop diagrams correcting the tree level Wick contractions. Speculations about possible extensions of our construction to all loop orders are given. We also match our results with the strong coupling predictions in the classical (Frolov-Tseytlin) limit.

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arXiv2012

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection we present an overview of the achievements and the status of this subject as of the year 2010.

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arXiv2011

Tailoring Three-Point Functions and Integrability III. Classical Tunneling

We compute three-point functions between one large classical operator and two large BPS operators at weak coupling. We consider operators made out of the scalars of N=4 SYM, dual to strings moving in the sphere. The three-point function exponentiates and can be thought of as a classical tunneling process in which the classical string-like operator decays into two classical BPS states. From an Integrability/Condensed Matter point of view, we simplified inner products of spin chain Bethe states in a classical limit corresponding to long wavelength excitations above the ferromagnetic vacuum. As a by-product we solved a new long-range Ising model in the thermodynamic limit.

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arXiv2011

OPE for Super Loops

We extend the Operator Product Expansion for Null Polygon Wilson loops to the Mason-Skinner-Caron-Huot super loop, dual to non MHV gluon amplitudes. We explain how the known tree level amplitudes can be promoted into an infinite amount of data at any loop order in the OPE picture. As an application, we re-derive all one loop NMHV six gluon amplitudes by promoting their tree level expressions. We also present some new all loops predictions for these amplitudes.

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arXiv2011

Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match

We compute three-point functions of single trace operators in planar N=4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.

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arXiv2011

Tailoring Three-Point Functions and Integrability

We use Integrability techniques to compute structure constants in N=4 SYM to leading order. Three closed spin chains, which represent the single trace gauge-invariant operators in N=4 SYM, are cut into six open chains which are then sewed back together into some nice pants, the three-point function. The algebraic and coordinate Bethe ansatz tools necessary for this task are reviewed. Finally, we discuss the classical limit of our results, anticipating some predictions for quasi-classical string correlators in terms of algebraic curves.

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arXiv2011

Bootstrapping Null Polygon Wilson Loops

We derive the two loop expressions for polygonal Wilson loops by starting from the one loop expressions and applying an operator product expansion. We do this for polygonal Wilson loops in R^{1,1} and find a result in agreement with previous computations. We also discuss the spectrum of excitations around flux tube that connects two null Wilson lines.

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arXiv2011

Pulling the straps of polygons

Using the Operator Product Expansion for Wilson loops we derive a simple formula giving the discontinuities of the two loop result in terms of the one loop answer. We also argue that the knowledge of these discontinuities should be enough to fix the full two loop answer, for a general number of sides. We work this out explicitly for the case of the hexagon and rederive the known result.

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arXiv2010

An Operator Product Expansion for Polygonal null Wilson Loops

We consider polygonal Wilson loops with null edges in conformal gauge theories. We derive an OPE-like expansion when several successive lines of the polygon are becoming aligned. The limit corresponds to a collinear, or multicollinear, limit and we explain the systematics of all the subleading corrections, going beyond the leading terms that were previously considered. These subleading corrections are governed by excitations of high spin operators, or excitations of a flux tube that goes between two Wilson lines. The discussion is valid for any conformal gauge theory, for any coupling and in any dimension. For N=4 super Yang Mills we check this expansion at strong coupling and at two loops at weak coupling . We also make predictions for the remainder function at higher loops. In the process, we also derived a new version for the TBA integral equations that determine the strong coupling answer and present the area as the associated Yang-Yang functional.

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arXiv2010

Y-system for Scattering Amplitudes

We compute N=4 Super Yang Mills planar amplitudes at strong coupling by considering minimal surfaces in AdS_5 space. The surfaces end on a null polygonal contour at the boundary of AdS. We show how to compute the area of the surfaces as a function of the conformal cross ratios characterizing the polygon at the boundary. We reduce the problem to a simple set of functional equations for the cross ratios as functions of the spectral parameter. These equations have the form of Thermodynamic Bethe Ansatz equations. The area is the free energy of the TBA system. We consider any number of gluons and in any kinematic configuration.

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arXiv2010

Exact AdS/CFT spectrum: Konishi dimension at any coupling

We compute the full dimension of Konishi operator in planar N=4 SYM theory it for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A.Kozak.

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arXiv2010

Integrability for the Full Spectrum of Planar AdS/CFT II

Using the thermodynamical Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in arXiv:0901.3753 for the spectrum of all operators in planar N=4 SYM theory follows from these equations. In particular, we present the integral equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analogue of DHM formula for the dressing kernel in the mirror kinematics.

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arXiv2009

Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics

We propose, using the example of the O(4) sigma model, a general method for solving integrable two dimensional relativistic sigma models in a finite size periodic box. Our starting point is the so-called Y-system, which is equivalent to the thermodynamic Bethe ansatz equations of Yang and Yang. It is derived from the Zamolodchikov scattering theory in the cross channel, for virtual particles along the non-compact direction of the space-time cylinder. The method is based on the integrable Hirota dynamics that follows from the Y-system. The outcome is a nonlinear integral equation for a single complex function, valid for an arbitrary quantum state and accompanied by the finite size analogue of Bethe equations. It is close in spirit to the Destri-deVega (DdV) equation. We present the numerical data for the energy of various states as a function of the size, and derive the general Luscher-type formulas for the finite size corrections. We also re-derive by our method the DdV equation for the SU(2) chiral Gross-Neveu model.

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arXiv2009

Symmetries of the N=4 SYM S-matrix

Under the assumption of a CSW generalization to loop amplitudes in N=4 SYM, (1) We prove that, formally the S-matrix is superconformal invariant to any loop order, and (2) We argue that superconformal symmetry survives regularization. More precisely, IR safe quantities constructed from the S-matrix are superconformal covariant. The IR divergences are regularized in a new holomorphic anomaly friendly regularization. The CSW prescription is known to be valid for all tree level amplitudes and for one loop MHV amplitudes. In these cases, our formal results do not rely on any assumptions.

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