118635378
From correlators to Wilson loops in Chern-Simons matter theories
We study n-point correlation functions for chiral primary operators in three dimensional supersymmetric Chern-Simons matter theories. Our analysis is carried on in $ \mathcal{N} = 2 $ superspace and covers $ \mathcal{N} = 2,3 $ supersymmetric CFT’s, the $ \mathcal{N} = 6 $ ABJM and the $ \mathcal{N} = 8 $ BLG models. In the limit where the positions of adjacent operators become light-like, we find that the one-loop n-point correlator divided by its tree level expression coincides with a light-like n-polygon Wilson loop. Remarkably, the result can be simply expressed as a linear combination of five dimensional two-mass easy boxes. We manage to evaluate the integrals analytically and find a vanishing result, in agreement with previous findings for Wilson loops.
123488833
Scattering amplitudes in three-dimensional superconformal field theory
Recent progress in computation of loop amplitudes in three-dimensional superconformal models is reviewed.
119108513
The 1/2 BPS Wilson loop in ABJ(M) at two loops: the details
A bstractWe compute the expectation value of the 1/2 BPS circular Wilson loop operator in ABJ(M) theory at two loops in perturbation theory. Our result turns out to be in exact agreement with the weak coupling limit of the prediction coming from localization, including finite N contributions associated to non-planar diagrams. It also confirms the identification of the correct framing factor that connects framing-zero and framing one expressions, previously proposed. The evaluation of the 1/2 BPS operator is made technically difficult in comparison with other observables of ABJ(M) theory by the appearance of integrals involving the coupling between fermions and gauge fields, which are absent for instance in the 1/6 BPS case. We describe in detail how to analytically solve these integrals in dimensional regularization with dimensional reduction (DRED). By suitably performing the physical limit to three dimensions we clarify the role played by short distance divergences on the final result and the mechanism of their cancellation.
52023598
On the ABJM four-point amplitude at three loops and BDS exponentiation
A bstractWe study the three-loop four-point amplitude in ABJM theory. We determine the dual conformal invariant integrals with highest number of propagators and fix their coefficients by two-particle cuts. Evaluating such a combination of integrals in dimensional regularization we provide evidence for exponentiation of the amplitude, including the finite terms. In addition we show that the three-loop amplitude can be expressed in terms of classical polylogarithms of uniform degree of transcendentality.
119238771
Scattering in ABJ theories
A bstractWe study the correspondence between scattering amplitudes and Wilson loops in three-dimensional Chern-Simons matter theories. In particular, using $ \mathcal{N} = {2} $ superspace formalism, we compute at one loop the whole spectrum of four-point superamplitudes for generic $ \mathcal{N} \geqslant {2} $ supersymmetric theories and find a vanishing result for $ \mathcal{N} = {6} $ ABJ(M) and $ \mathcal{N} = {8} $ BLG models. This restricts the possible range of theories for which Wilson loops/scattering amplitudes duality might work. At two loops, we present the computation of the four-point ABJ scattering amplitude for external chiral superfields. Extending the known result for the ABJM Wilson loop to the ABJ case we find perfect agreement. We also discuss the dual conformal invariance of our results and the relationship between the Feynman diagram computation and unitarity methods. While for the ABJM theory dual conformally invariant integrals exactly reproduce the amplitude, for the ABJ case this happens only up to a residual constant depending on the parity-violating parameter. Finally we propose a BDS-like exponentiation for the amplitude based on an analogy with the four dimensional $ \mathcal{N} = {4} $ SYM case, and discuss its strong coupling dual counterpart.
119117490
Nonplanarity through unitarity in the ABJM theory
We use unitarity techniques to compute the two-loop non-planar corrections to the Sudakov form factor and the four-point amplitude in ABJM theory. We start by reconstructing non-planar integrals from two-particle cuts in three dimensions. This causes ambiguities, due to the one-loop four-point amplitude being subleading in dimensional regularization. We provide a prescription to circumvent them and show that it leads to the correct results, as checked against the recent Feynman diagram computation. For the amplitude we point out an alternative basis of integrals, including a non-planar double-box with a numerator inspired by color-kinematics duality. We reproduce the result using a combination thereof with the coefficients fixed by generalized unitarity. For BLG theory we propose that this gives the form of the amplitude satisfying color-kinematics duality. Finally, we compute the complete two-loop amplitude of three-dimensional N = 8 SYM, and the corresponding four-point amplitude in N = 16 supergravity as a double copy.
14494446
Current algebra of the pure spinor superstring in AdS5 ? S5
We perform a Hamiltonian analysis of the classical type IIB superstring on AdS5 ? S5 in the pure spinor approach. Taking the spatial components of the left-invariant (super)currents and the pure spinor ghosts as canonical variables, we compute the classical graded Poisson brackets of the currents and ghosts and identify the first class constraints associated to the local SO(4,1) ? SO(5) symmetry and the pure spinor condition. We then study the properties of the BRST generators and the Hamiltonian along the constraints. For a natural choice of the the Lagrange multipliers, we show equivalence of the canonical equations of motion with the covariant ones. Finally we briefly discuss the (non) local currents, including the ghost contribution, that generate the global PSU(2,2|4) symmetry and its Yangian extension in the present framework.
18962115
Anomalous dimensions in N=4 SYM theory at order g4
Abstract We compute four-point correlation functions of scalar composite operators in the N =4 supercurrent multiplet at order g 4 using the N =1 superfield formalism. We confirm the interpretation of short-distance logarithmic behaviours in terms of anomalous dimensions of unprotected operators exchanged in the intermediate channels and we determine the two-loop contribution to the anomalous dimension of the N =4 Konishi supermultiplet.
18159913
ALE instantons in string effective theory
We show that the classical equations of motion of the low-energy effective field theory describing the massless modes of the heterotic (or type I) string admit two classes of supersymmetric self-dual backgrounds. The first class, which was already considered in the literature, consists of solutions with a (conformally) flat metric coupled to axionic instantons. The second includes Asymptotically Locally Euclidean (ALE) gravitational instantonic backgrounds coupled to gauge instantons through the so-called “standard embedding”. We show that some elements of these two classes of solutions are dual to each other in the sense of Buscher's duality. We give a world-sheet interpretation of the heterotic ALE istanton solutions in terms of superconformal N = (4, 4) σ-models and argue for their validity to all orders in α′. Specializing the gravitational background to the Eguchi-Hanson instanton, we compute the indices of the fermionic operators and give the explicit form of all the relevant fermionic and bozonic zero-modes.
15907576
Non-perturbative and flux superpotentials for type I strings on the Z3 orbifold
Abstract Non-perturbative effects are studied for type I strings on the Z 3 orbifold with Chan–Paton symmetry broken by Wilson lines. Generalizing previous analyses that have focussed on (bi)fundamentals, it is argued that (anti)symmetric representations of the resulting gauge group play a decisive role in generating an ADS-like superpotential in this and related cases. Non-perturbative corrections in the closed string moduli are only allowed if properly dressed with open string fields charged under the anomalous U ( 1 ) of the orbifold. A general discussion of instanton effects in SYM and string theories is given. Non-perturbative superpotentials induced by both ED5's and ED1's are analyzed. The superpotential generated by closed string fluxes, viz. Scherk–Schwarz shifts (torsion), R–R 3-form flux as well as non-geometric fluxes is derived. Some preliminary comments on the compatibility of the two kinds of superpotentials and the issue of moduli stabilization are presented.
12505991
Precision spectroscopy and higher spin symmetry in the ABJM model
We revisit Kaluza-Klein compactification of 11-d supergravity on $ {{{{S^7}}} \left/ {{{\mathbb{Z}_k}}} \right.} $ using group theory techniques that may find application in other flux vacua with internal coset spaces. Among the SO(2) neutral states, we identify marginal deformations and fields that couple to the recently discussed world-sheet instanton of Type IIA on $ \mathbb{C}{\mathbb{P}^3} $. We also discuss charged states, dual to monopole operators, and the $ {\mathbb{Z}_k} $ projection of the Osp(8|4) singleton and its tensor products. In particular, we show that the doubleton spectrum may account for $ \mathcal{N} = 6 $ higher spin symmetry enhancement in the limit of vanishing ’t Hooft coupling in the boundary Chern-Simons theory.