56038769
BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
A bstractWe study a family of circular BPS Wilson loops in $ \mathcal{N} $ = 6 super Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar and fermionic couplings depend on two deformation parameters and these operators can be considered as the ABJ(M) counterpart of the DGRT latitudes defined in $ \mathcal{N} $ = 4 SYM. We perform a complete two-loop analysis of their vacuum expectation value, discuss the appearance of framing-like phases and propose a general relation with cohomologically equivalent bosonic operators. We make an all-loop proposal for computing the Bremsstrahlung function associated to the 1/2-BPS cusp in terms of these generalized Wilson loops. When applied to our two-loop result it reproduces the known expression. Finally, we comment on the generalization of this proposal to the bosonic 1/6-BPS case.
123488833
Scattering amplitudes in three-dimensional superconformal field theory
Recent progress in computation of loop amplitudes in three-dimensional superconformal models is reviewed.
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.
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.
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.
119249635
ABJM amplitudes and WL at finite N
A bstractWe evaluate ABJM observables at two loops, for any value of the rank N of the gauge group. We compute the color subleading contributions to the four-point scattering amplitude in ABJM at two loops. Contrary to the four dimensional case, IR divergent N-subleading contributions are proportional to leading poles in the regularization parameter. We then exploit the non-planar calculation for the amplitude to derive an expression for the two-loop Sudakov form factor at any N. In the planar limit the result coincides with the one recently obtained in literature by using Feynman diagrams and unitarity. Finally, we analyze the subleading contributions to the light-like four-cusps Wilson loop and interpret the result in terms of the non-abelian exponentiation theorem. All these perturbative results satisfy the uniform transcendentality principle, hinting at its validity in ABJM beyond the planar limit.
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.
16319397
Instantons and BPS Wilson loops
The one-instanton contribution to a circular BPS Wilson loop in N=4 SU(2) Yang--Mills theory is evaluated in semiclassical approximation. This article amplifies part of a talk given by MBG at the Strings 2001 conference, Mumbai, India (January 5-10, 2001). The results are preliminary and a more complete exposition will be contained in a forthcoming paper.
15960460
Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory
The one-instanton contributions to various correlation functions of superconformal currents in four-dimensional = 4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory. Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5 ? S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang-Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS5 ? S5 background and its associated supermultiplet of zero modes. Speculations are made concerning instanton effects in the large-Nc limit of the SU(Nc) Yang-Mills theory.
122094181
The Partition Function of the SO(8192) Bosonic String
Abstract We discuss the partition function of the SO(8192) bosonic string at arbitrary genus. As in the genus-one case, diagrams defined in terms of involutions acting in the same way on the homology basis are weighted by identical mulitplicity factors. This property emerges as the basis feature of the SO(8192) theory. It corresponds to the picture of this model as a parameter-space orbifold of the closed bosonic string. By factorization we recover amplitudes in the degenerate limit.
119279808
On exact symmetries and massless vectors in holographic flows and other flux vacua
We analyze the isometries of Type IIB flux vacua based on the Papadopolous-Tseytlin ansatz and identify the related massless bulk vector fields. To this end we devise a general ansatz, valid in any flux compactification, for the fluctuations of the metric and p-forms that diagonalizes the coupled equations. We then illustrate the procedure in the simple case of holographic flows driven by the RR 3-form flux only. Specifically we study the fate of the isometries of the Maldacena-Nuñez solution associated to wrapped D5-branes.