54031010
Two-loop cusp anomaly in ABJM at strong coupling
A bstractWe compute the null cusp anomalous dimension of ABJM theory at strong coupling up to two-loop order. This is done by evaluating corrections to the corresponding superstring partition function, weighted by the AdS4 × ℂℙ3 action in AdS light-cone gauge. We compare our result, where we use an anomalous shift in the AdS4 radius, with the cusp anomaly of N$$ \mathcal{N} $$ = 4 SYM, and extract the two-loop contribution to the non-trivial integrable coupling h(λ) of ABJM theory. It coincides with the strong coupling expansion of the exact expression for h(λ) recently conjectured by Gromov and Sizov. Our work provides thus a non-trivial perturbative check for the latter, as well as evidence for two-loop UV-finiteness and quantum integrability of the Type IIA AdS4 × ℂℙ3 superstring in this gauge.
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.
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.
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.
54173371
One loop amplitudes in ABJM
A bstractFor three dimensional $ \mathcal{N} = 6 $ superconformal field theories we compute oneloop scattering amplitudes for any number of external particles. We focus on a particular subsector of $ \mathcal{N} = 2 $ invariant superamplitudes for which the ordinary perturbative evaluation becomes very easy. The result we obtain is in general non-vanishing. For six external particles our findings are sufficient for determining the complete expression of the $ \mathcal{N} = 6 $ superamplitude at this order. We discuss the symmetries of the result and its anomalous variation under superconformal generators.
94785817
Freezing E3-brane instantons with fluxes
E3-instantons that generate non-perturbative superpotentials in IIB N{script} = 1 compactifications have a much more frequent occurrence than currently believed. Worldvolume fluxes will typically lift the E3-brane geometric moduli and their fermionic superpartners, leaving only the two required universal fermionic zero-modes. We consistently incorporate SL(2, ℤ) monodromies and world-volume fluxes in the effective theory of the E3-brane fermions and study the resulting zero modes spectrum, highlighting the relation between F-theory and perturbative IIB results. This leads us to a IIB derivation of the index for generation of superpotential terms, which reproduces and generalizes available results. Furthermore, we show how E3 worldvolume fluxes can be explicitly constructed in a one-modulus compactification, such that the instanton has exactly two fermonic zero-modes. This construction is readily applicable to numerous scenarios. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
7861023
Holographic Renormalization
We systematically develop the procedure of holographic renormalization for RG flows dual to asymptotically AdS domain walls. All divergences of the on-shell bulk action can be cancelled by adding covariant local boundary counterterms determined by the near-boundary behavior of bulk fields. This procedure defines a renormalized action from which correlation functions are obtained by functional differentiation. The correlators are finite and well behaved at coincident points. Ward identities, corrected for anomalies, are satisfied. The correlators depend on parts of the solution of the bulk field equations which are not determined by near-boundary analysis. In principle a full nonlinear solution is required, but one can solve linearized fluctuation equations to define a bulk-to-boundary propagator from which 2-point correlation functions are easily obtained. We carry out the procedure explicitly for two known RG flows obtained from the maximal gauged D=5 supergravity theory, obtaining new results on correlators of vector currents and related scalar operators and giving further details on a recent analysis of the stress tensor sector. 1 M.Bianchi@damtp.cam.ac.uk 2 dzf@math.mit.edu kostas@feynman.princeton.edu
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.
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.
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.