arXiv subjects

Lorenzo Bianchi

Publications and source records attributed to Lorenzo Bianchi.

47 records · Page 3Linked to original sources

arXiv2016

Perturbation theory for string sigma models

In this thesis we investigate quantum aspects of the Green-Schwarz superstring in various AdS backgrounds relevant for the AdS/CFT correspondence, providing several examples of perturbative computations in the corresponding integrable sigma-models. We start by reviewing in details the supercoset construction of the superstring action in $AdS_5 \times S^5$, pointing out the limits of this procedure for $AdS_4$ and $AdS_3$ backgrounds. For the $AdS_4 \times CP^3$ case we give a thorough derivation of an alternative action, based on the double-dimensional reduction of eleven-dimensional super-membranes. We then consider the expansion about the BMN vacuum and the S-matrix for the scattering of worldsheet excitations in the decompactification limit. To evaluate its elements efficiently we describe a unitarity-based method resulting in a very compact formula yielding the cut-constructible part of any one-loop two-dimensional S-matrix. In the second part of this review we analyze the superstring action on $AdS_4 \times CP^3$ expanded around the null cusp vacuum. The free energy of this model, whose computation we reproduce up to two-loops at strong coupling, is related to the cusp anomalous dimension of the ABJM theory and, indirectly, to a non-trivial effective coupling $h(λ)$ featuring all integrability-based calculations in $AdS_4/CFT_3$. Finally, we extensively discuss the comparison of the perturbative results and the integrability predictions for the one-loop dispersion relation of GKP excitations. Our results provide valuable data in support of the quantum consistency of the string actions - often debated due to possible issues with cancellation of UV divergences and the lack of manifest power-counting renormalizability - and furnish non-trivial stringent tests for the quantum integrability of the analyzed models.

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arXiv2016

Lattice and string worldsheet in AdS/CFT: a numerical study

We consider a possible discretization for the gauge-fixed Green-Schwarz (two-dimensional) sigma-model action for the Type IIB superstring and use it for measuring the cusp anomalous dimension of planar $\mathcal{N}=4$ SYM as derived from string theory. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and a Wilson-like fermion discretization. In this preliminary study, we compare our results with the expected behavior for very large values of $g=\frac{\sqrtλ}{4π}$, which is the perturbative regime of the sigma-model, and find a qualitative agreement at finite lattice spacing. For smaller $g$ the continuum limit is obstructed by a divergence. We also detect a phase in the fermion determinant, whose origin we explain, which for small $g$ leads to a sign problem not treatable via standard reweigthing. Results presented here are discussed thoroughly in~\cite{toappear}.

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arXiv2015

Quantum dispersion relations for the $AdS_4 \times CP^3$ GKP string

We compute the one-loop correction to the dispersion relations of the excitations of the $AdS_4 \times CP^3$ sigma model dual to ABJM theory, expanded around the cusp background. The results parallel those of N = 4 SYM. As in that case, the dispersion relations are compatible with the predictions from the Bethe ansatz for the GKP string, though showing some known discrepancies on which we comment.

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arXiv2015

On the scattering of gluons in the GKP string

We compute the one-loop S-matrix for the light bosonic excitations of the GKP string at strong coupling. These correspond, on the gauge theory side, to gluon insertions in the GKP vacuum. We perform the calculation by Feynman diagrams in the worldsheet theory and we compare the result to the integrability prediction, finding perfect agreement for the scheme independent part. For scheme dependent rational terms we test different schemes and find that a recent proposal reproduces exactly the integrability prediction.

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arXiv2015

Worldsheet scattering for the GKP string

We initiate the perturbative study of the S-matrix for the excitations on top of the GKP vacuum at strong coupling. Using the string sigma model action expanded around the null cusp classical solution, we compute the tree-level S-matrix elements and compare them with the predictions from the asymptotic Bethe Ansatz. We also check the factorization of the three-body S-matrix for various bosonic processes, finding precise agreement with the constraints imposed by integrability.

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arXiv2014

Two-loop cusp anomaly in ABJM at strong coupling

We 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 $AdS_4\times \mathbb{CP}^3$ action in AdS light-cone gauge. We compare our result, where we use an anomalous shift in the $AdS_4$ radius, with the cusp anomaly of $\mathcal{N}=4$ 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 $AdS_4\times \mathbb{CP}^3$ superstring in this gauge.

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arXiv2014

$AdS_3 \times S^3 \times M^4$ string S-matrices from unitarity cuts

Continuing the program initiated in arXiv:1304.1798 we investigate unitarity methods applied to two-dimensional integrable field theories. The one-loop computation is generalized to encompass theories with different masses in the asymptotic spectrum and external leg corrections. Additionally, the prescription for working with potentially singular cuts is modified to cope with an ambiguity that was not encountered before. The resulting methods are then applied to three light-cone gauge string theories; i) $AdS_3 \times S^3 \times T^4$ supported by RR flux, ii) $AdS_3 \times S^3 \times S^3 \times S^1$ supported by RR flux and iii) $AdS_3 \times S^3 \times T^4$ supported by a mix of RR and NSNS fluxes. In the first case we find agreement with the exact result following from symmetry considerations and in the second case with one-loop semiclassical computations. This agreement crucially includes the rational terms and hence supports the conjecture that S-matrices of integrable field theories are cut-constructible, up to a possible shift in the coupling. In the final case, under the assumption that our methods continue to give all rational terms, we give a conjecture for the one-loop phases.

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arXiv2014

Two-dimensional S-matrices from unitarity cuts

Using unitarity methods, we compute, for several massive two-dimensional models, the cut-constructible part of the one-loop 2->2 scattering S-matrices from the tree-level amplitudes. We apply our method to various integrable theories, finding evidence that for supersymmetric models the one-loop S-matrix is cut-constructible, while for models without supersymmetry (but with integrability) the missing rational terms are proportional to the tree-level S-matrix and therefore can be interpreted as a shift in the coupling. Finally, applying our procedure to the world-sheet theory for the light-cone gauge-fixed AdS_5 x S^5 superstring we reproduce, at one-loop in the near-BMN expansion, the S-matrix known from integrability techniques.

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arXiv2014

Non-planarity through unitarity in ABJM

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.

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arXiv2014

Unitarity methods for scattering in two dimensions

The standard unitarity-cut method is applied to several massive two-dimensional models, including the world-sheet AdS$_5\times S^5$ superstring, to compute $2\to 2$ scattering S-matrices at one loop from tree level amplitudes. Evidence is found for the cut-constructibility of supersymmetric integrable models, while for models without supersymmetry (but integrable) the missing rational terms can be interpreted as a shift in the coupling.

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arXiv2013

On DIS Wilson coefficients in N = 4 super Yang-Mills theory

In this note we evaluate Wilson coefficients for "deep inelastic scattering" (DIS) in N=4 SYM theory at NLO in perturbation theory, using as a probe an R-symmetry conserved current. They exhibit uniform transcendentality and coincide with the piece of highest transcendentality in the corresponding QCD Wilson coefficients. We extract from the QCD result a NNLO prediction for the N=4 SYM Wilson coefficient, and comment on the features of its Regge limit asymptotics.

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