On regularizing the AdS superstring worldsheet

In this short review (to appear as a contribution to an edited volume) we discuss perturbative and non-perturbative approaches to the quantization of the Green-Schwarz string in AdS backgrounds with RR-fluxes, where the guiding thread is the use of genuine field theory methods, the search for a good regularization scheme associated to them and the generality of the analysis carried out. We touch upon various computational setups, both analytical and numerical, and on the role of their outcomes in understanding the detailed structure of the AdS/CFT correspondence

Reciprocity of gauge operators in N=4 SYM

A recently discovered generalized Gribov-Lipatov reciprocity holds for the anomalous dimensions of various twist operators in N=4 SYM. Here, we consider a class of scaling psu(2,2|4) operators that reduce at one-loop to twist-3 maximal helicity gluonic operators. We extract from the asymptotic long-range Bethe Ansatz a closed expression for the spin dependent anomalous dimension at four loop order and provide a complete proof of reciprocity. We comment about the interplay with possible, yet unknown, wrapping corrections.Comment: Latex, JHEP style, 36 pages, v2: references adde

Generalized Gribov-Lipatov Reciprocity and AdS/CFT

Planar N=4 SYM theory and QCD share the gluon sector, suggesting the investigation of Gribov-Lipatov reciprocity in the supersymmetric theory. Since the AdS/CFT correspondence links N=4 SYM and superstring dynamics on AdS5xS5, reciprocity is also expected to show up in the quantum corrected energies of certain classical string configurations dual to gauge theory twist-operators. We review recent results confirming this picture and revisiting the old idea of Gribov-Lipatov reciprocity as a modern theoretical tool useful for the study of open problems in AdS/CFT.Comment: 42 pages. Submitted to Advances in High Energy Physics, special issue on the "Gauge/String duality

Exact computation of one-loop correction to energy of spinning folded string in AdS_5 x S^5

We consider the 1-loop correction to the energy of folded spinning string solution in the AdS_3 part of AdS_5 x S^5. The classical string solution is expressed in terms of elliptic functions so an explicit computation of the corresponding fluctuation determinants for generic values of the spin appears to be a non-trivial problem. We show how it can be solved exactly by using the static gauge expression for the string partition function (which we demonstrate to be equivalent to the conformal gauge one) and observing that all the corresponding second order fluctuation operators can be put into the standard (single-gap) Lam\'e form. We systematically derive the small spin and large spin expansions of the resulting expression for the string energy and comment on some of their applications.Comment: 52 pp, 12 figures; v3: footnote 9 adde

New linearization and reweighting for simulations of string sigma-model on the lattice

We study the discretized worldsheet of Type IIB strings in the Gubser-Klebanov-Polyakov background in a new setup, which eliminates a complex phase previously detected in the fermionic determinant. A sign ambiguity remains, which a study of the fermionic spectrum shows to be related to Yukawa-like terms, including those present in the original Lagrangian before the linearization standard in a lattice QFT approach. Monte Carlo simulations are performed in a large region of the parameter space, where the sign problem starts becoming severe and instabilities appear due to the zero eigenvalues of the fermionic operator. To face these problems, simulations are conducted using the absolute value of a fermionic Pfaffian obtained introducing a small twisted-mass term, acting as an infrared regulator, into the action. The sign of the Pfaffian and the low modes of the quadratic fermionic operator are then taken into account by a reweighting procedure of which we discuss the impact on the measurement of the observables. In this setup we study bosonic and fermionic correlators and observe a divergence in the latter, which we argue - also via a one-loop analysis in lattice perturbation theory - to originate from the U(1)-breaking of our Wilson-like discretization for the fermionic sector

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 $g=\frac{\sqrt{\lambda}}{4\pi}$, 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}.Comment: Contribution to the proceedings of Lattice 2015, July 14--18, Kobe, Japa

Strings on the lattice and AdS/CFT

We present a new auxiliary field representation for the four-fermi term of the gauge-fixed Green-Schwarz superstring action which describes fluctuations around the null-cusp background in $AdS_5\times S^5$. We sketch the main features of the fermionic operator spectrum, identifying the region of parameter space where the sign ambiguity is absent. Measurements for the observables in the setup here described are presented and discussed in a forthcoming publication

Scattering and Unitarity Methods in Two Dimensions

The standard unitarity-cut method is applied to several massive two-dimensional models, including the world-sheet AdS5×S5 superstring, to compute 2→2 scattering S-matrices at one loop from tree level amplitudes. Evidence is found for the cut-constructibility of supersymmetric models, while for models without supersymmetry (but integrable) the missing rational terms can be interpreted as a shift in the coupling

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 × ℂℙ3 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 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 × ℂℙ3 superstring in this gauge

Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS(5) x S-5

We revisit the computation of the 1-loop string correction to the “latitude” minimal surface in AdS 5 × S 5 representing 1/4 BPS Wilson loop in planar N=4 SYM theory previously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of the exact gauge theory result (derived previously from localization) using a different method to compute determinants of 2d string fluctuation operators. We apply perturbation theory in a small parameter (angle of the latitude) corresponding to an expansion near the AdS 2 minimal surface representing 1/2 BPS circular Wilson loop. This allows us to compute the corrections to the heat kernels and zeta-functions of the operators in terms of the known heat kernels on AdS 2. We apply the same method also to two other examples of Wilson loop surfaces: generalized cusp and k-wound circle