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

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

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

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

Finite size corrections and integrability of N=2 SYM and DLCQ strings on a pp-wave

We compute the planar finite size corrections to the spectrum of the dilatation operator acting on two-impurity states of a certain limit of conformal Script N = 2 quiver gauge field theory which is a ZM-orbifold of Script N = 4 supersymmetric Yang-Mills theory. We match the result to the string dual, IIB superstrings propagating on a pp-wave background with a periodically identified null coordinate. Up to two loops, we show that the computation of operator dimensions, using an effective Hamiltonian technique derived from renormalized perturbation theory and a twisted Bethe ansatz which is a simple generalization of the Beisert-Dippel-Staudacher [1] long range spin chain, agree with each other and also agree with a computation of the analogous quantity in the string theory. We compute the spectrum at three loop order using the twisted Bethe ansatz and find a disagreement with the string spectrum very similar to the known one in the near BMN limit of Script N = 4 super-Yang-Mills theory. We show that, like in Script N = 4, this disagreement can be resolved by adding a conjectured ``dressing factor'' to the twisted Bethe ansatz. Our results are consistent with integrability of the Script N = 2 theory within the same framework as that of Script N = 4

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

Structure of large spin expansion of anomalous dimensions at strong coupling

The anomalous dimensions of planar N = 4 SYM theory operators like tr (ΦD S + Φ) expanded in large spin S have the asymptotics γ = f ln S + f c + 1 S (f 11 ln S + f 10 ) + ··· ,where f (the universal scaling function or cusp anomaly), f c and f mn are given by power series in the ’t Hooft coupling λ . The subleading coefficients appear to be related by the so-called functional relation and parity (reciprocity) property of the function expressing γ in terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS 5 . The large spin expansion of the classical string energy happens to have exactly the same structure as that of γ in the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f c , f 11 , f 10 and verify the functional/reciprocity relations at subleading 1 √ λ order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions

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

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