Valentina Forini

Generalized quark-antiquark potential at weak and strong coupling

We study a two-parameter family of Wilson loop operators in

Gauge invariant finite size spectrum of the giant magnon

\mathcal{N} = 4

Exact computation of one-loop correction to the energy of folded spinning string in AdS5 × S5

super-symmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. We calculate these loops on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. We comment about the feasibility of deriving all-loop results for these Wilson loops.

Twist-three at five loops, Bethe Ansatz and wrapping

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the R-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.

The generalized cusp in AdS(4) x CP3 and more one-loop results from semiclassical strings

We consider the one-loop correction to the energy of the folded spinning string solution in the AdS3 part of AdS5 × S5. 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) Lame 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.

Structure of large spin expansion of anomalous dimensions at strong coupling

We present a formula for the five-loop anomalous dimension of N = 4 SYM twist-three operators in the sl(2) sector. We obtain its asymptotic part from the Bethe Ansatz and finite volume corrections from the generalized Luscher formalism, considering scattering processes of spin chain magnons with virtual particles that travel along the cylinder. The complete result respects the expected large spin scaling properties and passes non-trivial tests including reciprocity constraints. We analyze the pole structure and find agreement with a conjectured resummation formula. In analogy with the twist-two anomalous di- mension at four-loops wrapping effects are of order (log 2 M/M 2 ) for large values of the spin.

The Scaling function at strong coupling from the quantum string Bethe equations

We evaluate the exact one-loop partition function for fundamental strings whose world surface ends on a cusp at the boundary of AdS4 and has a ‘jump’ in . This allows us to extract the stringy prediction for the ABJM-generalized cusp anomalous dimension ΓABJMcusp(ϕ, θ) up to NLO in sigma-model perturbation theory. With a similar analysis, we present the exact partition functions for folded closed string solutions moving in the AdS3 parts of and AdS3 × S3 × S3 × S1 backgrounds. Results are obtained applying to the string solutions relevant for the AdS4/CFT3 and AdS3/CFT2 correspondence the tools previously developed for their AdS5 × S5 counterparts.

Quark-antiquark potential in AdS at one loop

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.

Two-dimensional S-matrices from unitarity cuts

We study at strong coupling the scaling function describing the large spin anomalous dimension of twist two operators in Script N = 4 super Yang-Mills theory. In the spirit of AdS/CFT duality, it is possible to extract it from the string Bethe Ansatz equations in the fraktur sfraktur l(2) sector of the AdS5 × S5 superstring. To this aim, we present a detailed analysis of the Bethe equations by numerical and analytical methods. We recover several short string semiclassical results as a check. In the more difficult case of the long string limit providing the scaling function, we analyze the strong coupling version of the Eden-Staudacher equation, including the Arutyunov-Frolov-Staudacher phase. We prove that it admits a unique solution, at least in perturbation theory, leading to the correct prediction consistent with semiclassical string calculations.

A new rolling tachyon solution of cubic string field theory

We derive an exact analytical expression for the one-loop partition function of a string in AdS5 ×S5 background with world-surface ending on two anti-parallel lines. All quantum fluctuations are shown to be governed by integrable, single-gap Lamé operators. The first strong coupling correction to the quark-antiquark potential, as defined in