Alberto Faraggi

We construct the probe D5-brane solution in AdS ₅ × S ⁵ dual to the $$ \frac{1}{4} $$ 1 4 -BPS latitude Wilson loop in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory in the k-antisymmetric representation of SU(N). The solution is exact in the latitude parameter θ ₀ and correctly reproduces the $$ \frac{1}{2} $$ 1 2 -BPS limit. We compute the string charge k and the renormalized on-shell action perturbatively to order $$ \mathcal{O}\left({\theta}_0^{10}\right) $$ O θ 0 10 and find full agreement with the expectation value of the Wilson loop predicted by the Gaussian matrix model in the limit N ∼ k → ∞, λ → ∞.

We consider two-point correlators of local operator insertions in a system of two Wilson-Maldacena loops in ${\cal N}=4$ supersymmetric Yang-Mills theory on both sides of the AdS/CFT correspondence. On the holographic side the correlator of two Wilson-Maldacena loops is given by a classical string world-sheet which in one phase connects two asymptotically AdS$_2$ regions and in the other phase is given by two disconnected AdS$_2$ caps; this configuration breaks supersymmetry as well as conformal invariance. We present a complete systematic account of the string world-sheet fluctuations, including the fermionic sector, and study the behavior of the holographic two-point correlators. On the field theory side we compute certain two-point correlators of local operator insertions by resumming sets of ladder diagrams. Our results demonstrate the efficacy of previously developed methods in tackling this non-conformal, non-susy regime.

A bstract: We consider two-point correlators of local operator insertions in a system of two Wilson-Maldacena loops in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory on both sides of the AdS/CFT correspondence. On the holographic side the correlator of two Wilson-Maldacena loops is given by a classical string world-sheet which in one phase connects two asymptotically AdS ₂ regions and in the other phase is given by two disconnected AdS ₂ caps; this configuration breaks supersymmetry as well as conformal invariance. We present a complete systematic account of the string world-sheet fluctuations, including the fermionic sector, and study the behavior of the holographic two-point correlators. On the field theory side we compute certain two-point correlators of local operator insertions by resumming sets of ladder diagrams. Our results demonstrate the efficacy of previously developed methods in tackling this non-conformal, non-susy regime.

We consider two instances of boundary conditions for massless scalars on AdS₂ that interpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessing invariance under the full SL(2; ℝ) conformal group is not immediate given their non-local nature. To further clarify this issue, we compute holographically 2- and 4-point correlation functions using the aforementioned boundary conditions and study their transformation properties. Concretely, motivated by the dual description of some multi-parametric families of Wilson loops in ABJM theory, we look at the excitations of an open string around an AdS₂ ⊂ AdS₄ × ℂℙ³ worldsheet, thus obtaining correlators of operators inserted along a 1-dimensional defect in $$ \mathcal{N} $$N = 6 super Chern-Simons-matter theory at strong coupling. Of the two types of boundary conditions analyzed, only one leads to the expected functional structure for conformal primaries; the other exhibits covariance under translations and rescalings but not under special conformal transformations.

We consider two instances of boundary conditions for massless scalars on $AdS_2$ that interpolate between the Dirichlet and Neumann cases while preserving scale invariance. Assessing invariance under the full $SL(2;\mathds{R})$ conformal group is not immediate given their non-local nature. To further clarify this issue, we compute holographically 2- and 4-point correlation functions using the aforementioned boundary conditions and study their transformation properties. Concretely, motivated by the dual description of some multi-parametric families of Wilson loops in ABJM theory, we look at the excitations of an open string around an $AdS_2\subset AdS_4\times\mathbb{CP}^3$ worldsheet, thus obtaining correlators of operators inserted along a $1$-dimensional defect in ${\cal N}=6$ super Chern-Simons-matter theory at strong coupling. Of the two types of boundary conditions analyzed, only one leads to the expected functional structure for conformal primaries; the other exhibits covariance under translations and rescalings but not under special conformal transformations.

This is a long-overdue companion paper to [1]. We study the relation between sl(3|2) Chern-Simons supergravity on AdS₃ and two-dimensional CFT’s with $$ \mathcal{N} $$N = 2 super- $$ {\mathcal{W}}_3 $$W 3 symmetry. Specifically, we carry out a complete analysis of asymptotic symmetries in a basis that makes the superconformal structure transparent, allowing us to establish the precise dictionary between currents and transformation parameters in the bulk and their boundary counterparts. We also discuss the incorporation of sources and display in full detail the corresponding holographic Ward identities. By imposing suitable hermiticity conditions on the CFT currents, we identify the superalgebra su(2, 1|1, 1) as the appropriate real form of sl(3|2) in Lorentzian signature. We take the opportunity to review some of the properties of the $$ \mathcal{N} $$N = 2 super- $$ {\mathcal{W}}_3 $$W 3 conformal algebra, including its multiplet structure, OPE’s and spectral flow invariance, correcting some minor typos present in the literature.

We compute the one-loop effective action of string configurations embedded in AdS₄ × ℂℙ³ which are dual to $$ \frac{1}{6} $$ 1 6 -BPS latitude Wilson Loops in the ABJM theory. To avoid ambiguities in the string path integral we subtract the $$ \frac{1}{2} $$ 1 2 -BPS case. The one-loop determinants are computed by Fourier-decomposing the two dimensional operators and then using the Gel’fand-Yaglom method. We comment on various aspects related to the regularization procedure, showing the cancellation of a hierarchy of divergences. After taking into account an IR anomaly from a change in topology, we find a precise agreement with the field theory result known from supersymmetric localization.

We compute the one-loop effective action of string configurations embedded in $AdS_4\times\mathbb{CP}^3$ which are dual to $\frac{1}{6}$-BPS latitude Wilson Loops in the ABJM theory. To avoid ambiguities in the string path integral we subtract the $\frac{1}{2}$-BPS case. The one-loop determinants are computed by Fourier-decomposing the two dimensional operators and then using the Gel'fand-Yaglom method. We comment on various aspects related to the regularization procedure, showing the cancellation of a hierarchy of divergences. After taking into account an IR anomaly from a change in topology, we find a precise agreement with the field theory result known from supersymmetric localization.

We consider the vacuum expectation values of 1/2-BPS circular Wilson loops in $$ \mathcal{N}=4 $$ N = 4 super Yang-Mills theory in the totally antisymmetric representation of the gauge group U(N) or SU(N). Localization and matrix model techniques provide exact, but rather formal, expressions for these expectation values. In this paper we show how to extract the leading and sub-leading behavior in a 1/N expansion with fixed ’t Hooft coupling starting from these exact results. This is done by exploiting the relation between the generating function of antisymmetric Wilson loops and a finite-dimensional quantum system known as the truncated harmonic oscillator. Sum and integral representations for the 1/N terms are provided.