We construct the probe D5-brane solution in AdS 5 × S 5 dual to the   <math> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </math>  $$ \frac{1}{4} $$ -BPS latitude Wilson loop in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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   <math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math>  $$ \frac{1}{2} $$ -BPS limit. We compute the string charge k and the renormalized on-shell action perturbatively to order   <math> <mi>O</mi> <mfenced> <msubsup> <mi>θ</mi> <mn>0</mn> <mn>10</mn> </msubsup> </mfenced> </math>  $$ \mathcal{O}\left({\theta}_0^{10}\right) $$  and find full agreement with the expectation value of the Wilson loop predicted by the Gaussian matrix model in the limit N ∼ k → ∞, λ → ∞.

Chile

Alberto Faraggi

Cristóbal Moreno

On the D5-brane description of   <math> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </math>  $$ \frac{1}{4} $$ -BPS Wilson loops in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory

We consider two-point correlators of local operator insertions in a system of two Wilson-Maldacena loops in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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 AdS2 regions and in the other phase is given by two disconnected AdS2 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.

Argentina

Diego Correa

Italy

Wolfgang Mück

United States

Leopoldo Pando Zayas

Guillermo Silva

Beyond AdS2/dCFT1: insertions in two Wilson loops

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; 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 ⊂ AdS 4 × ℂℙ3 worldsheet, thus obtaining correlators of operators inserted along a 1-dimensional defect in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 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.

Anthonny Canazas Garay

Interpolating boundary conditions on AdS 2

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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 super-  <math> <msub> <mi>W</mi> <mn>3</mn> </msub> </math>  $$ {\mathcal{W}}_3 $$  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   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 super-  <math> <msub> <mi>W</mi> <mn>3</mn> </msub> </math>  $$ {\mathcal{W}}_3 $$  conformal algebra, including its multiplet structure, OPE’s and spectral flow invariance, correcting some minor typos present in the literature.

Netherlands

Alejandra Castro

Israel Osorio

A note on the   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 super-  <math> <msub> <mi>W</mi> <mn>3</mn> </msub> </math>  $$ {\mathcal{W}}_3 $$  holographic dictionary

The generating functions for the Wilson loops in the symmetric and antisymmetric representations of the gauge group U(N ) are expressed in terms of the connected correlators of multiply-wound Wilson loops, using ingredients from the representation theory of the symmetric group. This provides a proof of a recent observation by Okuyama. As a by-product, we present a new calculation of the connected 2-point correlator of multiplywound Wilson loops at leading order in 1/N.

Note on generating functions and connected correlators of 1/2-BPS Wilson loops in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM theory

We compute the one-loop effective action of string configurations embedded in AdS4 × ℂℙ3 which are dual to   <math> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> </math>  $$ \frac{1}{6} $$ -BPS latitude Wilson Loops in the ABJM theory. To avoid ambiguities in the string path integral we subtract the   <math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math>  $$ \frac{1}{2} $$ -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.

Marina David

Rodrigo León Ardón

One-loop holography with strings in AdS4 × ℂℙ3

We consider the vacuum expectation values of 1/2-BPS circular Wilson loops in  <math><mi>N</mi><mo>=</mo><mn>4</mn></math> $$ \mathcal{N}=4 $$ 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.

Antisymmetric Wilson loops in  <math><mi>N</mi><mo>=</mo><mn>4</mn></math> $$ \mathcal{N}=4 $$ SYM: from exact results to non-planar corrections

Using <math><mi>ζ</mi></math>-function regularization, we study the one-loop effective action of fundamental strings in <math><mrow><mi>A</mi><mi>d</mi><msub><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></math> dual to the latitude <math><mfrac><mn>1</mn><mn>4</mn></mfrac></math>-BPS Wilson loop in <math><mi>N</mi><mo>=</mo><mn>4</mn></math> super-Yang-Mills theory. To avoid certain ambiguities inherent to string theory on curved backgrounds we subtract the effective action of the holographic <math><mfrac><mn>1</mn><mn>2</mn></mfrac></math>-BPS Wilson loop. We find agreement with the expected field theory result at first order in the small latitude angle expansion but discrepancies at higher order.

Jeremías Aguilera-Damia

Leopoldo A. Pando Zayas

Vimal Rathee

Guillermo A. Silva

Zeta-function regularization of holographic Wilson loops

We study the one-loop effective action of certain classical type IIA string configurations in AdS4 × ℂℙ3. These configurations are dual to Wilson loops in the  <math><mi>N</mi><mo>=</mo><mn>6</mn></math> $$ \mathcal{N}=6 $$ U(N) k  × U(N)−k  Chern-Simons theory coupled to matter whose expectation values are known via supersymmetric localization. We compute the one-loop effective actions using two methods: perturbative heat kernel techniques and full ζ-function regularization. We find that the result of the perturbative heat kernel method matches the field theory prediction at the appropriate order while the ζ-function approach seems to lead to a disagreement.

Toward precision holography in type IIA with Wilson loops

We study the zeta-function regularization of functional determinants of Laplace and Dirac-type operators in two-dimensional Euclidean AdS 2 space. More specifically, we consider the ratio of determinants between an operator in the presence of background fields with circular symmetry and the free operator in which the background fields are absent. By Fourier-transforming the angular dependence, one obtains an infinite number of one-dimensional radial operators, the determinants of which are easy to compute. The summation over modes is then treated with care so as to guarantee that the result coincides with the two-dimensional zeta-function formalism. The method relies on some well-known techniques to compute functional determinants using contour integrals and the construction of the Jost function from scattering theory. Our work generalizes some known results in flat space. The extension to conformal AdS 2 geometries is also considered. We provide two examples, one bosonic and one fermionic, borrowed from the spectrum of fluctuations of the holographic  <math><mfrac><mn>1</mn><mn>4</mn></mfrac></math> $$ \frac{1}{4} $$ -BPS latitude Wilson loop.