arXiv subjects

Diego H. Correa

Publications and source records attributed to Diego H. Correa.

At least 19 recordsLinked to original sources

arXiv2026

Boundary bound states and integrable Wilson loops in ABJM

We derive an integrable reflection matrix for the scattering of excitations from a boundary with a degree of freedom when the reflection process preserves an $SU(1|2)$ symmetry. As this residual symmetry is not sufficient to fully determine the reflection matrix, we use the boundary remnant of the Yangian symmetry invariance and obtain a family of integrable solutions. A concrete realization of this setup is found when studying insertions in the 1/2 BPS Wilson loop in ABJM theory. The boundary degree of freedom appears as a boundary bound state due to poles in the dressing phase of the reflection matrix. We also compare our results with those obtained from the boundary bound state bootstrap procedure. The ABJM Wilson loop example enables us to perform perturbative verifications of our results.

hep-th↗

arXiv2025

Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension

We study the integrability properties of Wilson loops in the ${\cal N}=6$ three-dimensional Chern-Simons-matter (ABJM) theory. We begin with the construction of an open spin chain that describes the anomalous dimensions of operators inserted along the contour of a 1/2 BPS Wilson loop. Moreover, we compute the all-loop reflection matrices that govern the interaction of spin-chain excitations with the boundary, including their dressing factors, and we check them against weak- and strong-coupling results. Furthermore, we propose a $Y$-system of equations for the cusped Wilson line of ABJM, and we use it to reproduce the one-loop cusp anomalous dimension of ABJM from a leading-order finite-size correction. Finally, we write a set of BTBA equations consistent with the $Y$-system proposal.

hep-th↗

arXiv2025

Bootstrapping line defects in AdS$_3$/CFT$_2$

We study correlators of insertions along 1/2 BPS line defects in the holographic dual to type IIB string theory in $AdS_3 \times S^3 \times T^4$ with mixed Ramond-Ramond and Neveu Schwarz-Neveu Schwarz three-form flux. These defects break the symmetries of the bulk CFT$_2$ as $PSU(1,1|2)^2\times SO(4) \rightarrow PSU(1,1|2)\times SU(2)$, defining displacement and tilt supermultiplets. We focus on the two-, three- and four-point functions of these supermultiplets, which we compute using analytic conformal bootstrap up to next-to-leading order in their strong-coupling expansion. We obtain a bootstrap result that only depends on two OPE coefficients. We perform a Witten diagram check of the bootstrap result, obtaining an holographic interpretation of the two OPE coefficients that are not constrained by the bootstrap procedure.

hep-th↗

arXiv2024

Mixed boundary conditions in AdS$_2$/CFT$_1$ from the coupling with a Kalb-Ramond field

The open string dual to a 1/6 BPS Wilson line in the ${\cal N} = 6$ super Chern-Simons-matter theory is coupled to a flat Kalb-Ramond field. We show that the resulting boundary term imposes mixed boundary conditions on the fields that describe the fluctuations on the world-sheet. These boundary conditions fix a combination of the derivatives of the fluctuations, parallel and transverse to the boundary. We holographically compute the correlation functions of insertions on the Wilson line in terms of world-sheet Witten diagrams. We observe that their functional dependence is consistent with the conformal symmetry on the line.

hep-th↗

arXiv2023

Beyond AdS$_2$/dCFT$_1$: Insertions in Two Wilson Loops

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.

hep-th↗

arXiv2023

Interpolating Boundary Conditions on $AdS_2$

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.

hep-th↗

arXiv2021

On the abundance of supersymmetric strings in $AdS_3\times S^3\times S^3\times S^1$ describing BPS line operators

We study supersymmetric open strings in type IIB $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed R-R and NS-NS fields. We focus on strings ending along a straight line at the boundary of $AdS_3$, which can be interpreted as line operators in a dual CFT$_2$. We study both classical configurations and quadratic fluctuations around them. We find that strings sitting at a fixed point in $S^3 \times S^3 \times S^1$, i.e. satisfying Dirichlet boundary conditions, are 1/2 BPS. We also show that strings sitting at different points of certain submanifolds of $S^3 \times S^3 \times S^1$ can still share some fraction of the supersymmetry. This allows to define supersymmetric smeared configurations by the superposition of them, which range from 1/2 BPS to 1/8 BPS. In addition to the smeared configurations, there are as well 1/4 BPS and 1/8 BPS strings satisfying Neumann boundary conditions. All these supersymmetric strings are shown to be connected by a network of interpolating BPS boundary conditions. Our study reveals the existence of a rich moduli of supersymmetric open string configurations, for which the appearance of massless fermionic fields in the spectrum of quadratic fluctuations is crucial.

hep-th↗

arXiv2020

Supersymmetric Mixed Boundary Conditions in AdS$_2$ and DCFT$_1$ Marginal Deformations

We consider different supersymmetric mixed boundary conditions for scalar and fermionic fields in $AdS_2$, searching for the dual description of a family of interpolating Wilson Loops in ABJM theory. The family, which interpolates between the bosonic 1/6 BPS loop and the 1/2 BPS loop, can be thought of as an exact marginal deformation in a defect CFT$_1$. Confronting this property against holographic correlators and vacuum energy corrections singles out a particular boundary condition which we propose as dual to the interpolating family of Wilson loops.

hep-th↗

arXiv2019

Roadmap on Wilson loops in 3d Chern-Simons-matter theories

This is a compact review of recent results on supersymmetric Wilson loops in ABJ(M) and related theories. It aims to be a quick introduction to the state of the art in the field and a discussion of open problems. It is divided into short chapters devoted to different questions and techniques. Some new results, perspectives and speculations are also presented. We hope this might serve as a baseline for further studies of this topic.

hep-th↗

arXiv2018

Ladder Limit for Correlators of Wilson Loops

We study the correlator of concentric circular Wilson loops for arbitrary radii, spatial and internal space separations. For real values of the parameters specifying the dual string configuration, a typical Gross-Ooguri phase transition is observed. In addition, we explore some analytic continuation of a parameter $γ$ that characterizes the internal space separation. This enables a ladder limit in which ladder resummation and string theory computations precisely agree in the strong coupling limit. Finally, we find a critical value of $γ$ for which the correlator is supersymmetric and ladder diagrams can be exactly resummed for any value of the coupling constant.

hep-th↗

arXiv2017

Strings in Bubbling Geometries and Dual Wilson Loop Correlators

We consider a fundamental string in a bubbling geometry of arbitrary genus dual to a half-supersymmetric Wilson loop in a general large representation $\mathbf{R}$ of the $SU(N)$ gauge group in ${\cal N}=4$ Supersymmetric Yang-Mills. We demonstrate, under some mild conditions, that the minimum value of the string classical action for a bubbling geometry of arbitrary genus precisely matches the correlator of a Wilson loop in the fundamental representation and one in a general large representation. We work out the case in which the large representation is given by a rectangular Young Tableau, corresponding to a genus one bubbling geometry, explicitly. We also present explicit results in the field theory for a correlator of two Wilson loops: a large one in an arbitrary representation and a "small" one in the fundamental, totally symmetric or totally antisymmetric representation.

hep-th↗

arXiv2017

Circular Wilson loops in defect Conformal Field Theory

We study a D3-D5 system dual to a conformal field theory with a codimension-one defect that separates regions where the ranks of the gauge groups differ by $k$. With the help of this additional parameter, as observed by Nagasaki, Tanida and Yamaguchi, one can define a double scaling limit in which the quantum corrections are organized in powers of $λ/k^2$, which should allow to extrapolate results between weak and strong coupling regimes. In particular we consider a radius $R$ circular Wilson loop placed at a distance $L$, whose internal space orientation is given by an angle $χ$. We compute its vacuum expectation value and show that, in the double scaling limit and for small $χ$ and small $L/R$, weak coupling results can be extrapolated to the strong coupling limit.

hep-th↗

arXiv2015

Ladder exponentiation for generic large symmetric representation Wilson loops

A recent proposal was made for a large representation rank limit for which the expectation values of N = 4 super Yang-Mills Wilson loops are given by the exponential of the 1-loop result. We verify the validity of this exponentiation in the strong coupling limit using the holographic D3-brane description for straight Wilson loops following an arbitrary internal space trajectory.

hep-th↗

arXiv2015

Cusped Wilson lines in symmetric representations

We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank-$k$ symmetric representation of the gauge group $U(N)$ for ${\cal N} = 4$ super Yang-Mills. We find the holographic D3-brane description for Wilson loops with internal cusps in two different limits: small cusp angle and $k\sqrtλ\gg N$. This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental. Moreover, we observe that in the limit of $k\gg N$, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large $k$, independently of the contour on which they are supported.

hep-th↗

arXiv2014

Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM

We compute the 1-loop partition function for strings in $AdS_4\times\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.

hep-th↗

arXiv2014

Strings in AdS_4 x CP^3, Wilson loops in N=6 super Chern-Simons-matter and Bremsstrahlung functions

We find 1/6 BPS string configurations in AdS_4 x CP^3, which we identify as the duals of certain 1/6 BPS circular Wilson loops in N=6 super Chern-Simons-matter gauge theory. We use our results to verify -in the strong coupling limit- a proposal made in arXiv:1402.4128 for a relation between the expectation value of these Wilson loops and the Bremsstrahlung function from deforming 1/2 BPS Wilson lines with a cusp. We also derive an analogous relation between the expectation value of some particular 1/12 BPS Wilson loops and the Bremsstrahlung function from deforming 1/6 BPS Wilson lines with an internal space cusp.

hep-th↗

arXiv2013

Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion

The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in arXiv:1203.1913 and arXiv:1203.1617 to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic. We propose an alternative formulation based on real chemical potentials and additional source terms. We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension.

hep-th↗

arXiv2013

D5-brane boundary reflection factors

We compute the strong coupling limit of the boundary reflection factor for excitations on open strings attached to various kinds of D5-branes that probe AdS5 x S5. We study the crossing equation, which constrains the boundary reflection factor, and propose that some solutions will give the boundary reflection factors for all values of the coupling. Our proposal passes various checks in the strong coupling limit by comparison with diverse explicit string theory computations. In some of the cases we consider, the D5-branes correspond to 1/2 BPS Wilson loops in the k-th rank antisymmetric representation of the dual field theory. In the other cases they correspond in the dual field theory to the addition of a fundamental hypermultiplet in a defect.

hep-th↗