We study a fermion field coupled to a scalar via a Yukawa term. The scalar field is the $ϕ^4$ model with an impurity that preserves half of the BPS property. We analyze the spectrum of the defects of the model and collisions between them both close to the BPS regime and not. As the fermion binds to these defects, it may be transferred from one to the other, which we quantify via overlaps, known as Bogoliubov coefficients. BPS collisions are less likely to transfer the fermion between defects and can be adiabatic for non-relativistic velocities, especially for small coupling constants. Moreover, closer to the BPS limit only a small fraction of the fermion number is radiated away. In contrast, non-BPS collisions lead to more radiation in the fermion field and excitation of the fermion to higher bound states, and the result is more sensitive to the parameters.
A self-dual generalization of the lump-impurity system is introduced. This model possesses lump-antilump-like pairs as static solutions of the pertinent Bogomolny equations. This allows for a moduli space approximation analysis of the BPS solutions which are identified as lump-antilump configurations. Some geometrical properties of the resulting moduli are analyzed. In addition, it is argued that, this type of impurity models can be interpreted as a limit of certain non-impurity theories.
We show that the BPS Skyrme model, as well as its (2+1) dimensional baby version (restricted), can be coupled with an impurity in the BPS preserving manner. The corresponding Bogomolny equations are derived.
We find supersymmetric extensions of the half-BPS soliton-impurity models in (1+1) dimensions which preserve half of the $\mathcal{N}=1$ supersymmetry. This is related to the fact that in the bosonic sector (i.e., the half-BPS soliton-impurity model), only one soliton (for example, the kink) is a BPS configuration which solves the pertinent Bogomolnyi equation and saturates the topological energy bound. On the other hand, the topological charge conjugate state (the antikink) is not a BPS solution. This means that it obeys the full Euler-Lagrange equation and does not saturate the topological e…
It was recently shown that half BPS-solutions of M-theory can be expressed in terms of a single function satisfying the 3-d continuum Toda equation. In this note half-BPS solutions corresponding to separable solutions of the Toda equations are examined.
Using the pure spinor formalism for the superstring in an $AdS_5\times S^5$ background, a simple expression is found for half-BPS vertex operators. At large radius, these vertex operators reduce to the usual supergravity vertex operators in a flat background. And at small radius, there is a natural conjecture for generalizing these vertex operators to non-BPS states.
The $ϕ^4$ model is coupled to an impurity in a way that preserves one-half of the BPS property. This means that the antikink-impurity bound state is still a BPS solution, i.e., a zero-pressure solution saturating the topological energy bound. The kink-impurity bound state, on the other hand, does not saturate the bound, in general. We found that, although the impurity breaks translational invariance, it is, in some sense, restored in the BPS sector where the energy of the antikink-impurity solution does not depend on their mutual distance. This is reflected in the existence of a generalised tr…
We revisit non-marginal half-BPS solutions of M-theory in the framework of the possible existence of an underlying E11 Kac-Moody symmetry. In this context, non-marginal BPS solutions of M-theory can be described as exact solutions of the brane sigma-model E10/K(E10), extending results obtained earlier for marginal BPS solutions. We uncover an elegant and simple algebraic structure underlying the bound states by looking at subalgebras embedded in E10. Furthermore, we show that the non-marginal BPS solutions can be obtained from the elementary marginal ones by the action of K(E10) transformation…
We study Aharony-Bergman-Jafferis-Maldacena (ABJM) theory without and with mass deformation. It is shown that maximally supersymmetry preserving, D-term, and F-term mass deformations of single mass parameter are equivalent. We obtain vortex-type half-BPS equations and the corresponding energy bound. For the undeformed ABJM theory, the resulting half-BPS equation is the same as that in supersymmetric Yang-Mills theory and no finite energy regular BPS solution is found. For the mass-deformed ABJM theory, the half-BPS equations for U(2)xU(2) case reduce to the vortex equation in Maxwell-Higgs the…
We calculate the four-point correlation function of half-BPS operators with weights 2, 3, 3, 4 in N=4 SYM to two-loop order. The OPE of this correlation function provides a nontrivial check of the integrability conjecture for a class of three-point functions formulated in arXiv:1311.6404. Our perturbative calculation exploits the supergraph formalism in N=2 harmonic superspace.
We evaluated all two-loop conformal integrals of scalar half-BPS six-point functions in $\mathcal{N} = 4$ SYM restricted to a configuration where all points lie on a line. Moreover, we also computed some of these integrals in the kinematical limit where adjacent points become null-separated. Our results can serve as cross-checks for future works which obtain these integrals for general kinematics or by different methods such as integrability.
We consider a double OPE limit of the planar four-point function of stress tensor multiplets in N = 4 SYM theory. Loop integrands for this correlator have been constructed to very high order, but the corresponding integrals are explicitly known only up to three loops. Fortunately, the double coincidence limit of the four-loop integrals can be found by the method of expansion by regions, which reduces the problem of computing the four-point integrals to the evaluation of a large set of massless propagator integrals. These can in turn be evaluated by IBP reduction. The OPE limit of the stress te…
Recently, it was shown that half BPS Supergravity solution of theories with SU(2$|$4) symmetry algebra is given uniformly by determining a single function which obeys three dimensional continuous Toda equation. In this paper, we study the scale invariant solution of Toda equation. Our motivation is that some solutions of half BPS sector of IIB supergravity, as one excepts from the fermion description of the theory, are scale invariant. By defining two auxiliary functions we prove that such solutions of Toda equation obey cubic algebraic equation. We obtain some simpl solutions of Toda equation…
General local half-BPS solutions in M-theory, which have $SO(2,2)\times SO(4)\times SO(4)$ symmetry and are asymptotic to $AdS_{7}\times S^{4}$, were constructed in exact form by the authors in [arXiv:0806.0605]. In the present paper, suitable regularity conditions are imposed on these local solutions, and corresponding globally well-defined solutions are explicitly constructed. The physical properties of these solutions are analyzed, and interpreted in terms of the gravity duals to extended 1+1-dimensional half-BPS defects in the 6-dimensional CFT with maximal supersymmetry.
We establish a correspondence between certain Lie superalgebras with 16 fermionic generators, and half-BPS solutions to supergravities with 32 supersymmetries. Three cases are discussed. For Type IIB supergravity, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of PSU(2,2|4), to families of half-BPS solutions which are invariant under H, and locally asymptotic to AdS_5 x S^5. Similarly, for M-theory, we relate semi-simple Lie superalgebras H with 16 fermionic generators which are subalgebras of OSp(8^*|4) or OSp(8|4,R) to families of half-BPS soluti…
In a recent paper hep-th/0109064, quarter-BPS chiral primaries were constructed in the fully interacting four dimensional N=4 Super-Yang-Mills theory with gauge group SU(N). These operators are annihilated by four supercharges, and at order g^2 have protected scaling dimension and normalization. Here, we compute three-point functions involving these quarter-BPS operators along with half-BPS operators. The combinatorics of the problem is rather involved, and we consider the following special cases: (1) correlators < half half BPS > of two half-BPS primaries with an arbitrary chiral primary; (2)…
Type IIB superstring theory has AdS_3 x S^3 x M_4 (where the manifold M_4 is either K_3 or T^4) solutions which preserve sixteen supersymmetries. In this paper we consider half-BPS solutions which are locally asymptotic to AdS_3 x S^3 x M_4 and preserve eight of the sixteen supersymmetries. We reduce the BPS equations and the Bianchi identity for the self-dual five-form field to a set of four differential equations. The complete local solution can be parameterized in terms of two harmonic and two holomorphic functions and all bosonic fields have explicit expressions in terms of these functions…
We study systematically the BPS spectra of N=2 SYM coupled to half--hypermultiplets, the basic example being E_7 SYM coupled to a half--hyper in the 56 irrepr. In order to do this, we determine the BPS quivers with superpotential of such N=2 models using a new technique we introduce. The computation of the BPS spectra in the various chambers is then reduced to the Representation Theory of the resulting quivers. We use the quiver description to study the BPS spectrum at both strong and weak coupling. The following models are discussed in detail: SU(6) SYM coupled to a half 20, SO(12) SYM couple…
In this paper we probe the typical states of the superstar ensemble of (hep-th/0508023) using half-BPS states of type-IIB string theory on AdS$_5 \times$ S$^5$. We find a very simple universal result that has the structure $\log\, \lag\lag \y \; \y \rag\rag_\calo \approx \a\, h \, \log N$, where $h$ is the conformal weight of the probe $\y$ and $\a$ is a constant that depends mainly of the shape of the probe $\y$. A complete understanding of some properties of this leading term from the dual effective superstar geometry point of view is still lacking.
Half BPS correlators in N=4 super Yang-Mills theory are key quantities both in the AdS/CFT correspondence as well as in scattering amplitudes research. They are dual at strong coupling to quantum gravity amplitudes. At weak coupling on the other hand they contain all N=4 SYM amplitudes. They have been found to possess a number of hidden symmetries, for example non-trivial permutation symmetry of perturbative four-point integrands and a higher dimensional conformal symmetry. Their study has enjoyed continuous progress since the discovery of AdS/CFT and they are now some of the best understood q…
We analyze four- and six-derivative couplings in the low energy effective action of $D=3$ string vacua with half-maximal supersymmetry. In analogy with an earlier proposal for the $(\nablaΦ)^4$ coupling, we propose that the $\nabla^2(\nablaΦ)^4$ coupling is given exactly by a manifestly U-duality invariant genus-two modular integral. In the limit where a circle in the internal torus decompactifies, the $\nabla^2(\nablaΦ)^4$ coupling reduces to the $D^2 F^4$ and $R^2 F^2$ couplings in $D=4$, along with an infinite series of corrections of order $e^{-R}$, from four-dimensional 1/4-BPS dyons whos…
We obtain all planar four-point correlators of half-BPS operators in $\mathcal{N}=4$ SYM up to five loops. The ansatz for the integrand is fixed partially by imposing light-cone OPE relations between different correlators. We then fix the integrated correlators by comparing their asymptotic expansions with simple data obtained from integrability. We extract OPE coefficients and find a prediction for the triple wrapping correction of the hexagon form factors, which contributes already at the five-loop order.
We discuss collective coordinate quantization of the half-BPS geometries of Lin, Lunin and Maldacena (hep-th/0409174). The LLM geometries are parameterized by a single function $u$ on a plane. We treat this function as a collective coordinate. We arrive at the collective coordinate action as well as path integral measure by considering D3 branes in an arbitrary LLM geometry. The resulting functional integral is shown, using known methods (hep-th/9309028), to be the classical limit of a functional integral for free fermions in a harmonic oscillator. The function $u$ gets identified with the cla…
We obtain the planar correlation function of four half-BPS operators of arbitrary weights, up to three loops. Our method exploits only elementary properties of the integrand of the planar correlator, such as its symmetries and singularity structure. This allows us to write down a general ansatz for the integrand. The coefficients in the ansatz are fixed by means of a powerful light-cone OPE relation between correlators with different weights. Our result is formulated in terms of a limited number of functions built from known one-, two- and three-loop conformal integrals. These results are usef…
We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for these correlators and present them in a universal form. We then solve these identities, employing Jack polynomial expansions. We show that the general solution is parameterized by a set of arbitrary two-variable functions, with the exception of the case d=4, where in addition functions of a single variable appear. We also discuss the operator product expansion …
We construct new half-BPS cosmic string solutions in D=4 N=2 supergravity compatible with a consistent truncation to N=1 supergravity where they describe D-term cosmic strings. The constant Fayet-Iliopoulos term in the N=1 D-term is not put in by hand but is geometrically engineered by a gauging in the mother N=2 supergravity theory. The coupling of the N=2 vector multiplets is characterized by a cubic prepotential admitting an axion-dilaton field, a common property of many compactifications of string theory. The axion-dilaton field survives the truncation to N=1 supergravity. On the string co…
The near-horizon geometry of an asymptotically AdS_5 supersymmetric black hole discovered by Gutowski and Reall is analysed. After lifting the solution to 10 dimensions, we explicitly solve the Killing spinor equations in both Poincare and global coordinates. It is found that exactly four supersymmetries are preserved which is twice the number for the full black hole. The full set of isometries is constructed and the isometry supergroup is shown to be SU(1,1|1) X SU(2) X U(3). We further study half-BPS configurations of D3-branes in the near-horizon geometry in Poincare and global coordinates.…
In this note we study half-BPS operators in N=4 super Yang-Mills for gauge group SU(N) at finite N. In particular we elaborate on the results of hep-th/0410236, providing an exact formula for the null basis operators algorithmically constructed there. For gauge groups U(N) and SU(N) we show that this basis is dual to the basis of multi-trace operators with respect to the two point function. We use this to extend the results of hep-th/0611290 concerning factorisation and probabilities from U(N) to SU(N). We also give a construction for a separate diagonal basis of the SU(N) operators in terms o…
The BPS equations in M-theory for solutions with 16 residual supersymmetries, $SO(2,2)\times SO(4)\times SO(4)$ symmetry, and $AdS_4 \times S^7$ asymptotics, were reduced in [arXiv:0806.0605] to a linear first order partial differential equation on a Riemann surface with boundary, subject to a non-trivial quadratic constraint. In the present paper, suitable regularity and boundary conditions are imposed for the existence of global solutions. We seek regular solutions with multiple distinct asymptotic $AdS_4 \times S^7$ regions, but find that, remarkably, such solutions invariably reduce to mul…
We present a survey of the computation of the BPS spectrum of a general four-dimensional N=2 supersymmetric gauge theory in terms of the Representation Theory of quivers with superpotential. We focus on SYM with a general gauge group G coupled to standard matter in arbitrary representations of G (consistent with a non--positive beta--function). The situation is particularly tricky and interesting when the matter consists of an odd number of half-hypermultiplets: we describe in detail SU(6) SYM coupled to half a 20, SO(12) SYM coupled to half a 32, and E_7 SYM coupled to half a 56.
We analyze SU(2) invariant half-BPS states of the 3d \cN=8 or \cN=6 SCFT within the radial quantization of the ABJM theory, the theory proposed to describe N M2-branes in the R^3x C^4/Z_k background. After studying the classical moduli space of these configurations, we explicitly construct a set of gauge invariant operators involving 't Hooft monopole operators corresponding to these states. We show there is a one--to--one correspondence between the two sets carrying R-charge J and that they are labeled by Young tableaux of J boxes with a maximum of N rows. Restricting the full path integral t…
The entropy of a half-BPS black hole in N=4 supersymmetric heterotic string compactification is independent of the details of the charge vector and is a function only of the norm of the charge vector calculated using the appropriate Lorenzian metric. Thus in order for this to agree with the degeneracy of the elementary string states, the latter must also be a function of the same invariant norm. We show that this is true for generic CHL compactifications to all orders in a power series expansion in the inverse charges, but there are exponentially suppressed corrections which do depend on the d…
The tiny graviton matrix theory [hep-th/0406214] is proposed to describe DLCQ of type IIB string theory on the maximally supersymmetric plane-wave or AdS_5xS^5 background. In this paper we provide further evidence in support of the tiny graviton conjecture by focusing on the zero energy, half BPS configurations of this matrix theory and classify all of them. These vacua are generically of the form of various three sphere giant gravitons. We clarify the connection between our solutions and the half BPS configuration in N=4 SYM theory and their gravity duals. Moreover, using our half BPS solutio…
We investigate half-BPS Type IIB supergravity solutions with spacetime geometry $AdS_2\times S^6$ warped over a Riemann surface $Σ$. The general local solution was obtained in earlier work in terms of two holomorphic functions $\mathcal A_\pm$ on $Σ$. In the first part of this paper we seek global solutions corresponding to the near-horizon behavior of $(p,q)$-string junctions. We identify the type of singularity in $\mathcal A_\pm$ needed at the boundary of $Σ$ to match the solutions locally onto the classic $(p,q)$-string solution. We construct solutions with multiple $(p,q)$-strings, but th…
Recently a BPS Alice string has been found in a $U(1)\times SU(2)$ gauge theory coupled with a charged complex adjoint scalar field arXiv:1703.08971. It is a half BPS state preserving a half of supercharges when embedded into a supersymmetric gauge theory. In this paper, we study zero modes of a BPS Alice string. After presenting $U(1)$ and translational zero modes, we construct the effective action of these modes. In contrast to previous analysis of the conventional Alice string for which only large distance behaviors are known, we can perform calculation exactly in the full space thanks to B…
We consider the supergravity backgrounds that correspond to supersymmetric Wilson line operators in the context of AdS/CFT correspondence. We study the gravitino and dilatino conditions of the IIB supergravity under the appropriate ansatz, and obtain some necessary conditions for a supergravity background that preserves the same symmetry as the supersymmetric Wilson lines. The supergravity solutions are characterized by continuous version of maya diagrams. This diagram is related to the eigenvalue distribution of the Gaussian matrix model. We also consider the similar backgrounds of the 11-dim…
We use modern bootstrap techniques to study half-BPS line defects in 4d N=4 superconformal theories. Specifically, we consider the 1d CFT with OSP(4*|4) superconformal symmetry living on such a defect. Our analysis is general and based only on symmetries, it includes however important examples like Wilson and 't Hooft lines in N=4 super Yang-Mills. We present several numerical bounds on OPE coefficients and conformal dimensions. Of particular interest is a numerical island obtained from a mixed correlator bootstrap that seems to imply a unique solution to crossing. The island is obtained if so…
We find a family of (half) self-dual impurity models such that the self-dual (BPS) sector is exactly solvable, for any spatial distribution of the impurity, both in the topologically trivial case and for kink (or antikink) configurations. This allows us to derive the metric on the corresponding one-dimensional moduli space in an analytical form. Also the generalized translational symmetry is found in an exact form. This symmetry provides a motion on moduli space which transforms one BPS solution into another. Finally, we analyse exactly how vibrational properties (spectral modes) of the BPS so…
We consider 1/2-BPS states in AdS/CFT. Using the matrix model description of chiral primaries explicit mappings among configurations of fermions, giant gravitons and the dual-giant gravitons are obtained. These maps lead to a `duality' between the giant and the dual-giant configurations which is the reflection of particle-hole duality of the fermion picture. These dualities give rise to some interesting consequences which we study. We then calculate the degeneracy of 1/2-BPS states both from the CFT and string theory and show that they match. The asymptotic degeneracy grows exponentially with …
We compute form factors of half-BPS operators in N=4 super Yang-Mills dual to massive Kaluza-Klein modes in supergravity. These are appropriate supersymmetrisations T_k of the scalar operators Tr(ϕ^k) for any k, which for k=2 give the chiral part of the stress-tensor multiplet operator. Using harmonic superspace, we derive simple Ward identities for these form factors, which we then compute perturbatively at tree level and one loop. We propose a novel on-shell recursion relation which links form factors with different numbers of fields. Using this, we conjecture a general formula for the n-poi…
The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold $AdS_4 \times S^2 \times S^2 \times Σ$ with $SO(2,3) \times SO(3) \times SO(3)$ symmetry in terms of two holomorphic functions on a Riemann surface $Σ$, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrabl…
Solutions of type IIB supergravity which preserve half of the supersymmetries have a dual description in terms of free fermions, as elucidated by the "bubbling AdS" construction of Lin, Lunin and Maldacena. In this paper we study the half-BPS geometry associated with a gas of free fermions in thermodynamic equilibrium obeying the Fermi-Dirac distribution. We consider both regimes of low and high temperature. In the former case, we present a detailed computation of the ADM mass of the supergravity solution and find agreement with the thermal energy of the fermions. The solution has a naked null…
We construct SO(2,1) x SO(3)-invariant half-BPS solutions in six-dimensional (0,4) supergravity with m tensor multiplets. The space-time manifold of each one of these solutions consists of an AdS_2 x S^2 warped over a Riemann surface Sigma with boundary. The most general local solution is parametrized by one real harmonic function, and m+2 holomorphic functions which are subject to a quadratic constraint and a hermitian inequality, both of which are manifestly SO(2,m) invariant. Imposing suitable conditions on these harmonic and holomorphic functions, we construct globally regular supergravity…
We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in ${\cal N}=4$ super Yang-Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT$_1$ living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS$_5 \times S^5$ ending on the line at the boundary and can be thought of as light fields propagating on the AdS$_2$ worldsheet. We use AdS/CFT techniqu…
We construct local solutions to 11-dimensional supergravity (or M-theory), which are invariant under the superalgebra $D(2, 1; c'; 0)\oplus D(2, 1; c'; 0)$ for all values of the parameter $c'$. The BPS constraints are reduced to a single linear PDE on a complex function $G$. The PDE was solved in 0806.0605 modulo application of boundary and regularity conditions. The physical fields of the solutions are determined by $c'$, a harmonic function $h$, and the complex function $G$. $ h$ and $G$ are both functions on a 2-dimensional compact Riemannian manifold. The harmonic function $ h$ is freely c…
Half-BPS Boundaries and the RG-Wall of $\mathcal{N}=2$ $SU(N)$ SYM
Abdus Salam Centre for Theoretical Physics, Imperial College London（阿卜杜斯·萨拉姆理论物理中心，伦敦帝国理工学院）；INFN, Sezione di Trieste（意大利国家核物理研究所，的里雅斯特分部）；SISSA（的里雅斯特高等研究学院）
Fermion zero modes for abelian BPS monopoles are considered. In the spherically symmetric case the normalisable zero modes are determined for arbitrary monopole charge N. If N>1 the zero modes are zero along $N-1$ half-lines emanating from the monopole.
We show that the BPS property is a generic feature of field theories in (1+1) dimensions, which does not put any restriction on the action. Here, by BPS solutions we understand static solutions which i) obey a lower-order Bogomolny-type equation in addition to the Euler-Lagrange equation, ii) have an energy which only depends on a topological charge and the global properties of the fields, but not on the local behaviour (coordinate dependence) of the solution, and iii) have zero pressure density. Concretely, to accomplish this program we study the existence of BPS solutions in field theories w…
We classify Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 which are at least half BPS; equivalently, smooth quotients of the round 7-sphere by finite subgroups of SO(8) which admit an (N>3)-dimensional subspace of Killing spinors. The classification is given in terms of pairs consisting of an ADE subgroup of SU(2) and an automorphism defining its embedding in SO(8). In particular we find novel half-BPS quotients associated with the subgroups of type D_n (for n>5), E_7 and E_8 and their outer automorphisms.
We compute correlation functions of protected primaries on the $1/2$-BPS Wilson loop in ${\cal N}$ = 4 super Yang-Mills theory at weak coupling. We first perform direct perturbative computation at one loop in the planar limit and present explicit formulae for general two-, three- and four-point functions. The results for two- and three-point functions as well as four-point functions in special kinematics are in perfect agreement with the localization computation performed in arXiv:1802.05201. We then analyze the results in view of the integrability-based approach called "hexagonalization", whi…
We explicitly construct the fully back-reacted half-BPS solutions in Type IIB supergravity which are dual to Wilson loops with 16 supersymmetries in $\mathcal{N}=4$ super Yang-Mills. In a first part, we use the methods of a companion paper to derive the exact general solution of the half-BPS equations on the space $AdS_2 \times S^2 \times S^4 \times Σ$, with isometry group $SO(2,1)\times SO(3) \times SO(5)$ in terms of two locally harmonic functions on a Riemann surface $Σ$ with boundary. These solutions, generally, have varying dilaton and axion, and non-vanishing 3-form fluxes. In a second p…
The two-loop four-point amplitude of two massless SU(N) colored scalars and two color singlet operators with different virtuality described by a half-BPS and Konishi operators is calculated analytically in maximally supersymmetric Yang-Mills theory. We verify the ultraviolet behaviour of the unprotected composite operator and exponentiation of the infrared divergences with correct universal values of the anomalous dimensions in the modified dimensional reduction scheme. The amplitude is found to contain lower transcendental weight terms in addition to the highest ones and the latter has no sim…
We prove that the half-BPS Wilson loop operator of N=4 SYM in a symmetric representation of the gauge group has a bulk gravitational description in terms of a single D3-brane in AdS_5xS^5, as argued in hep-th/0604007. We also show that a half-BPS Wilson loop operator in an arbitrary representation is described by the D3-brane configuration proposed in hep-th/0604007. This is demonstrated by explicitly integrating out the degrees of freedom on the D3-branes and showing that they insert a half-BPS Wilson loop operator into the N=4 SYM path integral in the desired representation.
