arXiv subjects

Marius de Leeuw

Publications and source records attributed to Marius de Leeuw.

At least 55 records · Page 3Linked to original sources

arXiv2017

One-loop Wilson loops and the particle-interface potential in AdS/dCFT

We initiate the calculation of quantum corrections to Wilson loops in a class of four-dimensional defect conformal field theories with vacuum expectation values based on N=4 super Yang-Mills theory. Concretely, we consider an infinite straight Wilson line, obtaining explicit results for the one-loop correction to its expectation value in the large-N limit. This allows us to extract the particle-interface potential of the theory. In a further double-scaling limit, we compare our results to those of a previous calculation in the dual string-theory set-up consisting of a D5-D3 probe-brane system with flux, and we find perfect agreement.

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arXiv2017

A Quantum Check of AdS/dCFT

We build the framework for performing loop computations in the defect version of N=4 super Yang-Mills theory which is dual to the probe D5-D3 brane system with background gauge-field flux. In this dCFT, a codimension-one defect separates two regions of space-time with different ranks of the gauge group and three of the scalar fields acquire non-vanishing and space-time-dependent vacuum expectation values. The latter leads to a highly non-trivial mass mixing problem between different colour and flavour components, which we solve using fuzzy-sphere coordinates. Furthermore, the resulting space-time dependence of the theory's Minkowski space propagators is handled by reformulating these as propagators in an effective AdS4. Subsequently, we initiate the computation of quantum corrections. The one-loop correction to the one-point function of any local gauge-invariant scalar operator is shown to receive contributions from only two Feynman diagrams. We regulate these diagrams using dimensional reduction, finding that one of the two diagrams vanishes, and discuss the procedure for calculating the one-point function of a generic operator from the SU(2) subsector. Finally, we explicitly evaluate the one-loop correction to the one-point function of the BPS vacuum state, finding perfect agreement with an earlier string-theory prediction. This constitutes a highly non-trivial test of the gauge-gravity duality in a situation where both supersymmetry and conformal symmetry are partially broken.

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arXiv2016

One-loop one-point functions in gauge-gravity dualities with defects

We initiate the calculation of loop corrections to correlation functions in 4D defect CFTs. More precisely, we consider N=4 SYM with a codimension-one defect separating two regions of space, x_3>0 and x_3<0, where the gauge group is SU(N) and SU(N-k), respectively. This set-up is made possible by some of the real scalar fields acquiring a non-vanishing and x_3-dependent vacuum expectation value for x_3>0. The holographic dual is the D3-D5 probe brane system where the D5 brane geometry is AdS_4 x S^2 and a background gauge field has k units of flux through the S^2. We diagonalise the mass matrix of the defect CFT making use of fuzzy-sphere coordinates and we handle the x_3-dependence of the mass terms in the 4D Minkowski space propagators by reformulating these as standard massive AdS_4 propagators. Furthermore, we show that only two Feynman diagrams contribute to the one-loop correction to the one-point function of any single-trace operator and we explicitly calculate this correction in the planar limit for the simplest chiral primary. The result of this calculation is compared to an earlier string-theory computation in a certain double-scaling limit, finding perfect agreement. Finally, we discuss how to generalise our calculation to any single-trace operator, to finite N and to other types of observables such as Wilson loops.

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arXiv2016

AdS/dCFT one-point functions of the SU(3) sector

We propose a closed formula for the tree-level one-point functions of non-protected operators belonging to an SU(3) sub-sector of the defect CFT dual to the D3-D5 probe brane system with background gauge field flux, k, valid for k=2. The formula passes a number of non-trivial analytical and numerical tests. Our proposal is based on expressing the one-point functions as an overlap between a Bethe eigenstate of the SU(3) spin chain and a certain matrix product state, deriving various factorization properties of the Gaudin norm and performing explicit computations for shorter spin chains. As its SU(2) counterpart, the one-point function formula for the SU(3) sub-sector is of determinant type. We discuss the the differences with the SU(2) case and the challenges in extending the present formula beyond k=2.

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arXiv2016

Maximally extended sl(2|2) as a quantum double

We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(2|2) using Drinfeld's quantum double construction. We are led to enlarging the algebra by additional generators corresponding to an sl(2) automorphism. For this maximally extended algebra we construct a consistent Hopf algebra structure where the extensions exhibit several uncommon features. We determine the corresponding universal R-matrix containing some non-standard functions. Curiously, this Hopf algebra has one extra deformation parameter for which the R-matrix does not factorize into products of exponentials.

math-ph↗

arXiv2015

One-point Functions in AdS/dCFT from Matrix Product States

One-point functions of certain non-protected scalar operators in the defect CFT dual to the D3-D5 probe brane system with k units of world volume flux can be expressed as overlaps between Bethe eigenstates of the Heisenberg spin chain and a matrix product state. We present a closed expression of determinant form for these one-point functions, valid for any value of k. The determinant formula factorizes into the k=2 result times a k-dependent prefactor. Making use of the transfer matrix of the Heisenberg spin chain we recursively relate the matrix product state for higher even and odd k to the matrix product state for k=2 and k=3 respectively. We furthermore find evidence that the matrix product states for k=2 and k=3 are related via a ratio of Baxter's Q-operators. The general k formula has an interesting thermodynamical limit involving a non-trivial scaling of k, which indicates that the match between string and field theory one-point functions found for chiral primaries might be tested for non-protected operators as well. We revisit the string computation for chiral primaries and discuss how it can be extended to non-protected operators.

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arXiv2015

An algebraic approach to the Hubbard model

We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.

math-ph↗

arXiv2015

One-point Functions in Defect CFT and Integrability

We calculate planar tree level one-point functions of non-protected operators in the defect conformal field theory dual to the D3-D5 brane system with k units of the world volume flux. Working in the operator basis of Bethe eigenstates of the Heisenberg XXX_{1/2} spin chain we express the one-point functions as overlaps of these eigenstates with a matrix product state. For k=2 we obtain a closed expression of determinant form for any number of excitations, and in the case of half-filling we find a relation with the Néel state. In addition, we present a number of results for the limiting case of infinite k.

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arXiv2015

Fusion for the one-dimensional Hubbard model

We discuss a formulation of the fusion procedure for integrable models which is suitable for application to non-standard R-matrices. It allows for construction of bound state R-matrices for AdS/CFT worldsheet scattering or equivalently for the one-dimensional Hubbard model. We also discuss some peculiar cases that arise in these models.

math-ph↗

arXiv2014

Factorized soft graviton theorems at loop level

We analyze the low-energy behavior of scattering amplitudes involving gravitons at loop level in four dimensions. The single-graviton soft limit is controlled by soft operators which have been argued to separate into a factorized piece and a non-factorizing infrared divergent contribution. In this note we show that the soft operators responsible for the factorized contributions are strongly constrained by gauge and Poincare invariance under the assumption of a local structure. We show that the leading and subleading orders in the soft-momentum expansion can not receive radiative corrections. The first radiative correction occurs for the sub-subleading soft graviton operator and is one-loop exact. It depends on only two undetermined coefficients which should reflect the field content of the theory under consideration.

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arXiv2014

A dictionary between R-operators, on-shell graphs and Yangian algebras

We translate between different formulations of Yangian invariants relevant for the computation of tree-level scattering amplitudes in N=4 super-Yang--Mills theory. While the R-operator formulation allows to relate scattering amplitudes to structures well known from integrability, it can equally well be connected to the permutations encoded by on-shell graphs.

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arXiv2014

Constraining subleading soft gluon and graviton theorems

We show that the form of the recently proposed subleading soft graviton and gluon theorems in any dimension are severely constrained by elementary arguments based on Poincaré and gauge invariance as well as a self-consistency condition arising from the distributional nature of scattering amplitudes. Combined with the assumption of a local form as it would arise from a Ward identity the orbital part of the subleading operators is completely fixed by the leading universal Weinberg soft pole behavior. The polarization part of the differential subleading soft operators in turn is determined up to a single numerical factor for each hard leg at every order in the soft momentum expansion. In four dimensions, factorization of the Lorentz group allows to fix the subleading operators completely.

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arXiv2014

Deformed one-loop amplitudes in N = 4 super-Yang-Mills theory

We investigate Yangian-invariant deformations of one-loop amplitudes in N = 4 super-Yang-Mills theory employing an algebraic representation of amplitudes. In this language, we reproduce the deformed massless box integral describing the deformed four-point one-loop amplitude and compare different realizations of said amplitude.

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arXiv2014

On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring

We discuss the spectrum of a string propagating on eta-deformed AdS_5 x S^5 by treating its world-sheet theory as an integrable quantum field theory. The exact S-matrix of this field theory is given by a q-deformation of the AdS_5 x S^5 world-sheet S-matrix with real deformation parameter. By considering mirror (double Wick-rotated) versions of these world-sheet theories we give the Thermodynamic Bethe Ansatz description of their exact finite size spectra. Interestingly, this class of models maps onto itself under the mirror transformation. At the level of the string this appears to say that the light-cone worldsheet theories of strings on particular pairs of backgrounds are related by a double Wick rotation, a feature we call 'mirror duality'. We provide a partial check of these statements at the level of the sigma model by considering reduced actions and their corresponding (mirror) giant magnon solutions.

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arXiv2013

Integrable Deformations of the XXZ Spin Chain

We consider integrable deformations of the XXZ spin chain for periodic and open boundary conditions. In particular, we classify all long-range deformations and study their impact on the spectrum. As compared to the XXX case, we have the z-spin at our disposal, which induces two additional deformations: the short-range magnetic twist and a new long-range momentum-dependent twist.

math-ph↗

arXiv2013

Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane

We consider the worldsheet boundary scattering and the corresponding boundary algebras for the Z=0 giant graviton and the Z=0 D7-brane in the AdS/CFT correspondence. We consider two approaches to the boundary scattering, the usual one governed by the (generalized) twisted Yangians and the q-deformed model of these boundaries governed by the quantum affine coideal subalgebras. We show that the q-deformed approach leads to boundary algebras that are of a more compact form than the corresponding twisted Yangians, and thus are favourable to use for explicit calculations. We obtain the q-deformed reflection matrices for both boundaries which in the q->1 limit specialize to the ones obtained using twisted Yangians.

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arXiv2013

The Quantum Deformed Mirror TBA II

We discuss the description of generic excited states in the quantum deformed AdS_5 x S^5 mirror thermodynamic Bethe ansatz and derive the associated Y-system. This Y-system shows an interesting new feature; it depends explicitly on the excited state under consideration. Similarly, it also depends on twisted boundary conditions. We construct the asymptotic solution of these TBA and Y-system equations by deriving the twisted transfer matrix for the quantum deformed Hubbard model and finding the deformed mirror bound state dressing phase. This asymptotic construction is insensitive to the precise nature of the deformation, and thereby provides a nontrivial check of the interesting new features which arise precisely at roots of unity.

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arXiv2012

The Quantum Deformed Mirror TBA I

We derive the ground state thermodynamic Bethe ansatz equations for the quantum deformation of the AdS_5 x S^5 mirror model, taking the deformation parameter to be a root of unity. By virtue of the deformation, the resulting equations show an interesting structure between a finite number of Y-functions.

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