arXiv subjects

Charlotte Kristjansen

Publications and source records attributed to Charlotte Kristjansen.

At least 19 recordsLinked to original sources

arXiv2026

Monodromy defects in ABJM theory and integrability

We establish that supersymmetric monodromy defects in ABJM theory, also known as vortex loops, define integrable boundary states of the underlying alternating SU(4) spin chain. Exploiting the KT relation within the framework of the algebraic Bethe ansatz, we derive a closed-form expression for the leading-order one-point functions of non- protected operators in the presence of these defects. As a special case, our result reproduces the spin-chain overlap governing the three-point functions of two maximal giant gravitons and a single tiny graviton. We furthermore investigate the quantization of the theory in the defect background and compute the first quantum correction to the one-point functions in the simplest setting. Finally, we discuss possible extensions of our overlap formula.

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arXiv2026

Black Hole States in Quantum Spin Chains

We define a black hole state in a spin chain by studying thermal correlators in holography. Focusing on the Heisenberg model we investigate the thermal and complexity properties of the black hole state by evaluating its entanglement entropy, emptiness formation probability and Krylov complexity. The entanglement entropy grows logarithmically with effective central charge c=5.2. We find evidence for thermalization at infinite temperature.

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arXiv2025

Integrable Corners in the Space of Gukov-Witten Surface Defects

We investigate integrability properties of Gukov-Witten 1/2-BPS surface defects in $SU(N)$ $\mathcal{N}=4$ super-Yang-Mills (SYM) theory in the large-$N$ limit. We demonstrate that ordinary Gukov-Witten defects, which depend on a set of continuous parameters, are not integrable except for special sub-sectors. In contrast to these, we show that rigid Gukov-Witten defects, which depend on a discrete parameter but not on continuous ones, appear integrable in a corner of the discrete parameter space. Whenever we find an integrable sector, we derive a closed-form factorised expression for the leading-order one-point function of unprotected operators built out of the adjoint scalars of $\mathcal{N}=4$ SYM theory. Our results raise the possibility of finding an all-loop formula for one-point functions of unprotected operators in the presence of a rigid Gukov-Witten defect at the corner in parameter space.

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arXiv2025

The spectrum of defect ABJM theory

We determine the spectrum of quantum fluctuations in a 1/2-BPS domain wall version of ABJM theory, thereby enabling the perturbative exploration of the corresponding defect CFT. As expected, the spectrum reflects the supersymmetry of the model.

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arXiv2025

't Hooft loops in N=4 super-Yang-Mills

We set up a perturbative framework for the 't Hooft line in the N=4 super-Yang-Mills theory, and apply it to correlators thereof with Wilson loops and local operators. Using this formalism we obtain a number of perturbative and non-perturbative results that directly connect to localization, holography and integrability.

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arXiv2025

On exact overlaps of integrable matrix product states: inhomogeneities, twists and dressing formulas

Invoking a quantum dressing procedure as well as the representation theory of twisted Yangians we derive a number of summation formulas for the overlap between integrable matrix product states and Bethe eigenstates which involve only eigenvalues of fused transfer matrices and which are valid in the presence of inhomogeneities as well as twists. Although the method is general we specialize to the $SO(6)$ spin chain for which integrable matrix product states corresponding to evaluation representations of the twisted Yangian $Y^+(4)$ encode the information about one-point functions of the D3-D5 domain wall version of ${\cal N}=4$ SYM. Considering the untwisted and homogeneous limit of our summation formulas we finally fill the last gap in the analytical understanding of the overlap formula for the $SO(6$) sector of the D3-D5 domain wall system.

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arXiv2024

Integrable Holographic Defect CFTs

We review a class of integrable, supersymmetric defect conformal field theories which have holographic duals in the form of probe brane models. Our main examples are defect versions of N=4 SYM and ABJM theory, both involving a domain wall with Nahm pole boundary conditions, and the case of a 't Hooft line embedded in N=4 SYM. The field theory defect respectively the probe D-brane can be described as an integrable boundary state of the integrable system underlying the AdS/CFT correspondence.

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arXiv2024

Superconformal Two-Point Functions of the Nahm Pole Defect in $\mathcal{N}=4$ Super-Yang-Mills Theory

We derive a manifestly superconformal expression for the leading-order two-point functions of all single trace chiral primary operators in 4d $\mathcal{N}=4$ super-Yang-Mills theory with a co-dimension one Nahm pole defect. Notably, our result involves only a finite number of superblocks that correspond to 1/2-BPS representations in the defect channel. The derivation builds on a non-trivial exact result for traces of fuzzy spherical harmonics in combination with powers of $\mathfrak{su}(2)$ generators, which leads to a remarkably compact expression for the bulk-to-defect couplings. Apart from being interesting in its own right as a closed-form expression at finite $N$, the final result is an essential prerequisite for applying the defect superconformal bootstrap programme to this model.

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arXiv2023

't Hooft loops and integrability

We consider the defect CFT defined by a 't Hooft line embedded in N=4 super Yang-Mills theory. By explicitly quantizing around the given background we exactly reproduce a prediction from S-duality for the correlators between the 't Hooft line and chiral primaries in the bulk and pave the way for higher loop analyses for non-protected operators. Furthermore, we demonstrate at the leading perturbative order that correlators between the 't Hooft line and non-protected bulk operators can be efficiently computed using integrability. As a byproduct we find new integrable overlaps in sl(2) spin chains in different representations.

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arXiv2023

B-type anomaly coefficients for the D3-D5 domain wall

We compute type-B Weyl anomaly coefficients for the domain wall version of N = 4 SYM that is holographically dual to the D3-D5 probe-brane system with flux. Our starting point is the explicit expression for the improved energy momentum tensor of N = 4 SYM. We determine the two-point function of this operator in the presence of the domain wall and extract the anomaly coefficients from the result. In the same process we determine the two-point function of the displacement operator.

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arXiv2022

Spin Chain Overlaps and the Twisted Yangian

Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the $SO(6)$ spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of $\mathfrak{so}(5)$. The latter play the role of boundary states in a domain wall version of ${\cal N}=4$ SYM theory which has non-vanishing, $SO(5)$ symmetric vacuum expectation values on one side of a co-dimension one wall. This theory, which constitutes a defect CFT, is known to be dual to a D3-D7 probe brane system. We likewise show that the same methodology makes it possible to prove an overlap formula, earlier presented without proof, which is of relevance for the similar D3-D5 probe brane system.

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arXiv2022

Overlaps for Matrix Product States of Arbitrary Bond Dimension in ABJM theory

We find a closed formula for the overlap of Bethe eigenstates of an alternating $SU(4)$ spin chain, describing the scalar sector of ABJM theory, and matrix product states of any bond dimension representing 1/2 BPS co-dimension one domain walls in the field theory. One point functions of the defect CFTs involved, being directly expressible in terms of these overlaps, are hence completely determined.

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arXiv2022

Integrable domain walls in ABJM theory

One-point functions of local operators are studied, at weak and strong coupling, for the ABJM theory in the presence of a 1/2 BPS domain wall. In the underlying quantum spin chain the domain wall is represented by a boundary state which we show is integrable yielding a compact determinant formula for one-point functions of generic operators.

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arXiv2021

Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT

The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a universal formula in the case of overlaps between Bethe eigenstates and integrable boundary states, of relevance for AdS/dCFT, by determining the transformation properties of the overlaps under fermionic as well as bosonic dualities which allows us to move between any two descriptions of the spin chain encoded in the QQ-system. An important part of our analysis involves introducing a suitable regularization for singular Bethe root configurations.

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arXiv2021

Overlaps and Fermionic Dualities for Integrable Super Spin Chains

The psu(2,2|4) integrable super spin chain underlying the AdS/CFT correspondence has integrable boundary states which describe set-ups where k D3-branes get dissolved in a probe D5-brane. Overlaps between Bethe eigenstates and these boundary states encode the one-point functions of conformal operators and are expressed in terms of the superdeterminant of the Gaudin matrix that in turn depends on the Dynkin diagram of the symmetry algebra. The different possible Dynkin diagrams of super Lie algebras are related via fermionic dualities and we determine how overlap formulae transform under these dualities. As an application we show how to consistently move between overlap formulae obtained for k=1 from different Dynkin diagrams.

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arXiv2020

Wilson lines in AdS/dCFT

We consider the expectation value of Wilson lines in two defect versions of N = 4 SYM, both with supersymmetry completely broken, where one is described in terms of an integrable boundary state, the other one not. For both cases, imposing a certain double scaling limit, we find agreement to two leading orders between the expectation values calculated from respectively the field theory and the string theory side of the AdS/dCFT correspondence.

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arXiv2020

Integrable boundary states in D3-D5 dCFT: beyond scalars

A D3-D5 intersection gives rise to a defect CFT, wherein the rank of the gauge group jumps by k units across a domain wall. The one-point functions of local operators in this set-up map to overlaps between on-shell Bethe states in the underlying spin chain and a boundary state representing the D5 brane. Focussing on the k=1 case, we extend the construction to gluonic and fermionic sectors, which was prohibitively difficult to achieve for k>1. As a byproduct, we test an all-loop proposal for the one-point functions in the su(2) sector at the half-wrapping order of perturbation theory.

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arXiv2019

A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on $S^4$

We consider a non-supersymmetric domain-wall version of $\mathcal{N} = 4$ SYM theory where five out of the six scalar fields have non-zero classical values on one side of a wall of codimension one. The classical fields have commutators which constitute an irreducible representation of the Lie algebra $\mathfrak{so}(5)$ leading to a highly non-trivial mixing between color and flavor components of the quantum fields. Making use of fuzzy spherical harmonics on $S^4$, we explicitly solve the mixing problem and derive not only the spectrum of excitations at the quantum level but also the propagators of the original fields needed for perturbative quantum computations. As an application, we derive the one-loop one-point function of a chiral primary and find complete agreement with a supergravity prediction of the same quantity in a double-scaling limit which involves a limit of large instanton number in the dual D3-D7 probe-brane setup.

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