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Charlotte Kristjansen

Publications and source records attributed to Charlotte Kristjansen.

At least 37 records · Page 2Linked to original sources
arXiv2019

A non-integrable quench from AdS/dCFT

We study the matrix product state which appears as the boundary state of the AdS/dCFT set-up where a probe D7 brane wraps two two-spheres stabilized by fluxes. The matrix product state plays a dual role, on one hand acting as a tool for computing one-point functions in a domain wall version of N=4 SYM and on the other hand acting as the initial state in the study of quantum quenches of the Heisenberg spin chain. We derive a number of selection rules for the overlaps between the matrix product state and the eigenstates of the Heisenberg spin chain and in particular demonstrate that the matrix product state does not fulfill a recently proposed integrability criterion. Accordingly, we find that the overlaps can not be expressed in the usual factorized determinant form. Nevertheless, we derive some exact results for one-point functions of simple operators and present a closed formula for one-point functions of more general operators in the limit of large spin-chain length.

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arXiv2019

A Quantum Check of Non-Supersymmetric AdS/dCFT

Via a challenging field-theory computation, we confirm a supergravity prediction for the non-supersymmetric D3-D7 probe-brane system with probe geometry AdS_4 x S^2 x S^2, stabilized by fluxes. Supergravity predicts, in a certain double-scaling limit, the value of the one-point functions of chiral primaries of the dual defect version of N=4 SYM theory, where the fluxes translate into SO(3) x SO(3)-symmetric, Lie-algebra-valued vacuum expectation values for all six scalar fields. Using a generalization of the technique based on fuzzy spherical harmonics developed for the related D3-D5 probe-brane system, we diagonalize the resulting mass matrix of the field theory. Subsequently, we calculate the planar one-loop correction to the vacuum expectation values of the scalars in dimensional reduction and find that it is UV finite and non-vanishing. We then proceed to calculating the one-loop correction to the planar one-point function of any single-trace scalar operator and explicitly evaluate this correction for a 1/2-BPS operator of length L at two leading orders in the double-scaling limit, finding exact agreement with the supergravity prediction.

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arXiv2018

One-Point Functions of Non-protected Operators in the SO(5) symmetric D3-D7 dCFT

We study tree level one-point functions of non-protected scalar operators in the defect CFT, based on N=4 SYM, which is dual to the SO(5) symmetric D3-D7 probe brane system with non-vanishing instanton number. Whereas symmetries prevent operators from the SU(2) and SU(3) sub-sectors from having non-vanishing one-point functions, more general scalar conformal operators, which in particular constitute Bethe eigenstates of the integrable SO(6) spin chain, are allowed to have non-trivial one-point functions. For a series of operators with a small number of excitations we find closed expressions in terms of Bethe roots for these one-point functions, valid for any value of the instanton number. In addition, we present some numerical results for operators with more excitations.

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arXiv2018

Scalar one-point functions and matrix product states of AdS/dCFT

We determine in a closed form all scalar one-point functions of the defect CFT dual to the D3-D5 probe brane system with k units of flux which amounts to calculating the overlap between a Bethe eigenstate of the integrable SO(6) spin chain and a certain matrix product state of bond dimension k. In particular, we show that the matrix product state is annihilated by all the parity odd charges of the spin chain which has recently been suggested as the criterion for such a state to correspond to an integrable initial state. Finally, we discuss the properties of the analogous matrix product state for the SO(5) symmetric D3-D7 probe brane set-up.

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arXiv2017

Asymptotic one-point functions in AdS/dCFT

We take the first step in extending the integrability approach to one-point functions in AdS/dCFT to higher loop orders. More precisely, we argue that the formula encoding all tree-level one-point functions of SU(2) operators in the defect version of N=4 SYM theory, dual to the D5-D3 probe-brane system with flux, has a natural asymptotic generalization to higher loop orders. The asymptotic formula correctly encodes the information about the one-loop correction to the one-point functions of non-protected operators once dressed by a simple flux-dependent factor, as we demonstrate by an explicit computation involving a novel object denoted as an amputated matrix product state. Furthermore, when applied to the BMN vacuum state, the asymptotic formula gives a result for the one-point function which in a certain double-scaling limit agrees with that obtained in the dual string theory up to wrapping order.

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arXiv2017

Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations

We calculate the leading contributions to the connected two-point functions of protected scalar operators in the defect version of N=4 SYM theory which is dual to the D5-D3 probe-brane system with k units of background gauge field flux. This involves several types of two-point functions which are vanishing in the theory without the defect, such as two-point functions of operators of unequal conformal dimension. We furthermore exploit the operator product expansion (OPE) and the boundary operator expansion (BOE), which form the basis of the boundary conformal bootstrap equations, to extract conformal data both about the defect CFT and about N=4 SYM theory without the defect. From the knowledge of the one- and two-point functions of the defect theory, we extract certain structure constants of N=4 SYM theory using the (bulk) OPE and constrain certain bulk-bulk-to-boundary couplings using the BOE. The extraction of the former relies on a non-trivial, polynomial k dependence of the one-point functions, which we explicitly demonstrate. In addition, it requires the knowledge of the one-point functions of SU$(2)$ descendant operators, which we likewise explicitly determine.

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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

The D3-probe-D7 brane holographic fractional topological insulator

The D3-probe-D7 brane system, oriented so as to have 2+1-dimensional Poincare symmetry, is argued to be the holographic representation of a strongly correlated fractional topological insulator which exhibits a zero-field quantized Hall effect with half-units of Hall conductivity. The phase diagram of the system with charge density and external magnetic field is found and, as well as charge gapped quantum Hall states, it exhibits metallic and semi-metallic phases with interesting behaviours. The relationship of this to other models of fractional topological insulators is discussed.

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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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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

On the Regularization of Extremal Three-point Functions Involving Giant Gravitons

In the AdS_5/CFT_4 set-up, extremal three-point functions involving two giant 1/2 BPS gravitons and one point-like 1/2 BPS graviton, when calculated using semi-classical string theory methods, match the corresponding three-point functions obtained in the tree-level gauge theory. The string theory computation relies on a certain regularization procedure whose justification is based on the match between gauge and string theory. We revisit the regularization procedure and reformulate it in a way which allows a generalization to the ABJM set-up where three-point functions of 1/2 BPS operators are not protected and where a match between tree-level gauge theory and semi-classical string theory is hence not expected.

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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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arXiv2013

Giant D5 Brane Holographic Hall State

We find a new holographic description of strongly coupled defect field theories using probe D5 branes. We consider a system where a large number of probe branes, which are asymptotically D5 branes, blow up into a D7 brane suspended in the bulk of anti-de Sitter space. For a particular ratio of charge density to external magnetic field, so that the Landau level filling fraction per color is equal to one, the D7 brane exhibits an incompressible charge-gapped state with one unit of integer quantized Hall conductivity. The detailed configuration as well as ungapped, compressible configurations for a range of parameters near the gapped one are found by solving the D5 and D7 brane embedding equations numerically and the D7 is shown to be preferred over the D5 by comparing their energies. We then find integer quantum Hall states with higher filling fractions as a stack of D5 branes which blow up to multiple D7 branes where each D7 brane has filling fraction one. We find indications that the n D7 branes describing the filling fraction n state are coincident with a residual SU(n) symmetry when n is a divisor of the total number of D5 branes. We examine the issue of stability of the larger filling fraction Hall states. We argue that, in the D7 brane phase, chiral symmetry restoration could be a first order phase transition.

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arXiv2013

On Three-point Functions in the AdS_4/CFT_3 Correspondence

We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we generalize the determinant representation, found by Foda for the three-point functions of the SU(2) sector of N=4 SYM, to the present case and find that the ABJM result up to normalization factors factorizes into a product of two N=4 SYM correlation functions. Secondly, we treat the case where two operators are heavy and one is light and BPS, using a coherent state description of the heavy ones. We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.

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arXiv2012

Chiral primary one-point functions in the D3-D7 defect conformal field theory

We compute the one-point functions of chiral primary operators in the non-supersymmetric defect conformal field theory that is dual to the IIB string theory on $AdS_5\times S^5$ background with a probe D7 brane with internal gauge field flux, both in perturbative Yang-Mills theory and in the string theory dual. The former is expected to be accurate at weak coupling whereas the latter should be accurate in the planar strong coupling limit of the gauge theory. We consider the distinct cases where the D7 brane has geometry $AdS_4\times S^4$ with an instanton bundle of the worldvolume gauge fields on $S^4$ and $AdS_4\times S^2\times S^2$ with Dirac monopole bundles on each $S^2$. The gauge theory computation and the string theory computation can be compared directly in the planar limit and then a subsequent limit where the worldvolume flux is large. We find that there is exact agreement between the two in the leading order.

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