One-point functions in defect CFT and integrability

Leeuw, Marius de; Kristjansen, Charlotte; Zarembo, Konstantin

doi:10.1007/jhep08(2015)098

Cited by 127 publications

(299 citation statements)

References 71 publications

(119 reference statements)

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“…The approach championed in the original papers [6][7][8][9] is that the superconformal 2 A class of 1 2 -BPS interfaces in N = 4 SYM were constructed in [25]. In the context of integrability, there have been perturbative calculations of one-point functions in this setup, see [26][27][28][29] and references therein. Defect CFTs have also been studied from the point of view of holography, see [30][31][32][33] and references thereafter.…”

Section: Jhep01(2017)122mentioning

confidence: 99%

Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

Liendo

Meneghelli

2017

J. High Energ. Phys.

123

174

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This paper focuses on the analysis of 4d N = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is a boundary that preserves half of the supersymmetry. After studying the constraints imposed by supersymmetry, we will obtain the Ward identities associated to two-point functions of 1 2 -BPS operators and write their solution as a superconformal block expansion. Due to a surprising connection between spacetime and R-symmetry conformal blocks, our results not only apply to 4d N = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4d N = 4 superconformal theories with a line defect, 3d N = 4 superconformal theories with no defect, and OSP(4 * |4) superconformal quantum mechanics. The superconformal algebra implies that all these systems possess a closed subsector of operators in which the bootstrap equations become polynomial constraints on the CFT data. We derive these truncated equations and initiate the study of their solutions.

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Section: Jhep01(2017)122mentioning

confidence: 99%

Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

Liendo

Meneghelli

2017

J. High Energ. Phys.

123

174

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“…In the present paper we continue our study [6] of the one-point functions in the defect CFT resulting from this semiclassical description. We also do some rudimentary analysis on the strong-coupling side of the AdS/CFT duality.…”

Section: Jhep02(2016)052mentioning

confidence: 99%

“…It maps to an SU(2) operator built of L − M fields of type Z and M fields of type W . As pointed out in [6] one can implement the transformation (2.4) for a given Bethe eigenstate by taking the inner product of the state with a matrix product state, defined as…”

Section: Jhep02(2016)052mentioning

confidence: 99%

“…Conformal operators belonging to this SU(2) sub-sector are known to be expressible as Bethe eigenstates of the Heisenberg XXX 1/2 spin chain of length L in the sector with L − M spins up and M spins down. Each operator is characterized by a set of M Bethe roots and, as shown in [6], only parity-symmetric operators with paired rapidities {u j , −u j } M/2 j=1 and even length, L, can have non-trivial one-point functions at tree level. The one-point functions are constrained by conformal symmetry to take the form…”

Section: Jhep02(2016)052mentioning

confidence: 99%

“…The brane intersection introduces a domain wall that separates the vacua with respectively unbroken SU(N ) and SU(N − k) gauge symmetry in the N = 4 supersymmetric Yang-Mills (SYM) theory, with additional degrees of freedom living on the defect [2,3]. One-point functions in this dCFT were studied in [2,[4][5][6] whereas two-point functions of defect operators were considered in [2,[7][8][9][10][11], where integrability of the underlying N = 4 SYM proved particularly useful. The defect operators are mapped to spin chains with open boundary conditions and are dual to open strings attached to the probe D5-brane.…”

Section: Introductionmentioning

confidence: 99%

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One-point functions in AdS/dCFT from matrix product states

Buhl-Mortensen

Leeuw

Kristjansen

et al. 2016

J. High Energ. Phys.

Self Cite

104

172

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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 pre-factor. 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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Defects in Conformal Field Theories

Lauria¹

2019

Springer Theses

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One-point functions in defect CFT and integrability

Cited by 127 publications

References 71 publications

Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

One-point functions in AdS/dCFT from matrix product states

Defects in Conformal Field Theories

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