Exact solution of a boundary conformal field theory

Curtis G. Callan; Igor R. Klebanov; Andreas W.W. Ludwig; Juan M. Maldacena

doi:10.1016/0550-3213(94)90440-5

Exact solution of a boundary conformal field theory

Curtis G. Callan, Igor R. Klebanov, Andreas W.W. Ludwig, Juan M. Maldacena

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Abstract

We study the conformal field theory of a free massless scalar field living on the half-line with interactions introduced via a periodic potential at the boundary. An SU(2) current algebra underlies this system and the interacting boundary state is given by a global SU(2) rotation of the left-moving fields in the zero-potential (Neumann) boundary state. As the potential strength varies from zero to infinity, the boundary state interpolates between the Neumann and the Dirichlet values. The full S-matrix for scattering from the boundary, with arbitrary particle production, is explicitly computed. To maintain unitarity, it is necessary to attribute a hidden discrete "soliton" degree of freedom to the boundary. The same unitarity puzzle occurs in the Kondo problem, and we anticipate a similar solution.

Original language	English (US)
Pages (from-to)	417-448
Number of pages	32
Journal	Nuclear Physics, Section B
Volume	422
Issue number	3
DOIs	https://doi.org/10.1016/0550-3213(94)90440-5
State	Published - Jul 11 1994

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

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10.1016/0550-3213(94)90440-5

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title = "Exact solution of a boundary conformal field theory",

abstract = "We study the conformal field theory of a free massless scalar field living on the half-line with interactions introduced via a periodic potential at the boundary. An SU(2) current algebra underlies this system and the interacting boundary state is given by a global SU(2) rotation of the left-moving fields in the zero-potential (Neumann) boundary state. As the potential strength varies from zero to infinity, the boundary state interpolates between the Neumann and the Dirichlet values. The full S-matrix for scattering from the boundary, with arbitrary particle production, is explicitly computed. To maintain unitarity, it is necessary to attribute a hidden discrete {"}soliton{"} degree of freedom to the boundary. The same unitarity puzzle occurs in the Kondo problem, and we anticipate a similar solution.",

author = "Callan, {Curtis G.} and Klebanov, {Igor R.} and Ludwig, {Andreas W.W.} and Maldacena, {Juan M.}",

note = "Funding Information: We thank A. Yegulalp for useful discussions. The work of C.G.C. was supported in part by DOE grant DE-FGO2-90ER40542 and by the Monell Foundation. The work of I.R.K. was supported in part by DOE grant DE-FGO2-91ER40671, NSF Presidential Young Investigator Grant No. PHY-9157482, James S. McDonnell Foundation Grant No. 91-48 and the A.P. Sloan Foundation.",

year = "1994",

month = jul,

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doi = "10.1016/0550-3213(94)90440-5",

language = "English (US)",

volume = "422",

pages = "417--448",

journal = "Nuclear Physics B",

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publisher = "Elsevier",

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TY - JOUR

T1 - Exact solution of a boundary conformal field theory

AU - Callan, Curtis G.

AU - Klebanov, Igor R.

AU - Ludwig, Andreas W.W.

AU - Maldacena, Juan M.

N1 - Funding Information: We thank A. Yegulalp for useful discussions. The work of C.G.C. was supported in part by DOE grant DE-FGO2-90ER40542 and by the Monell Foundation. The work of I.R.K. was supported in part by DOE grant DE-FGO2-91ER40671, NSF Presidential Young Investigator Grant No. PHY-9157482, James S. McDonnell Foundation Grant No. 91-48 and the A.P. Sloan Foundation.

PY - 1994/7/11

Y1 - 1994/7/11

N2 - We study the conformal field theory of a free massless scalar field living on the half-line with interactions introduced via a periodic potential at the boundary. An SU(2) current algebra underlies this system and the interacting boundary state is given by a global SU(2) rotation of the left-moving fields in the zero-potential (Neumann) boundary state. As the potential strength varies from zero to infinity, the boundary state interpolates between the Neumann and the Dirichlet values. The full S-matrix for scattering from the boundary, with arbitrary particle production, is explicitly computed. To maintain unitarity, it is necessary to attribute a hidden discrete "soliton" degree of freedom to the boundary. The same unitarity puzzle occurs in the Kondo problem, and we anticipate a similar solution.

AB - We study the conformal field theory of a free massless scalar field living on the half-line with interactions introduced via a periodic potential at the boundary. An SU(2) current algebra underlies this system and the interacting boundary state is given by a global SU(2) rotation of the left-moving fields in the zero-potential (Neumann) boundary state. As the potential strength varies from zero to infinity, the boundary state interpolates between the Neumann and the Dirichlet values. The full S-matrix for scattering from the boundary, with arbitrary particle production, is explicitly computed. To maintain unitarity, it is necessary to attribute a hidden discrete "soliton" degree of freedom to the boundary. The same unitarity puzzle occurs in the Kondo problem, and we anticipate a similar solution.

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U2 - 10.1016/0550-3213(94)90440-5

DO - 10.1016/0550-3213(94)90440-5

M3 - Article

AN - SCOPUS:0000205223

SN - 0550-3213

VL - 422

SP - 417

EP - 448

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -

Exact solution of a boundary conformal field theory

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