A modified c = 1 matrix model with new critical behavior

Steven S. Gubser; Igor R. Klebanov

doi:10.1016/0370-2693(94)91294-7

A modified c = 1 matrix model with new critical behavior

Steven S. Gubser, Igor R. Klebanov

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Abstract

By introducing a ∫ dt g (TrΦ²(t))² term into the action of the c = 1 matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical "bubbles" which touch one another at single points. At a special value of g, the sum over connected surfaces behaves as Δ²log Δ, where Δ is the cosmological constant (the sum over surfaces of area A goes as A^-3). For comparison, in the conventional c = 1 model the sum over planar surfaces behaves as Δ² log Δ.

Original language	English (US)
Pages (from-to)	35-42
Number of pages	8
Journal	Physics Letters B
Volume	340
Issue number	1-2
DOIs	https://doi.org/10.1016/0370-2693(94)91294-7
State	Published - Dec 1 1994

All Science Journal Classification (ASJC) codes

Nuclear and High Energy Physics

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10.1016/0370-2693(94)91294-7

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title = "A modified c = 1 matrix model with new critical behavior",

abstract = "By introducing a ∫ dt g (TrΦ2(t))2 term into the action of the c = 1 matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical {"}bubbles{"} which touch one another at single points. At a special value of g, the sum over connected surfaces behaves as Δ2log Δ, where Δ is the cosmological constant (the sum over surfaces of area A goes as A-3). For comparison, in the conventional c = 1 model the sum over planar surfaces behaves as Δ2 log Δ.",

author = "Gubser, {Steven S.} and {R. Klebanov}, Igor",

note = "Funding Information: tigator Award PHY-9157482, James S. McDonnell Foundation grant No. 91-48, and an A.P. Sloan Foundation Research Fellowship. Funding Information: We thank David Gross for interesting discussions. This work was supported in part by DOE grant DE-FG02-91ER40671, the NSF Presidential Young Inves-",

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AU - R. Klebanov, Igor

N1 - Funding Information: tigator Award PHY-9157482, James S. McDonnell Foundation grant No. 91-48, and an A.P. Sloan Foundation Research Fellowship. Funding Information: We thank David Gross for interesting discussions. This work was supported in part by DOE grant DE-FG02-91ER40671, the NSF Presidential Young Inves-

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N2 - By introducing a ∫ dt g (TrΦ2(t))2 term into the action of the c = 1 matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical "bubbles" which touch one another at single points. At a special value of g, the sum over connected surfaces behaves as Δ2log Δ, where Δ is the cosmological constant (the sum over surfaces of area A goes as A-3). For comparison, in the conventional c = 1 model the sum over planar surfaces behaves as Δ2 log Δ.

AB - By introducing a ∫ dt g (TrΦ2(t))2 term into the action of the c = 1 matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical "bubbles" which touch one another at single points. At a special value of g, the sum over connected surfaces behaves as Δ2log Δ, where Δ is the cosmological constant (the sum over surfaces of area A goes as A-3). For comparison, in the conventional c = 1 model the sum over planar surfaces behaves as Δ2 log Δ.

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A modified c = 1 matrix model with new critical behavior

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