Duality in Quantum Liouville Theory

O’Raifeartaigh, L.; Pawlowski, Jan M.; Sreedhar, V. V.

doi:10.1006/aphy.1999.5951

Cited by 20 publications

(35 citation statements)

References 10 publications

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“…This was observed in [DO] [ZZ], and elaborated upon in [OPS1]. It seems natural to interpret the modification (34) as describing a quantum correction to the path integral measure that could be described by adding a second interaction termμ d 2 ze 2b −1 φ to the action.…”

Section: Duality B → B −1mentioning

confidence: 74%

Liouville theory revisited

Teschner

2001

Class. Quantum Grav.

396

640

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Abstract:We try to develop a coherent picture of Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we need to develop further some of these approaches. This includes in particular a construction of general exponential field operators from a set of covariant chiral operators. The latter are shown to satisfy braid relations that allow one to prove the locality of the former.

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Section: Duality B → B −1mentioning

confidence: 74%

Liouville theory revisited

Teschner

2001

Class. Quantum Grav.

396

640

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“…However, the mth eigenvalue in the nth spectrum behaves like the energy levels in the Balmer series for the hydrogen atom, and decays like n −2 . The parameter g does not appear in (15); it appears only in higher-order WKB. The theories corresponding to different values of n are all inequivalent -they are associated with different pairs of Stokes wedges and have different energy spectra.…”

Section: Fig 5: Graphical Solution Tomentioning

confidence: 99%

“…[If φ were a pseudoscalar field, the Lagrangian would be PT invariant because under parity reflection P, φ would change sign Pφ(x, t)P = −φ(−x, t), and under time reversal T , i changes sign T iT = −i.] However, we let P represent an S duality reflection [15],and with this definition of P, L is manifestly PT symmetric. A non-Hermitian PT -invariant theory can have a positive real spectrum and unitary time evolution [14].…”

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confidence: 99%

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Infinite Class ofPT-Symmetric Theories from One Timelike Liouville Lagrangian

Bender¹,

Hook²,

Mavromatos³

et al. 2014

Phys. Rev. Lett.

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Logarithmic time-like Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field φ. In Euclidean space the Lagrangian of such a theory, L = 1 2 (∇φ) 2 − igφ exp(iaφ), is analyzed using the techniques of PT -symmetric quantum theory. It is shown that L defines an infinite number of unitarily inequivalent sectors of the theory labeled by the integer n. In one-dimensional space (quantum mechanics) the energy spectrum is calculated in the semiclassical limit and the mth energy level in the nth sector is given by Em,n ∼ (m + 1/2) 2 a 2 /(16n 2 ).PACS numbers: 11.30. Er, 03.70.+k Motivated by studies of time-like logarithmic Liouville quantum field theory, we examine here the interaction −igφ exp(iaφ) in field theory and its quantummechanical analog −igx exp(iax). This remarkable interaction gives rise to a countably infinite number of inequivalent quantum theories.The interaction −igφ exp(iaφ) has its origin in conformal field theory (CFT) of Liouville type, whose interaction has the form e αφ [1][2][3][4][5][6]. This exponential arises in string theory and in two-dimensional gravity, which are defined on two-dimensional manifolds. Using general coordinate invariance, one can show that the metric tensor g µν for these theories can be reduced locally to g µν = η µν e αφ , where η µν is the Minkowski metric. String theory and two-dimensional gravity are conformally invariant at the classical level, but quantum effects can produce an anomaly that destroys conformal invariance. Conformal symmetry is restored if the field φ is governed by the Liouville actionRecoil effects for zero-dimensional D-branes scattering off closed strings are described by the interaction φe αφ in addition to the usual Liouville interaction e αφ [7]. Such pairs of operators define a logarithmic CFT [8]. Logarithmic CFTs also arise in descriptions of quenched disordered condensed matter systems [9,10]. Supercritical strings [11] and the condensation of tachyons [12,13] is studied in the context of time-like Liouville theories, whose interaction term has α replaced by ia. Thus, combining the ideas of Liouville and logarithmic CFT, we are led to consider the d-dimensional Euclidean Lagrangianwhere φ is a scalar field and a, g, and h are treated as positive real parameters.The Lagrangian (1) is not Hermitian and one cannot make such a theory Hermitian by adding its Hermitian conjugate because this would destroy the conformality property of the theory. Nevertheless, the techniques of PT quantum theory [14] can be used to study this field theory. The Lagrangian is not obviously PT invariant because in Liouville theory the field φ is assumed to transform as a scalar, so it does not change sign under space reflection. [If φ were a pseudoscalar field, the Lagrangian would be PT invariant because under parity reflection P, φ would change sign Pφ(x, t)P = −φ(−x, t), and under time reversal T , i changes sign T iT = −i.] However, we let P represent a...

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“…Motivated by the results of Drury and Mendonça, O'Raifeartaigh and Sreedhar [4] where D is the convective derivative, D = ∂ t + u · ∇, and the fields ρ and u are the density and the velocity. V is the viscosity term, with components 4) where d is the spatial dimension, ξ and η represent the bulk and shear viscosity fields, respectively.…”

Section: Introductionmentioning

confidence: 99%

Symmetries of fluid dynamics with polytropic exponent

Horváthy

2001

Physics Letters A

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The symmetries of the general Euler equations of fluid dynamics with polytropic exponent are determined using the Kaluza-Klein type framework of Duval et al . In the standard polytropic case the recent results of O'Raifeartaigh and Sreedhar are confirmed. Similar results are proved for polytropic exponent γ = −1, which corresponds to the dimensional reduction of d-branes. The relation between the duality transformation used in describing supernova explosion and Cosmology is explained.

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Duality in Quantum Liouville Theory

Cited by 20 publications

References 10 publications

Liouville theory revisited

Liouville theory revisited

Infinite Class ofPT-Symmetric Theories from One Timelike Liouville Lagrangian

Symmetries of fluid dynamics with polytropic exponent

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