The complete structure of W∞

Pope, C.N.; Romans, L.J.; Shen, Xianfeng

doi:10.1016/0370-2693(90)90822-n

Cited by 220 publications

(241 citation statements)

References 11 publications

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“…This indeed turns out to be the case; the Lie algebra in question here is GL(∞, R) [3]. It can in fact be described as the algebra generated by the "wedge" of W 1+∞ generators V i m [4](where m is the Laurent-mode index in the expansion of the spin-(i + 2) W 1+∞ current V i (z)), with m is restricted to lie in the range…”

Section: The Gl(∞ R) Symmetry Of W 1+∞ Gravitymentioning

confidence: 93%

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symmetry of quantum W∞ gravity

Pope

Shen

et al. 1992

Nuclear Physics B

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Two-dimensional gravity in the light-cone gauge was shown by Polyakov to exhibit an underlying SL(2, R) Kac-Moody symmetry, which may be used to express the energy-momentum tensor for the metric component h ++ in terms of the SL(2, R) currents via the Sugawara construction. We review some recent results which show that in a similar manner, W ∞ and W 1+∞ gravities have underlying SL(∞, R) and GL(∞, R) Kac-Moody symmetries respectively.

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Section: The Gl(∞ R) Symmetry Of W 1+∞ Gravitymentioning

confidence: 93%

“…Details of the W ∞ and W 1+∞ algebras may be found in [4], and also in the lectures on W algebras and W gravity in this volume [5]. We are adopting the notation of [5] here, and using V i to denote the currents of W 1+∞ , and V i to denote those for W ∞ .…”

Section: The Gl(∞ R) Symmetry Of W 1+∞ Gravitymentioning

confidence: 99%

symmetry of quantum W∞ gravity

Pope

Shen

et al. 1992

Nuclear Physics B

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“…1+∞ chiral algebra W 1+∞ is the unique nontrivial central extension [31,39] of the Lie algebra w ∞ [3] of the areapreserving diffeomorphisms on the circle; its representation theory was developed in [33,22,1].…”

Section: The W (M)mentioning

confidence: 99%

A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)

Cristofano

Marotta

Niccoli

2006

J. High Energy Phys.

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A new Rational Conformal Field Theory extension of the fully degenerate W (m) 1+∞Gerardo Cristofano 1 , Vincenzo Marotta 1 , Giuliano Niccoli 2 AbstractWe found new identities among the Dedekind η-function, the characters of the W m algebra and those of the level 1 affine Lie algebra su(m) 1 . They allow to characterize the Z m -orbifold of the m-component free bosons u(1) Km,p (our theory TM) as an extension of the fully degenerate representations of W (m) 1+∞ . In particular, TM is proven to be a Γ θ -RCFT extension of the chiral fully degenerate W (m) 1+∞ .

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“…Now while this is an exact equation gives an infinite number of constraints of the form < W n >= 0, where W n are the generators of the W ∞ algebra of the system. It should be noted that since the central charge of the Virasoro algebra is zero so is the central charge of the W algebra so that there is no c-number term coming from multiple (n > 2) operator products [12]. These additional constraints imply that the classical ghost configurations in our coherent state satisfies an infinite set of conditions.…”

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confidence: 99%

On the passage from the quantum theory to the semi-classical theory in 2D dilaton gravity

Alwis

1993

Physics Letters B

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In this paper an attempt is made to understand the passage from the exact quantum treatment of the CGHS theory to the semi-classical physics discussed by many authors. We find first that to the order of accuracy to which Hawking effects are calculated in the theory, it is inconsistent to ignore correlations in the dilaton gravity sector. Next the standard Dirac or BRST procedure for implementing the constraints is followed. This leads to a set of physical states, in which however the semi-classical physics of the theory seems to be completely obscured. As an alternative, we construct a coherent state formalism, which is the natural framework for understanding the semi-classical calculations, and argue that it satisfies all necessary requirements of the theory, provided that there exist classical ghost configurations which solve an infinite set of equations. If this is the case it may be interpreted as a spontaneous breakdown of general covariance.

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The complete structure of W∞

Cited by 220 publications

References 11 publications

symmetry of quantum W∞ gravity

symmetry of quantum W∞ gravity

A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)

On the passage from the quantum theory to the semi-classical theory in 2D dilaton gravity

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The complete structure of W∞

Cited by 220 publications

References 11 publications

symmetry of quantum W∞ gravity

symmetry of quantum W∞ gravity

A new rational conformal field theory extension of the fully degenerate W1+∞(m)

On the passage from the quantum theory to the semi-classical theory in 2D dilaton gravity

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A new rational conformal field theory extension of the fully degenerate W_1+∞^(m)